A method for calculating the day-night equilibrium altitude of an aerostat

Abstract

The application discloses a kind of aerostat day-night balance height calculation method, comprising: the average temperature of calculating helium in aerostat, calculating aerostat internal pressure, calculating aerostat internal and external pressure difference ΔP, update aerostat volume V after deformation, according to the height h of aerostat balance after updating buoyancy balance, calculate internal and external pressure difference ΔP', according to the internal and external pressure difference ΔP' obtained after updating, calculate the difference between internal and external pressure difference ΔP' and internal and external pressure difference ΔP, the difference is compared with given error threshold value and the like steps, and determine final balance height or continue iteration according to the comparison result. By decoupling the coupling effect of aerostat volume and height, and considering the structural deformation of aerostat caused by the change of day-night solar radiation environment, a more accurate aerostat day-night balance height is obtained through a limited number of iteration calculations, compared with the existing dynamic solving method, the calculation efficiency of aerostat balance height solving is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of near-space airship overall design, and particularly relates to a method for calculating the day-night balance altitude of near-space airships considering the fluid-heat-structure coupling effect. Background Technology

[0002] Near-space aerostats possess the capability for long-term aloft operation, high-resolution Earth observation, and real-time information acquisition. They can provide solutions for applications such as Earth monitoring, communication relay, environmental monitoring, network coverage, and disaster prevention and mitigation, and have enormous strategic and economic value. The United States, Europe, Japan, and South Korea have all invested heavily in the development of near-space aerostats; my country also regards near-space aerostats as an important component of its high-resolution Earth observation system, focusing on their development to fill a strategic gap in the nation's economy.

[0003] Near-space aerostats are generally enormous, exceeding 100 meters in length and tens of meters in diameter. These massive aerostats are extremely sensitive to the external thermal environment. Due to the diurnal and intense nature of solar radiation, coupled with weak convective heat transfer in near space, the temperature of the gas inside the aerostat varies significantly throughout the day and night. This large diurnal temperature difference affects the thermal properties of the gas inside the aerostat, thus influencing its shape, lift, and ultimately its equilibrium altitude. Accurate calculation of the equilibrium altitude of near-space aerostats is crucial for the research of aerostat control systems. Current calculations of aerostat equilibrium altitude often fail to consider the diurnal thermal deformation effect, assuming a constant volume and calculating the equilibrium altitude based on buoyancy balance. However, in reality, solar radiation varies periodically. During the day, the gas inside the aerostat expands under solar radiation, increasing its volume; at night, without solar radiation, the temperature of the gas inside decreases, correspondingly reducing the volume of the aerostat. This diurnal periodic change in volume causes changes in the buoyancy of the airship, which in turn affects the change in the airship's equilibrium height.

[0004] Accurate calculation of the equilibrium altitude of an airship is of great significance for the overall parameter design of the airship, the calculation of internal overpressure, the design of the flight control system, and the evaluation of skin fatigue performance. However, there is currently no method for calculating the airship volume due to thermal deformation during airborne operation, or the day-night equilibrium altitude. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the day-night equilibrium altitude of an airship, in order to solve the problem mentioned in the background art that there is currently no method for calculating the airship volume and the day-night equilibrium altitude that takes into account the thermal deformation of the airship during its voyage.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the day-night equilibrium altitude of an airship, comprising the following steps:

[0007] Step S1: Based on the current airship's flight altitude h, latitude, date, current time t, and external conditions, calculate the average temperature of the helium gas inside the airship;

[0008] Step S2: Assuming the helium inside the airship follows the ideal gas law, calculate the internal pressure of the airship based on the ideal gas law:

[0009]

[0010] Where, m he R is the mass of helium inside the airship, R is the molar gas constant, and V is the volume of the airship.

[0011] Step S3: Calculate the pressure difference ΔP inside and outside the airship; specifically including:

[0012] 1) Based on the current flight altitude h of the airship, the atmospheric pressure P outside the airship is calculated using the US standard atmospheric model. atmh for:

[0013]

[0014] 2) Based on the internal pressure P of the airship in and external pressure P atmh The internal and external pressure difference ΔP is obtained;

[0015]

[0016] Step S4: Based on the assumption that the expansion / contraction process of the airship is regarded as a quasi-steady-state process of isothermal expansion / contraction, update the volume V of the airship after deformation according to the deformation theory of flexible membrane structure;

[0017] The deformation of the membrane structure of the near-space aerostat is derived using the thin-shell moment-free theory. The surface of the aerostat capsule is discretized into triangular membrane units, and the nonlinear equations of each membrane structure unit can be expressed as follows:

[0018] (K L +K NL )ΔU=RF

[0019] Among them, K L K is the linear stiffness matrix of the membrane element. NL Let be the nonlinear stiffness matrix of the membrane element, ΔU be the positional variation of each node, R be the load vector of the membrane element, and F be the direction of the equivalent nodal force of the membrane element.

[0020] By solving for the positional changes of each node, the volume V of the airship after deformation can be obtained, and the volume V of the airship after deformation can be updated with this volume.

[0021] Step S5: Update the height h of the buoyant airship after balancing based on the buoyancy balance;

[0022] The buoyancy force on the airship can be expressed as B = ρ atm (h)gV,

[0023] Where, ρ atm (h) represents the atmospheric density at altitude h, and g represents the acceleration due to gravity; according to the American Standard Atmospheric Model, the atmospheric temperature T atm and air pressure P atm They can be represented as:

[0024]

[0025]

[0026]

[0027] Therefore, atmospheric density ρ atm (h) can be represented as:

[0028]

[0029] Among them, R m_atm The molar gas constant of the atmosphere.

[0030] The gravitational force acting on the airship is G = mg, where m is the mass of the airship;

[0031] When the buoyant weight is balanced, ρ atm (h)gV=mg, from which the altitude can be obtained. That is, the inverse function of density with respect to height is:

[0032]

[0033] By combining formulas (1), (2), and (3), the height h can be calculated.

[0034] Step S6: Update the internal pressure P of the airship after deformation according to the ideal gas law. in Combined with the external atmospheric pressure P at flight altitude h atmh Calculate the internal and external pressure difference ΔP';

[0035] This process is also based on the assumption in step S4 that the expansion / contraction process of the airship is regarded as a quasi-steady-state process of isothermal expansion / contraction;

[0036] Step S7: Based on the updated internal and external pressure difference ΔP' obtained in step S6, calculate the difference between the internal and external pressure difference ΔP' and the internal and external pressure difference ΔP, and compare the difference with a given error threshold.

[0037] 1) If the difference is within the given error threshold, it is determined that the airship deformation has reached a stable state, and the corresponding equilibrium height h is the final equilibrium height after stabilization at time t.

[0038] 2) Conversely, if the deformation of the airship has not reached a stable state, the internal and external pressure difference should be reset. Repeat steps S3 to S7 until the difference between the internal and external pressure difference ΔP' and the internal and external pressure difference ΔP is within the error range. The corresponding equilibrium height h at this time is the final equilibrium height after stabilization at time t.

[0039] As a preferred technical solution, in step S7, the given error threshold is determined based on engineering experience, and the error range is defined here:

[0040] ε=|ΔP-ΔP′|<5Pa.

[0041] As a preferred technical solution, by setting different day and night times t and repeating steps S1 to S7, the equilibrium height of the airship at different times of day and night can be obtained.

[0042] As a preferred technical solution, the thermal environment of the near-space airship 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, atmospheric infrared radiation, Earth infrared radiation, and convective heat transfer between the balloon and the external environment. The internal thermal environment consists of natural convection of internal gas and infrared radiation between internal gas and the skin.

[0043] Therefore, the average temperature T of the helium gas inside the airship He The calculation method is as follows:

[0044] Direct radiation from the sun I D It can be represented as:

[0045] I D =T atm ·I sun

[0046] Where, τ atm I represents the transmittance of direct solar radiation in the Earth's atmosphere. sun It represents the intensity of direct solar radiation outside the Earth's atmosphere.

[0047] Intensity of direct solar radiation outside the Earth (I) sun for

[0048]

[0049] Where I0 is the solar radiation constant, I0 = 1367 W / m 2 e earth For the Earth's eccentricity, e earth =0.016708, The angle at the true periphery of Earth can be expressed as

[0050]

[0051] Among them, the sun angle θ day It can be represented as

[0052] θ day =2π·(N-N0) / 365.2422

[0053] Where N represents the number of days in a year of the current date, and N0 represents the leap year correction term for the number of days;

[0054]

[0055] In the formula, year represents the year corresponding to the calculation date.

[0056] The transmittance τ of direct solar radiation in the Earth's atmosphere atm for:

[0057]

[0058] In the formula, p h p0 and c represent the atmospheric pressure at altitude h and the atmospheric pressure at sea level, respectively. low and c high Let λ represent the low-altitude calibration factor and the high-altitude calibration factor, respectively. AM The air mass ratio (λ) represents the mass ratio of air as solar radiation passes through the atmosphere. AM With the altitude angle θ of the airship ele Related to different elevation angles θ ele The corresponding air quality is shown in the formula:

[0059]

[0060] In a geodetic coordinate system, the direction of direct solar radiation It is the solar altitude angle θ ele And solar azimuth θ azi Functions:

[0061]

[0062] The solar altitude angle and azimuth angle can be expressed as:

[0063] θele =arcsin(sin(θ) dec sin(Φ) + cos(θ) dec )·cos(Φ)·cos(θ hour ))

[0064]

[0065] Where, θ dec Φ represents the solar declination angle, Φ represents the local latitude, and θ represents the local latitude. hour Indicates solar hour angle;

[0066] θ 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

[0067] θ hour =15(time+e) t / 60-12.0)·π / 180

[0068] e t =0.0028-1.9857·sin(θ) day )+9.9059·sin(2θ day -7.0924·cos(θ) day )-0.6882·cos(2θ day )

[0069] The intensity of scattered radiation from the sky can be expressed as:

[0070]

[0071] For any tilt angle of The plane can be approximated by the intensity of sky-scattered radiation it receives as:

[0072]

[0073] In addition, when sunlight passes through the atmosphere, some of its energy is absorbed by gases such as water vapor, carbon dioxide, and ozone, causing the atmospheric temperature to rise and thus generating infrared radiation from the sky. Generally, assuming the atmosphere is a blackbody, according to the Stefan-Boltzman law, the infrared radiation power of the sky can be expressed as:

[0074] I IR_sky =σ·T sky

[0075] Among them, T sky The equivalent temperature of the sky can be expressed as the sky emissivity ε. sky and atmospheric temperature T atm Functions:

[0076]

[0077] Ground-based infrared radiation primarily originates from long-wave radiation originating from the Earth's surface. The intensity of this radiation is related to the Earth's surface emissivity ε. g and Earth's surface temperature T g Relevant. The radiation intensity at the ground level is...

[0078]

[0079] Where, ε g T represents the emissivity of the Earth's surface, which is related to surface properties. The emissivity of desert areas is around 0.85, the average emissivity of the Earth's surface is about 0.95, and it is taken as 0.98 when there is snow cover. g Let h be the Earth's surface temperature (emissivity is low in warmer areas and high in colder areas). Surface radiation is perpendicular to the ground and is also lost during its upward radiation into the atmosphere. At a height h, the intensity of surface radiation can be expressed as:

[0080] I IR_gh =τ IR_gh ·I IR_g

[0081] Where τ IR_gh The transmittance of surface radiation at height h in the atmosphere is expressed as:

[0082] τ IR_gh =1.716-0.5(exp(-0.65p) h / p0)+exp(-0.95p h / p0))

[0083] The energy absorbed by the skin from direct solar radiation, atmospheric scattering, and Earth reflection can be expressed as:

[0084] q D =α·I D ·S projected ·(1+τ / (1-r))

[0085] q S =α·I s ·S surf ·(1+τ / (1-r))

[0086] q R =α·I R ·S projected ·(1+τ / (1-r))

[0087] Infrared radiation from the atmosphere, Earth, and internal balloons can be represented as:

[0088] q IR_atm =α IR ·I IR_atm ·S surf ·(1+τ IR / (1-r IR ))

[0089] q IR_ear =α IR ·I IR_ear ·S projected ·(1+τ IR / (1-r IR ))

[0090] q IR_He =α IR ·I IR_He ·S surf_He ·(1 / (1-r IR ))

[0091] Where α, τ, and r represent the average visible light absorptivity, transmittance, and reflectivity of the skin, respectively. IR τ IR and r IR S represents the average infrared absorptivity, transmittance, and reflectivity of the skin, respectively. surf and S projected These represent the surface area and projected area of ​​the cyst, respectively.

[0092] The convective heat transfer between the skin and the external environment can be expressed as:

[0093] q conv_ex =h ex ·S surf ·(T atm -T f )

[0094] h ex The external convective heat transfer coefficient can be expressed as:

[0095]

[0096] Among them, h ex_force h is the external forced convection heat transfer coefficient. ex_natural The external natural convection heat transfer coefficient is h. The external forced convection heat transfer coefficient is h.ex_force It can be represented as:

[0097]

[0098] Among them, Re atm k represents the atmospheric Reynolds number. atmh L represents the atmospheric thermal conductivity at an altitude of h, and L0 represents the characteristic length of the airship.

[0099]

[0100]

[0101]

[0102] Where D represents the characteristic diameter of the airship, υ atm ρ represents air velocity. atmh μ atmh and T atmh represents the atmospheric density, atmospheric viscosity coefficient, and atmospheric temperature at an altitude h, respectively.

[0103] External natural convection heat transfer coefficient h ex_natural It can be represented as:

[0104]

[0105] Among them, Nu atm_natural L0 is the external atmospheric Nusselt number, and L0 is the characteristic length of the airship.

[0106]

[0107] In the formula, Gr atmh and Pr atmh represents the atmospheric Grashof number and Prandtl number at an altitude of h, respectively.

[0108]

[0109] Pr atmh =0.804 - 3.25·10 -4 ·T atmh

[0110] Therefore, the temperature of the skin can be expressed as:

[0111]

[0112] Where, m f c f and T f These represent the mass, specific heat capacity, and temperature of the skin, respectively.

[0113] The temperature of helium can be expressed as:

[0114]

[0115] Where V is the volume of the airship, m He ,c v_He and T He Given the mass, volumetric specific heat capacity, and temperature of helium, γ = c p_He / c v_He ;

[0116] Solving the above system of differential equations yields the helium temperature T. He .

[0117] Compared with the prior art, the beneficial effects of the present invention are:

[0118] 1) By decoupling the coupling effect between the volume and height of the airship and considering the structural deformation of the airship caused by the changes in the solar radiation environment during the day and night, a relatively accurate day and night balance height of the airship was obtained through a finite number of iterative calculations. Compared with the dynamic solution method, this effectively improves the computational efficiency of solving the balance height of the airship.

[0119] 2) The airship is continuously subjected to the external thermal environment, and its temperature change is small, approximating a quasi-steady-state process. Therefore, the expansion / contraction process of the airship can be regarded as isothermal expansion / contraction. Based on this assumption, the calculation process of the thermally induced structural deformation of the airship can be greatly simplified, and the calculation efficiency can be improved while ensuring a certain level of calculation accuracy. Attached Figure Description

[0120] Figure 1 This is a flowchart of a method for calculating the day-night balance altitude of an airship according to the present invention. Detailed Implementation

[0121] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0122] Please see Figure 1 This invention provides a technical solution: This invention provides a method for calculating the day-night equilibrium altitude of a near-space airship considering thermally induced deformation, comprising:

[0123] 1. Based on the current flight altitude h, latitude, date, and current time t of the airship, calculate the average temperature T of the helium gas inside the airship. He .

[0124] Specifically, the calculation method is as follows:

[0125] 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, atmospheric infrared radiation, Earth's infrared radiation, and convective heat transfer between the balloon and the external environment. The internal thermal environment consists of natural convection of internal gases and infrared radiation between internal gases and the skin.

[0126] Direct radiation from the sun I D It can be represented as:

[0127] I D =τ atm ·I sun

[0128] Where τ atm I represents the transmittance of direct solar radiation in the Earth's atmosphere. sun It represents the intensity of direct solar radiation outside the Earth's atmosphere.

[0129] Intensity of direct solar radiation outside the Earth (I) sun for

[0130]

[0131] Where I0 is the solar radiation constant, I0 = 1367 W / m 2 e earth For the Earth's eccentricity, e earth =0.016708, The angle at the true periphery of Earth can be expressed as

[0132]

[0133] Where the sun angle θ day It can be represented as

[0134] θ day =2π·(N-N0) / 365.2422

[0135] Where N represents the number of days in a year for the current date, such as N=1 for January 1st of each year, and N=365 for December 31st of each year. N0 represents the leap year correction term for the number of days.

[0136]

[0137] In the formula, year represents the year corresponding to the calculation date.

[0138] The transmittance τ of direct solar radiation in the Earth's atmosphere atm for

[0139]

[0140] In the formula p h p0 and c represent the atmospheric pressure at altitude h and the atmospheric pressure at sea level, respectively. low and c high Let λ represent the low-altitude calibration factor and the high-altitude calibration factor, respectively. AM The air mass ratio (λ) represents the mass ratio of air as solar radiation passes through the atmosphere. AM With the altitude angle θ of the airship ele Related to different elevation angles θ ele The corresponding air quality is shown in the formula.

[0141]

[0142] In a geodetic coordinate system, the direction of direct solar radiation It is the solar altitude angle θ ele And solar azimuth θ azi The function.

[0143]

[0144] The solar altitude angle and azimuth angle can be expressed as:

[0145] θ ele =arcsin(sin(θ) dec sin(Φ) + cos(θ) dec )·cos(Φ)·cos(θ hour ))

[0146]

[0147] Where, θ dec Φ represents the solar declination angle, Φ represents the local latitude, and θ represents the local latitude. hour It represents the solar hour angle.

[0148] θ 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

[0149] θ hour =15(time+e) t / 60-12.0)·π / 180

[0150] e t =0.0028-1.9857·sin(θ) day )+9.9059·sin(2θ day -7.0924·cos(θ) day )-0.6882·cos(2θ day )

[0151] The intensity of scattered radiation from the sky can be expressed as:

[0152]

[0153] For any tilt angle of The plane can be approximated by the intensity of sky-scattered radiation it receives.

[0154]

[0155] In addition, when sunlight passes through the atmosphere, some of its energy is absorbed by gases such as water vapor, carbon dioxide, and ozone, causing the atmospheric temperature to rise and thus generating infrared radiation from the sky. Generally, assuming the atmosphere is a blackbody, according to the Stefan-Boltzman law, the infrared radiation power of the sky can be expressed as...

[0156] I IR_sky =σ·T sky

[0157] Where T sky The equivalent temperature of the sky can be expressed as the sky emissivity ε. sky and atmospheric temperature T atm Functions:

[0158]

[0159] Ground-based infrared radiation primarily originates from long-wave radiation originating from the Earth's surface. The intensity of this radiation is related to the Earth's surface emissivity ε. g and Earth's surface temperature T g Relevant. The radiation intensity at the ground level is...

[0160]

[0161] Where ε g T represents the emissivity of the Earth's surface, which is related to surface properties. The emissivity of desert areas is around 0.85, the average emissivity of the Earth's surface is about 0.95, and it is taken as 0.98 when there is snow cover. gLet h be the Earth's surface temperature (emissivity is low in warmer areas and high in colder areas). Surface radiation is perpendicular to the ground and is also lost during its upward radiation into the atmosphere. At a height h, the intensity of surface radiation can be expressed as...

[0162] I IR_gh =τ IR_gh ·I IR_g

[0163] Where τ IR_gh The transmittance of surface radiation in the atmosphere at height h is expressed as follows:

[0164] τ IR_gh =1.716-0.5(exp(-0.65p) h / p0)+exp(-0.95p h / p0))

[0165] The energy absorbed by the skin from direct solar radiation, atmospheric scattering, and Earth reflection can be expressed as:

[0166] q D =α·I D ·S projected ·(1+τ / (1-r))

[0167] q S =α·I s ·S surf ·(1+τ / (1-r))

[0168] q R =α·I R ·S projected ·(1+τ / (1-r))

[0169] Infrared radiation from the atmosphere, Earth, and internal balloons can be represented as follows:

[0170] q IR_atm =α IR ·I IR_atm ·S surf ·(1+τ IR / (1-r IR ))

[0171] q IR_ear =α IR ·I IR_ear ·S projected ·(1+τ IR / (1-r IR ))

[0172] q IR_He =α IR ·I IR_He ·Ssurf_He ·(1 / (1-r IR ))

[0173] Where α, τ, and r represent the average visible light absorptivity, transmittance, and reflectivity of the skin, respectively. IR τ IR and r IR S represents the average infrared absorptivity, transmittance, and reflectivity of the skin, respectively. surf and S projected These represent the surface area and projected area of ​​the cyst, respectively.

[0174] The convective heat transfer between the skin and the external environment can be expressed as:

[0175] q conv_ex =h ex ·S surf ·(T atm -T f )

[0176] h ex The external convective heat transfer coefficient can be expressed as:

[0177]

[0178] Where h ex_force h is the external forced convection heat transfer coefficient. ex_natural The external natural convection heat transfer coefficient is h. The external forced convection heat transfer coefficient is h. ex_force It can be represented as

[0179]

[0180] Where Re atm k represents the atmospheric Reynolds number. atmh L represents the atmospheric thermal conductivity at an altitude of h, and L0 represents the characteristic length of the airship.

[0181]

[0182]

[0183]

[0184] Where D represents the characteristic diameter of the airship, υ atm ρ represents air velocity. atmh μ atmh and T atmh represents the atmospheric density, atmospheric viscosity coefficient, and atmospheric temperature at an altitude h, respectively.

[0185] External natural convection heat transfer coefficient h ex_natural It can be represented as:

[0186]

[0187] Among them, Nu atm_natural L0 is the external atmospheric Nusselt number, and L0 is the characteristic length of the airship.

[0188]

[0189] In the formula, Gr atmh and Pr atmh represents the atmospheric Grashof number and Prandtl number at an altitude of h, respectively.

[0190]

[0191] Pr atmh =0.804 - 3.25·10 -4 ·T atmh

[0192] Therefore, the temperature of the skin can be expressed as:

[0193]

[0194] Where m f c f and T f These represent the mass, specific heat capacity, and temperature of the skin, respectively.

[0195] The temperature of helium can be expressed as:

[0196]

[0197] Where V is the volume of the airship, m He ,c v_He and T He Given the mass, volumetric specific heat capacity, and temperature of helium, γ = c p_He / c v_He .

[0198] Solving the above system of differential equations yields the helium temperature T. He .

[0199] 2. Assuming the helium inside the airship follows the ideal gas law, calculate the internal pressure of the airship based on the ideal gas law. Where m he R is the mass of helium inside the airship, R is the molar gas constant, and V is the volume of the airship.

[0200] 3. Based on the current flight altitude h of the airship and the US standard atmospheric model, the atmospheric pressure outside the airship is calculated as follows:

[0201]

[0202] Based on the internal pressure Pin and external pressure P of the airship atmh The internal and external pressure difference ΔP is obtained;

[0203]

[0204] The airship expands / contracts under the influence of the internal and external pressure difference, causing a change in its volume.

[0205] 4. The airship is continuously subjected to the external thermal environment, and its temperature change is small, approximating a quasi-steady-state process. Therefore, the expansion / contraction process of the airship can be regarded as isothermal expansion / contraction. Based on this assumption, the volume V of the airship after deformation is updated according to the deformation theory of flexible membrane structures.

[0206] The deformation of the membrane structure of near-space airships is derived using the thin-shell moment-free theory. The surface of the airship capsule is discretized into triangular membrane elements, and the nonlinear equations of each membrane element can be expressed as follows:

[0207] (K L +K NL )ΔU=RF

[0208] Where K L K is the linear stiffness matrix of the membrane element. NL Let be the nonlinear stiffness matrix of the membrane element, ΔU be the positional variation of each node, R be the load vector of the membrane element, and F be the direction of the equivalent nodal force of the membrane element. By solving for the positional variation of each node, the volume V of the airship after deformation can be obtained.

[0209] 5. Update the height h of the buoyant airship after balancing based on the buoyancy balance.

[0210] The buoyancy force received by the airship can be expressed as B = ρ atm (h)gV, where ρ atm (h) represents the atmospheric density at height h, and g represents the acceleration due to gravity. According to the US Standard Atmosphere model (1976), the atmospheric temperature T... atm and air pressure P atm It can be represented as:

[0211]

[0212]

[0213] Therefore, atmospheric density ρ atm (h) can be expressed as

[0214]

[0215] Where R m_atmis the molar gas constant of the atmosphere.

[0216] The gravitational force acting on the airship is G = mg, where m is the mass of the airship.

[0217] When the buoyant weight is balanced, ρ atm (h)gV=mg, from which the altitude can be obtained. That is, the inverse function of density with respect to height.

[0218]

[0219] By combining the above formulas, the height h can be calculated.

[0220] 6. Update the internal pressure Pin of the airship after deformation according to the ideal gas law, and calculate the internal and external pressure difference ΔP' by combining it with the external atmospheric pressure Patmh at the flight altitude h.

[0221] The volume change of the airship caused by diurnal radiation variation is a slow process, and the airship is continuously subjected to external thermal radiation. Therefore, the temperature of the helium gas inside remains essentially constant. Hence, the isothermal expansion / contraction assumption was proposed in step 4. This assumption is adopted here, assuming that the temperature of the helium gas remains constant.

[0222] 7. If the difference between the internal and external pressure difference ΔP' and the internal and external pressure difference ΔP is within the error range, then the deformation of the airship is considered to have reached a stable state, and the corresponding equilibrium height h is the final equilibrium height after stabilization at time t.

[0223] The error range is determined based on engineering experience; here, the error range ε ​​= |ΔP - ΔP′| < 5Pa can be defined.

[0224] 8. If the difference between the internal and external pressure difference ΔP' and the internal and external pressure difference ΔP exceeds the error range, the airship deformation has not reached a stable state, and the internal and external pressure difference should be reset. Repeat steps 2 to 8 until the difference between the internal and external pressure difference ΔP' and the internal and external pressure difference ΔP is within the error range. The corresponding equilibrium height h at this time is the final equilibrium height after stabilization at time t.

[0225] 9. By setting different day and night times t and repeating steps 1 to 8, the equilibrium height of the airship can be obtained at different times of day and night.

[0226] The airship is continuously subjected to the external thermal environment, and its temperature change is small, approximating a quasi-steady-state process. Therefore, the expansion / contraction process of the airship can be regarded as isothermal expansion / contraction. Based on this assumption, the calculation process of the thermally induced structural deformation of the airship can be greatly simplified, improving computational efficiency while ensuring a certain level of accuracy. Currently, the calculation of the airship's equilibrium height in the literature generally obtains the airship's height through steps S1, S2, S3, and S5. In reality, the airship's volume and equilibrium height are strongly coupled. Specifically, changes in the near-space thermal environment cause changes in the airship's volume, which in turn causes changes in the equilibrium height. Due to differences in atmospheric pressure at different altitudes, the pressure difference between the airship's interior and exterior changes with altitude, further causing changes in the airship's volume. The imbalance between buoyancy and weight leads to further changes in volume and height. This process is dynamic, and it is difficult to obtain an accurate airship equilibrium height using traditional static methods to describe this dynamic process. This scheme decouples the above dynamic process and obtains a more accurate day-night balance altitude of the airship through iterative calculations in steps 2 to 8, which greatly improves the computational efficiency compared with the dynamic solution method.

[0227] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the day-night equilibrium altitude of an airship, characterized in that, Includes the following steps: Step S1: Based on the current airship's flight altitude h, latitude, date, current time t, and external conditions, calculate the average temperature T of the helium gas inside the airship; Step S2: Assuming the helium inside the airship follows the ideal gas law, calculate the internal pressure of the airship based on the ideal gas law: ， in, R is the mass of helium inside the airship, R is the molar gas constant, and V is the volume of the airship. Step S3: Calculate the pressure difference ∆P between the inside and outside of the airship; specifically including: 1) Based on the current flight altitude h of the airship, the atmospheric pressure P outside the airship is calculated using the US standard atmospheric model. atmh for: 2) Based on the internal pressure P of the airship in and external pressure P atmh The internal and external pressure difference ∆P is obtained; ； Step S4: Based on the assumption that the expansion / contraction process of the airship is regarded as a quasi-steady-state process of isothermal expansion / contraction, update the volume V of the airship after deformation according to the deformation theory of flexible membrane structure; The deformation of the membrane structure of the near-space aerostat is derived using the thin-shell moment-free theory. The surface of the aerostat capsule is discretized into triangular membrane units, and the nonlinear equations of each membrane structure unit can be expressed as follows: in, Here is the linear stiffness matrix of the membrane element. Here is the nonlinear stiffness matrix of the membrane element. This refers to the changes in the position of each node. For membrane unit load vector, The equivalent nodal force direction of the membrane unit is given. By solving the positional changes of each node, the volume V of the airship after deformation can be obtained, and the volume V of the airship after deformation can be updated with this volume. Step S5: Update the height h of the buoyant aircraft after balancing based on the buoyancy balance; The buoyancy force acting on the airship can be expressed as: , in, Let h be the atmospheric density at altitude h. For gravitational acceleration; according to the American Standard Atmospheric Model, atmospheric temperature... and air pressure They can be represented as: （1） （2） Therefore, atmospheric density It can be represented as: in, is the molar gas constant of the atmosphere; The gravity acting on the airship is ,in The mass of the airship; When the buoyant weight is balanced, we have The height can be obtained. That is, the inverse function of density with respect to height is: （3） By combining formulas (1), (2), and (3), the height h can be calculated. Step S6: Update the internal pressure P of the airship after deformation according to the ideal gas law. in Combined with the external atmospheric pressure P at flight altitude h atmh Calculate the internal and external pressure difference ∆P'; This process is also based on the assumption in step S4 that the expansion / contraction process of the airship is regarded as a quasi-steady-state process of isothermal expansion / contraction; Step S7: Based on the updated internal and external pressure difference ∆P' obtained in step S6, calculate the difference between the internal and external pressure difference ∆P' and the internal and external pressure difference ∆P, and compare the difference with a given error threshold; 1) If the difference is within the given error threshold, it is determined that the airship deformation has reached a stable state, and the corresponding equilibrium height h is the final equilibrium height after stabilization at time t. 2) Conversely, if the deformation of the airship has not reached a stable state, the internal and external pressure difference is reset to [value missing]. Repeat steps S3 to S7 until the difference between the internal and external pressure difference ∆P' and the internal and external pressure difference ∆P is within the error range. The corresponding equilibrium height h at this time is the final equilibrium height after stabilization at time t.

2. The method for calculating the day-night equilibrium altitude of an airship according to claim 1, characterized in that, In step S7, the given error threshold is determined based on engineering experience, and the error range is defined here: 。 3. The method for calculating the day-night equilibrium altitude of an airship according to claim 1, characterized in that, By setting different day and night times t and repeating steps S1 to S7, the balance height of the airship can be obtained at different times of day and night.

4. The method for calculating the day-night equilibrium altitude of an airship according to claim 1, characterized in that, The thermal environment of a near-space airship 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, atmospheric infrared radiation, Earth infrared radiation, and convective heat transfer between the balloon and the external environment. The internal thermal environment consists of natural convection of internal gas and infrared radiation between internal gas and the skin. Therefore, the average temperature of the helium gas inside the airship The calculation method is as follows: Direct radiation from the sun It can be represented as: in, This represents the transmittance of direct solar radiation into the Earth's atmosphere. This represents the intensity of direct solar radiation outside the Earth's atmosphere; Intensity of direct solar radiation outside the Earth for: in, The solar radiation constant, , For the Earth's eccentricity, , The angle at Earth's true anomaly can be expressed as: Among them, the sun horn It can be represented as: Where N represents the number of days in a year that the current date falls on. Leap year correction term indicating the number of days; In the formula, This indicates the year corresponding to the calculation date. Transmittance of direct solar radiation into the Earth's atmosphere for: ； In the formula, and represents the atmospheric pressure at an altitude of h and the atmospheric pressure at sea level, respectively. and These represent the low-altitude calibration factor and the high-altitude calibration factor, respectively. The air mass ratio represents the ratio of the amount of solar radiation passing through the atmosphere; air mass ratio with the altitude angle of the airship Related to different elevation angles The corresponding air quality is, for example, the formula. As shown: In a geodetic coordinate system, the direction of direct solar radiation It is the solar altitude angle. and solar azimuth Functions: The solar altitude angle and azimuth angle can be expressed as: in, Indicates the solar declination angle. Indicates the local latitude. Indicates solar hour angle; The intensity of scattered radiation from the sky can be expressed as: For any tilt angle of The plane can be approximated by the intensity of sky-scattered radiation it receives as: In addition, when sunlight passes through the atmosphere, some of its energy is absorbed by water vapor, carbon dioxide, and ozone gas, causing the atmospheric temperature to rise and thus generating infrared radiation from the sky. Generally, assuming the atmosphere is a blackbody, according to the Stefan-Boltzman law, the infrared radiation power of the sky can be expressed as: in, The equivalent temperature of the sky can be expressed as the sky emissivity. and atmospheric temperature Functions: Ground-based infrared radiation primarily originates from long-wave radiation from the Earth's surface, and its intensity is related to the Earth's surface emissivity. and Earth's surface temperature Related to the radiation intensity at the ground level is in, This represents the emissivity of the Earth's surface, which is related to surface properties. The emissivity of desert areas is 0.85, the average emissivity of the Earth's surface is 0.95, and it is taken as 0.98 when there is snow cover. Let be the Earth's surface temperature. The direction of surface radiation is perpendicular to the ground. During radiation into the upper atmosphere, losses also occur. At a height h, the intensity of surface radiation can be expressed as: in, The transmittance of surface radiation at height h in the atmosphere is expressed as: The energy absorbed by the skin from direct solar radiation, atmospheric scattering, and Earth reflection can be expressed as: Infrared radiation from the atmosphere, Earth, and internal balloons can be represented as: in, , and These represent the average visible light absorptivity, transmittance, and reflectivity of the skin, respectively. , and These represent the average infrared absorptivity, transmittance, and reflectivity of the skin, respectively. and These represent the surface area and projected area of ​​the capsule, respectively. The convective heat transfer between the skin and the external environment can be expressed as: The external convective heat transfer coefficient can be expressed as: in, The external forced convection heat transfer coefficient is... External natural convection heat transfer coefficient; External forced convection heat transfer coefficient It can be represented as: in, Represents the atmospheric Reynolds number. This represents the atmospheric thermal conductivity at an altitude of h. Indicates the characteristic length of the airship; in, Indicates the characteristic diameter of the airship. Indicates air velocity. , and These represent the atmospheric density, atmospheric viscosity, and atmospheric temperature at a height h, respectively. External natural convection heat transfer coefficient It can be represented as: in, For the external atmospheric Nusselt number, The characteristic length of the airship; In the formula, and These represent the atmospheric Grashof number and Prandtl number at an altitude of h, respectively. Therefore, the temperature of the skin can be expressed as: in, , and These represent the mass, specific heat capacity, and temperature of the skin, respectively. The temperature of helium can be expressed as: in, For the volume of the airship, , and Given the mass, volumetric specific heat capacity, and temperature of helium. ; Solving the above system of differential equations simultaneously yields the temperature of the helium gas. .

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