A flexible aerostat heat flow structure coupling calculation method

Abstract

The application discloses a flexible aerostat flow-heat structure coupling calculation method, which comprises the following steps: establishing a stratosphere environment heat model, establishing a stratosphere airship heat model, solving the helium temperature field and the helium average temperature in the airship by adopting a finite element method, establishing an airship external flow field model, solving the aerodynamic pressure of the airship external flow field on the surface of the airship, establishing a near space airship structure deformation simulation model, and solving the structure deformation under the flow-heat-structure coupling effect of the airship, wherein the bidirectional coupling process of the existing calculation method is decoupled, the accurate stratosphere airship flow-heat-structure coupling characteristics are obtained through iterative calculation, and the calculation efficiency is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of airship design technology, specifically to a method for coupled calculation of thermal flow structure of flexible airships. Background Technology

[0002] Soft stratospheric vehicles are characterized by their enormous size and weight, significant variations in mass and inertia, and severe thermal and dynamic coupling. The thermodynamic state of their internal gases has a significant impact on flight performance and operational safety. During operation, the vehicle is subject to a complex interplay of physical fields, including solar radiation, Earth reflection, infrared radiation, forced convection heat transfer from external atmospheric winds, natural convection heat transfer from internal gases, cooling and heating caused by thermal expansion and compression, and thermal conductivity from the skin composite materials. The simulation and calculation of their thermal characteristics are therefore quite complex.

[0003] Soft stratospheric vehicles typically utilize lightweight, flexible skin materials, relying on internal overpressure to form a specific shape envelope. When internal overpressure or external pressure changes occur, the vehicle structure is prone to nonlinear deformation, which can impact its safe operation. During normal flight, the vehicle's interior is primarily affected by overpressure and flow of the rising gas. The overpressure mainly originates from diurnal temperature variations in the rising gas, while the flow primarily stems from natural convection within the interior. Externally, it is subjected to aerodynamic pressure from varying wind speeds. Therefore, the deformation of the vehicle is a fluid-heat transfer-thermo-mechanical coupling deformation of the inflatable film structure.

[0004] The fluid-thermal-structural coupling characteristics of stratospheric aircraft have varying degrees of impact on their cyclic energy systems, lift capabilities, flight control characteristics, and skin materials. Researching calculation methods for these fluid-thermal-structural coupling characteristics will enable effective prediction of the aircraft's operational state, promoting the development of stratospheric aircraft design and control, ensuring their stability and controllability, and laying the foundation for future stratospheric aircraft technology development. Studying these issues is not only crucial for mastering stratospheric aircraft technology but also significantly enriches and develops the research scope of heat transfer.

[0005] Current literature generally only considers the unidirectional coupling of flow-heat-structure in stratospheric vehicles. In reality, flow, heat, and structure influence each other. The calculation method for unidirectional coupling has a large error because it does not consider the change in internal and external pressure difference caused by altitude changes. On the other hand, the traditional calculation method for bidirectional coupling is too complicated and difficult to solve quickly. Summary of the Invention

[0006] The purpose of this invention is to provide a computational method for the coupling of fluid-thermal structure in flexible airships, in order to solve the problems mentioned in the background art, where the current computational method for the coupling of fluid-thermal structure in flexible airships has large errors due to the mutual influence between fluid-thermal-structure, while the computational method for bidirectional coupling is too complex and difficult to solve quickly.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for coupled thermal and fluid dynamics calculation of a flexible airship, comprising the following steps:

[0008] Step S1: Establish a thermal model of the stratospheric environment;

[0009] Direct radiation from the sun I D It can be represented as:

[0010] I D =τ atm ·I sun

[0011] Where, τ atm I represents the transmittance of direct solar radiation in the Earth's atmosphere. sun Indicates the intensity of direct solar radiation outside the Earth's atmosphere;

[0012] Intensity of direct solar radiation outside the Earth (I) sun for:

[0013]

[0014] In the formula, 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 Earth's true anomaly can be expressed as:

[0015]

[0016] Where the sun angle θ day It can be represented as:

[0017] θ day =2π·(N-N0) / 365.2422

[0018] 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;

[0019]

[0020] In the formula, year represents the year corresponding to the calculation date;

[0021] The transmittance τ of direct solar radiation in the Earth's atmosphere atm for:

[0022]

[0023] 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 ratio of air mass to solar radiation as it passes through the atmosphere. AM With the airship's altitude angle θ ele If it is related, then different elevation angles θ ele The corresponding air quality is shown in the following formula:

[0024]

[0025] 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.

[0026]

[0027] The solar altitude angle and azimuth angle can be expressed as:

[0028] θ ele =arcsin(sin(θ) dec sin(Φ) + cos(θ) dec )·cos(Φ)·cos(θ hour ));

[0029]

[0030] 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;

[0031] 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

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

[0034] The intensity of scattered radiation from the sky can be expressed as:

[0035]

[0036] For any tilt angle of The plane can be approximated by the intensity of sky-scattered radiation it receives as:

[0037]

[0038] 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:

[0039] I IR_sky =σ·T sky

[0040] 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:

[0041]

[0042] 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 Regarding the radiation intensity at the ground level:

[0043]

[0044] 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. e0Let H 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...

[0045] I IR_gh =τ IR_gh ·I IR_g

[0046] Where τ IR_gh The transmittance of surface radiation at height h in the atmosphere is expressed as:

[0047] τ IR_gh =1.716-0.5(exp(-0.65p) h / p0)+exp(-0.95p h / p0));

[0048] Step S2: Establish a thermal model of a stratospheric airship;

[0049] 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's 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.

[0050] The energy absorbed by the skin from direct solar radiation, atmospheric scattering, and Earth reflection can be expressed as:

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

[0052] q S =α·I s ·S surf ·(1+τ / (1-r))

[0053] q R =α·I R ·S projected ·(1+τ / (1-r))

[0054] Infrared radiation from the atmosphere, Earth, and internal balloons can be represented as:

[0055] q IR_atm =α IR ·I IR_atm ·S surf ·(1+τ IR / (1-r IR ))

[0056] qIR_ear =α IR ·I IR_ear ·S projected ·(1+τ IR / (1-r IR ))

[0057] q IR_He =α IR ·I IR_He ·S surf_He ·(1 / (1-r IR ))

[0058] 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 capsule, respectively.

[0059] The convective heat transfer between the skin and the external environment can be expressed as:

[0060] q conv_ex =h ex ·S surf ·(T atm -T f )

[0061] h ex The external convective heat transfer coefficient can be expressed as:

[0062]

[0063] Among them, h ex_force h is the external forced convection heat transfer coefficient. ex_natural h represents the external natural convection heat transfer coefficient and the external forced convection heat transfer coefficient. ex_force It can be represented as:

[0064]

[0065] Among them, Re atm k represents the atmospheric Reynolds number. atmh L0 represents the atmospheric thermal conductivity at an altitude of h, and L0 represents the characteristic length of the airship.

[0066]

[0067]

[0068]

[0069] Where D represents the characteristic diameter of the airship, υ atm ρ represents air velocity. atmh μ atmh and T atmh These represent the atmospheric density, atmospheric viscosity, and atmospheric temperature at a height h, respectively.

[0070] External natural convection heat transfer coefficient h ex_natural It can be represented as

[0071]

[0072] Among them, Nu atm_natural L0 is the Nusselt number of the external atmosphere and L0 is the characteristic length of the airship.

[0073]

[0074] In the formula, Gr atmh and Pr atmh represent the atmospheric Grashof number and Prandtl number at an altitude of h, respectively;

[0075]

[0076] Pr atmh =0.804 - 3.25·10 -4 ·T atmh ;

[0077] Step S3: Combining the wind speed and direction of the external wind field of the airship, and based on the above-mentioned stratospheric environment thermal model and stratospheric airship thermal model, the finite element method is used to solve the helium temperature field and the average helium temperature inside the airship.

[0078] Step S4: Establish an external flow field model for the airship and solve for the aerodynamic pressure of the external flow field on the airship surface. Based on the airship simulation model established in Step S3, use Fluent software to calculate the aerodynamic pressure of the external flow field on the airship surface. Select a velocity inlet at the front end of the computational domain and a pressure outlet at the rear end. Use a steady-state pressure basis to solve the continuity equation and the RANS equation. Select the Realizable model for turbulence. Use the SIMPLE algorithm for pressure and velocity coupling and discretize the equations using a second-order upwind scheme. Set the computational residual to 10. -4 ;

[0079] Step S5: Establish a near-space airship structural deformation simulation model; import the airship geometric model established in step S3 into Abaqus software, set the elastic modulus and Poisson's ratio of the skin according to the actual mechanical properties of the skin material, and set the constraint conditions as follows: constrain the displacement in the X, Y and Z directions of the airship head, constrain the displacement in the Y and Z directions of the airship tail, and do not constrain the displacement in the X direction.

[0080] Step S6: Solve for the structural deformation under the airship flow-thermal-structural coupling effect according to the following steps:

[0081] 1) Based on the average helium temperature T inside the airship calculated in step S3, calculate the internal pressure of the airship according to the ideal gas law:

[0082]

[0083] Where, m he R is the mass of helium inside the airship, R is the molar gas constant of helium, and V is the volume of the airship.

[0084] 2) Based on the airship's current flight altitude h, the external atmospheric pressure of the airship is calculated using the US standard atmospheric model.

[0085] The atmospheric pressure of the part is:

[0086]

[0087] According to the internal pressure P of the airship in and external atmospheric pressure P atmh The internal and external pressure difference ΔP1 is obtained:

[0088]

[0089] 3) Based on the assumption that the expansion / contraction process of the airship is considered as isothermal expansion / contraction, the internal pressure P of the airship is... in External atmospheric pressure P atmh and the aerodynamic pressure distribution P on the airship surface calculated in step S4. w Import the Abaqus software and load it onto the airship skin surface. Use Abaqus software to calculate the airship structural deformation and the volume V after deformation.

[0090] 4) Calculate the height h after balancing based on the buoyancy weight. The calculation method is as follows:

[0091] The buoyancy force acting on the airship can be expressed as B = ρ atm (h)gV, where ρ atm (h) represents the atmospheric density at altitude h, g represents the acceleration due to gravity, and according to the American Standard Atmospheric Model, the atmospheric temperature T atm and air pressure P atm It can be represented as

[0092]

[0093]

[0094] Therefore, atmospheric density ρ atm (h) can be represented as:

[0095]

[0096] Where R m_atm ρ is the molar gas constant of the atmosphere; the gravitational force on the airship is G = mg, where m is the mass of the airship;

[0097] 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, where

[0098]

[0099] By combining the above formulas, the height h can be calculated;

[0100] 5) Update the internal pressure P of the airship after deformation according to step 1). in ;

[0101] 6) Update the atmospheric pressure P according to step 2). atmh And calculate the internal and external pressure difference ΔP2=|P in -P atmh |;

[0102] 7) Assume aerodynamic pressure distribution P w The convergence condition ε is set without changing with the deformation of the airship structure. Generally, ε = 5 Pa can be taken. Under this premise, the following judgment is made:

[0103] If |ΔP1-ΔP2|≤ε, then the airship deformation is considered to have reached stability, and the corresponding structural deformation cloud map, skin stress distribution cloud map, and deformed volume V are the final stable state.

[0104] If |ΔP1-ΔP2|>ε, then the airship deformation has not reached a steady state. The airship volume V in this unsteady state is derived using Abaqus software, and the internal and external pressure difference is reset. Repeat steps 3) to 7) until |ΔP1-ΔP2|≤ε. At this point, the airship deformation is considered to have reached stability. The corresponding structural deformation cloud map, skin stress distribution cloud map, and deformed volume V are the final stable state.

[0105] As a preferred technical solution, in step S3, the finite element method is used to analyze the helium temperature field and average helium temperature inside the airship: a geometric model of the airship is established in Space Claim software, where the airship coordinate system adopts a right-handed coordinate system, the airship axis is in the X direction, and the altitude direction is in the Z direction. Fluent Meshing is used for mesh generation, and Poly-Hexcore volume mesh is used for mesh generation. Based on the stratospheric environment thermal model established in step S1 and the airship thermal model established in step S2, an airship thermal model UDF program is written in Fluent software. The UDF program is used to accurately load the airship thermal environment model established in step S2 and the wind field and wind speed corresponding to the current airship altitude. The mass, momentum, and energy control equations are solved based on the finite volume method.

[0106] As a preferred technical solution, the flow field governing equations of the finite volume method are as follows:

[0107] The fluid domain quality control equation is:

[0108]

[0109] The momentum governing equation for the fluid domain is:

[0110]

[0111] The energy control equation for the fluid domain is:

[0112]

[0113] The boundary conditions are:

[0114] Mass and momentum conservation equations: It is assumed that there is no helium leakage in the airship skin, so there is no mass transfer between the airship and the external environment. In addition, it is assumed that the velocity of the skin is zero.

[0115] Energy conservation equation: There are two forms of heat exchange between the airship and the external environment, namely heat convection and heat radiation. Therefore, the energy equation of the skin can be expressed as follows:

[0116] S Tf =q D +q S +q R +q IR_atm +q IR_ear +q IR_grid +q IR_in +q conv_ex +q conv_in -q power .

[0117] As a preferred technical solution, the helium temperature field is obtained after thermal analysis using Fluent software and UDF program. The average temperature of the helium is obtained using the volume averaging method. Some parameters were selected during the thermal analysis as follows:

[0118] (1) Set the working conditions to an operating pressure of 5829 Pa and an operating temperature of 230 K. Assume that the helium inside the airship is an incompressible gas. Select the pressure-based solver, the steady state time type, and the absolute velocity format.

[0119] (2) Open the energy equation;

[0120] (3) The standard k-ε model is used for the turbulence model;

[0121] (4) The radiation model selected is the S2S model;

[0122] (5) Boundary condition selection: Mixed boundary conditions are selected for the wall conditions of the skin and solar cells;

[0123] (6) Solution method selection: The Coupled method is selected as the solution method, PRESTO is selected for pressure, and the second-order upwind scheme is selected for momentum equation, turbulent kinetic energy equation, turbulent dissipation rate equation and energy equation.

[0124] (7) Relaxation factor selection: Select pressure relaxation factor 0.5, momentum relaxation factor 0.5, density relaxation factor 1, body force relaxation factor 1, turbulent kinetic energy relaxation factor 0.75, turbulent dissipation rate relaxation factor 0.75, turbulent viscosity relaxation factor 1, and energy relaxation factor 0.75.

[0125] (8) Select standard initialization, reference temperature 220K.

[0126] Compared with the prior art, the beneficial effects of the present invention are:

[0127] (1) 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. In addition, the external wind field environment mainly affects the thermal characteristics of the airship. The aerodynamic pressure on the airship surface caused by the external wind field environment has little impact on structural deformation. At the same time, the change in aerodynamic pressure distribution caused by the deformation of the airship structure is also small. Therefore, the two-way coupling between aerodynamic pressure and structural deformation can be simplified to a one-way coupling relationship. Based on the above assumptions, the two-way coupling of flow-heat-structure in the stratospheric airship can be simplified to a one-way coupling of flow-heat-structure, which greatly simplifies the calculation process of the flow-heat-structure coupling effect of the airship and improves the calculation efficiency while ensuring a certain calculation accuracy.

[0128] (2) Current literature on the calculation methods for airship flow-heat-structure coupling generally only calculates up to step S6(3). In reality, the structural deformation and the volume V after deformation obtained in this step are not the stable state. The structural deformation of the airship is strongly coupled with the flight altitude. Specifically, the airship volume changes, which leads to changes in flight altitude. Since the atmospheric pressure is different at different altitudes, the pressure difference between the inside and outside of the airship changes with altitude, which in turn leads to changes in the volume of the airship. The imbalance of buoyancy and weight leads to further changes in volume and altitude. This process is a two-way coupling process between structural deformation and flight altitude.

[0129] This invention decouples the above-mentioned bidirectional coupling process and obtains more accurate stratospheric airship flow-heat-structure coupling characteristics through iterative calculations in steps S6(4) to S6(7), while greatly improving the calculation efficiency. Attached Figure Description

[0130] Figure 1 This is a flowchart of a method for calculating the thermal-fluid coupling structure of a flexible airship according to the present invention. Detailed Implementation

[0131] 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.

[0132] Please see Figure 1 This invention provides a technical solution: a method for coupled calculation of the thermal and fluid structure of a flexible airship, comprising:

[0133] 1. Establish a thermal model of the stratosphere.

[0134] Direct radiation from the sun I D It can be represented as:

[0135] I D =τ atm ·I sun

[0136] 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.

[0137] Intensity of direct solar radiation outside the Earth (I) sun for

[0138]

[0139] 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

[0140]

[0141] Where the sun angle θ day It can be represented as

[0142] θ day =2π·(N-N0) / 365.2422

[0143] 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.

[0144]

[0145] In the formula, year represents the year corresponding to the calculation date.

[0146] The transmittance τ of direct solar radiation in the Earth's atmosphere atm for

[0147]

[0148] 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 airship's altitude angle θ ele Related to different elevation angles θ ele The corresponding air quality is shown in the following formula.

[0149]

[0150] 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.

[0151]

[0152] The solar altitude angle and azimuth angle can be expressed as:

[0153] θele =arcsin(sin(θ) dec sin(Φ) + cos(θ) dec )·cos(Φ)·cos(θ hour ))

[0154]

[0155] 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.

[0156] 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

[0157] θ hour =15(time+e) t / 60-12.0)·π / 180

[0158] e t =0.0028-1.9857·sin(θ) day )+9.9059·sin(2θ day -7.0924·cos(θ) day )-0.6882·cos(2θ day )

[0159] The intensity of scattered radiation from the sky can be expressed as:

[0160]

[0161] For any tilt angle of The plane can be approximated by the intensity of sky-scattered radiation it receives.

[0162]

[0163] 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...

[0164] I IR_sky =σ·T sky

[0165] Where T sky The equivalent temperature of the sky can be expressed as the sky emissivity ε. sky and atmospheric temperature T atm Functions:

[0166]

[0167] 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 is...

[0168]

[0169] 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. e0 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...

[0170] I IR_gh =τ IR_gh ·I IR_g

[0171] Where τ IR_gh The transmittance of surface radiation in the atmosphere at height h is expressed as follows:

[0172] τ IR_gh =1.716-0.5(exp(-0.65p) h / p0)+exp(-0.95p h / p0))

[0173] 2. Establish a thermal model of a stratospheric airship

[0174] 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'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.

[0175] The energy absorbed by the skin from direct solar radiation, atmospheric scattering, and Earth reflection can be expressed as:

[0176] q D =α·I D ·S projected ·(1+τ / (1-r))

[0177] q S =α·I s ·S surf ·(1+τ / (1-r))

[0178] q R =α·I R ·S projected ·(1+τ / (1-r))

[0179] Infrared radiation from the atmosphere, Earth, and internal balloons can be represented as follows:

[0180] q IR_atm =α IR ·I IR_atm ·S surf ·(1+τ IR / (1-r IR ))

[0181] q IR_ear =α IR ·I IR_ear ·S projected ·(1+τ IR / (1-r IR ))

[0182] q IR_He =α IR ·I IR_He ·S surf_He ·(1 / (1-r IR ))

[0183] 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.

[0184] The convective heat transfer between the skin and the external environment can be expressed as:

[0185] q conv_ex =h ex ·S surf ·(T atm -T f )

[0186] hex The external convective heat transfer coefficient can be expressed as:

[0187]

[0188] Where h ex_force h is the external forced convection heat transfer coefficient. ex_natural Here, h represents the external natural convection heat transfer coefficient. The external forced convection heat transfer coefficient is also represented by h. ex_force It can be represented as

[0189]

[0190] Where Re atm k represents the atmospheric Reynolds number. atmh L0 represents the atmospheric thermal conductivity at an altitude of h, and L0 represents the characteristic length of the airship.

[0191]

[0192]

[0193]

[0194] 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.

[0195] External natural convection heat transfer coefficient h ex_natural It can be represented as

[0196]

[0197] Nu atm_natural L0 is the Nusselt number of the external atmosphere and L0 is the characteristic length of the airship.

[0198]

[0199] In the formula Gr atmh and Pr atmh represents the atmospheric Grashof number and Prandtl number at an altitude of h, respectively.

[0200]

[0201] Pr atmh =0.804 - 3.25·10 -4 ·T atmh

[0202] 3. By combining the wind speed and direction of the external wind field of the airship, solve for the temperature field of helium gas inside the airship and the average temperature T of helium gas.

[0203] The finite element method was used to analyze the helium temperature field and the average helium temperature T inside the airship.

[0204] A geometric model of the airship was created using Space Claim software, with a right-handed coordinate system, the airship axis being the X-axis and the altitude direction being the Z-axis. Fluent Meshing was used for mesh generation, employing a Poly-Hexcore volumetric mesh.

[0205] Based on the stratospheric environment thermal model established in step 1 and the airship thermal model established in step 2, a UDF program for the airship thermal model was written in Fluent software. The UDF program was used to accurately load the airship thermal environment model established in step 2 and the wind speed corresponding to the current airship altitude. The mass, momentum, and energy control equations were solved using the finite volume method. The flow field control equations are as follows:

[0206] The fluid domain quality control equation is

[0207]

[0208] The momentum governing equations of the fluid domain are

[0209]

[0210] The energy control equation for the fluid domain is

[0211]

[0212] The boundary conditions are:

[0213] Mass and momentum conservation equations: It is assumed that there is no helium leakage in the airship skin, therefore there is no mass transfer between the airship and the external environment. Furthermore, it is assumed that the velocity of the skin is zero.

[0214] Energy conservation equation: There are two forms of heat exchange between the airship and the external environment, namely heat convection and heat radiation. Therefore, the energy equation of the skin can be expressed as follows:

[0215] S Tf =q D +q S +q R +q IR_atm +q IR_ear +q IR_grid +q IR_in +q conv_ex +q conv_in -q power

[0216] When performing thermal analysis using Fluent software and UDF programs, some settings are as follows:

[0217] (1) Set the operating conditions as operating pressure 5829 Pa and operating temperature 230 K. Assume that the helium inside the airship is an incompressible gas, select the pressure-based solver, select steady state for time type, and select absolute velocity for velocity format.

[0218] (2) Open the energy equation.

[0219] (3) The standard k-ε model is used for the turbulence model.

[0220] (4) The radiation model selected is the S2S model.

[0221] (5) Boundary condition selection: Mixed boundary conditions are selected for the wall conditions of the skin and solar cells.

[0222] (6) Solution method selection: The Coupled method is selected as the solution method, PRESTO is selected for pressure, and the second-order upwind scheme is selected for momentum equation, turbulent kinetic energy equation, turbulent dissipation rate equation and energy equation.

[0223] (7) Relaxation factor selection: Select pressure relaxation factor 0.5, momentum relaxation factor 0.5, density relaxation factor 1, volume force relaxation factor 1, turbulent kinetic energy relaxation factor 0.75, turbulent dissipation rate relaxation factor 0.75, turbulent viscosity relaxation factor 1, and energy relaxation factor 0.75.

[0224] (8) Select standard initialization, reference temperature 220K.

[0225] After thermal analysis using Fluent software and UDF program, the helium temperature field was obtained, and the average temperature T of the helium was obtained by volume averaging method.

[0226] 4. Establish an external flow field model for the airship and solve for the aerodynamic pressure P on the airship surface. w .

[0227] The flow field of an airship can be divided into internal and external flow fields. The internal flow field is mainly natural convection caused by the temperature difference of helium, with a flow velocity generally less than 3 m / s. Therefore, the dynamic pressure of the internal flow field has a negligible effect on the deformation of the airship structure. The external flow field is mainly the relative wind speed between the near-space atmosphere and the airship. In the quasi-zero wind layer around 20 km, the wind speed is generally as low as a few meters per second to tens of meters per second. The airship's speed is also relatively low, resulting in a small relative wind speed. Therefore, the external flow field can be regarded as a low-speed incompressible flow field.

[0228] Based on the airship simulation model established in step 3, the aerodynamic pressure of the external flow field on the airship surface was calculated using Fluent software. A velocity inlet was selected at the front end of the computational domain, and a pressure outlet at the rear end. The continuity equation and RANS equation were solved using a steady-state pressure basis. The Realizable k-ε turbulence model was selected. The pressure and velocity coupling was performed using the SIMPLE algorithm, and the equations were discretized using a second-order upwind scheme. The computational residual was set to 10. -4 .

[0229] 5. Establish a simulation model of near-space airship structural deformation.

[0230] Import the airship geometric model established in step 3 into Abaqus software. Set the elastic modulus and Poisson's ratio of the skin according to the actual mechanical properties of the skin material. At the same time, set the constraints as follows: constrain the displacement in the X, Y, and Z directions of the airship head, constrain the displacement in the Y and Z directions of the airship tail, and do not constrain the displacement in the X direction.

[0231] 6. Solve for the structural deformation under the airship's flow-thermal-structure coupling effect. The solution process is as follows:

[0232] (1) Based on the average temperature T of the helium gas inside the airship calculated in step 3, calculate the internal pressure of the airship according to the ideal gas law. Where m he Let R be the mass of helium inside the airship, R be the molar gas constant of helium, and V be the volume of the airship.

[0233] (2) Based on the airship's current flight altitude h, the atmospheric pressure outside the airship is calculated using the American Standard Atmospheric Model.

[0234]

[0235] (3) Based on the internal pressure P of the airship in and external atmospheric pressure P atmh The internal and external pressure difference ΔP1 is obtained:

[0236]

[0237] The airship expands / contracts under the influence of the internal and external pressure difference, resulting in a change in volume. During this process, the airship is continuously subjected to the external thermal environment, but its temperature change is small, approximating a quasi-steady-state process. Therefore, the expansion / contraction process of the airship can be considered as isothermal expansion / contraction. Based on this assumption, the internal pressure P of the airship is... in External atmospheric pressure P atmh and the aerodynamic pressure distribution P on the airship surface calculated in step 4. w Import the Abaqus software and load it onto the airship skin surface. Use Abaqus software to calculate the airship structural deformation and the volume V after deformation.

[0238] (4) As the volume V changes, the airship's equilibrium height h will also change. The equilibrium height h is calculated based on the buoyancy balance, and the calculation method is as follows:

[0239] The buoyancy force acting on the airship can be expressed as B = ρ atm (h)gV, 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 It can be represented as

[0240]

[0241]

[0242] Therefore, atmospheric density ρ atm (h) can be expressed as

[0243]

[0244] Where R m_atm is the molar gas constant of the atmosphere.

[0245] The gravitational force acting on the airship is G = mg, where m is the mass of the airship.

[0246] 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.

[0247]

[0248] By combining the above formulas, the height h can be calculated.

[0249] (5) Update the internal pressure P of the airship after deformation according to step (1). in .

[0250] (6) 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 basically constant, and the isothermal expansion / contraction assumption proposed in step (3) is adopted here. This assumption is used here, and the temperature of the helium gas is assumed to remain constant. According to step (2), the atmospheric pressure P is updated. atmh And calculate the internal and external pressure difference ΔP2=|P in -P atmh |

[0251] (7) Under the influence of solar radiation and external wind fields, although the airship will undergo structural deformation leading to changes in volume and altitude, the structural deformation is relatively small compared to the airship's diameter. Furthermore, the aerodynamic pressure P caused by low external wind speeds... w Not significant, generally ranging from a few Pascals to over ten Pascals. This is related to the internal pressure P inside the airship. in In comparison, the aerodynamic pressure is relatively small. Therefore, to simplify the calculation of the airship's flow-heat-structure coupling characteristics, the effect of structural deformation on the aerodynamic pressure P can be ignored. w The effect is to simplify the two-way coupling between aerodynamic pressure and structural deformation into a one-way coupling relationship. To improve computational efficiency, we assume an aerodynamic pressure distribution P. w It does not change with the deformation of the airship structure.

[0252] (8) Set the convergence condition ε, which can generally be taken as ε = 5Pa.

[0253] (9) If |ΔP1-ΔP2|≤ε, then the airship deformation is considered to have reached stability, and the corresponding structural deformation cloud map, skin stress distribution cloud map and deformed volume V are the final stable state.

[0254] (10) If |ΔP1-ΔP2|>ε, then the airship deformation has not reached a stable state. Use Abaqus software to export the airship volume V in this unstable state, and reset the internal and external pressure difference to ε. Repeat steps (3) to (10) until |ΔP1-ΔP2|≤ε. At this point, the airship deformation is considered to have reached stability. The corresponding structural deformation cloud map, skin stress distribution cloud map, and deformed volume V are the final stable state.

[0255] Existing technologies for performing fluid-thermal-structural coupling calculations on flexible airships generally assume that the airship's flight altitude is constant. Based on this, a one-way coupling method is used to calculate the fluid-thermal-structural coupling effect of the stratospheric airship, without considering the strong coupling relationship between the airship's structural deformation and its flight altitude.

[0256] This scheme considers the strong two-way coupling relationship between airship flow-heat-structural deformation and flight altitude changes. By decoupling this strong two-way coupling relationship and performing a finite number of iterative calculations, a more accurate thermal and structural deformation characteristic of the airship is obtained, while improving computational efficiency.

[0257] 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 coupled calculation of thermal flux structure of a flexible airship, characterized in that, Includes the following steps: Step S1: Establish a thermal model of the stratospheric environment; Direct radiation from the sun I D It can be represented as: I D =τ atm ·I sun Where, τ atm I represents the transmittance of direct solar radiation in the Earth's atmosphere. sun This represents the intensity of direct solar radiation outside the Earth's atmosphere; Intensity of direct solar radiation outside the Earth I sun for: In the formula, I0 is the solar radiation constant, I0 = 1367 W / m 2 e earth For the Earth's eccentricity, e earth =0.016708, ζ earth Let the angle be the true anomaly of Earth, and it is expressed as: Where the sun angle θ day It can be represented as: i day =2π·(N-N0) / 365.2422 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; In the formula, year represents the year corresponding to the calculation date; The transmittance τ of direct solar radiation in the Earth's atmosphere atm for: 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 ratio of air mass to solar radiation as it passes through the atmosphere. AM With the airship's altitude angle θ ele If it is related, then different elevation angles θ ele The corresponding air quality is shown in the following formula: In a geodetic coordinate system, the direction of direct solar radiation It is the solar altitude angle θ ele and solar azimuth θ az A function of i; The solar altitude angle and azimuth angle can be expressed as: i ele =arcsin(sin(θ) dec )·sin(Φ)+cos(θ dec )·cos(Φ)·cos(θ hour )); 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; 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 intensity of scattered radiation from the sky can be expressed as: For a plane with any tilt angle θ, the intensity of the scattered radiation from the sky can be approximated as: Generally, assuming the atmosphere is a blackbody, according to the Stefan-Boltzman law, the infrared radiation power of the sky can be expressed as: I IR_sky =σ·T sky 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: 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 Regarding the radiation intensity at the ground level: 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. e0 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: I IR_gh =τ IR_gh ·I IR_g Where, τ IR_gh The transmittance of surface radiation at height h in the atmosphere is expressed as: t IR_gh =1.716-0.5(exp(-0.65p h / p0)+exp(-0.95p h / p0)); Step S2: Establish a thermal model of a stratospheric airship; 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's 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. The energy absorbed by the skin from direct solar radiation, atmospheric scattering, and Earth reflection can be expressed as: q D =α·I D ·S projected ·(1+τ / (1-r)) q S =α·I s ·S surf ·(1+τ / (1-r)) q R =α·I R ·S projected ·(1+τ / (1-r)) Infrared radiation from the atmosphere, Earth, and internal balloons can be represented as: q IR_atm =a IR ·I IR_atm ·S surf ·(1+τ IR / (1-r IR )) q IR_ear =a IR ·I IR_ear ·S projected ·(1+τ IR / (1-r IR )) q IR_He =α IR ·I IR_He ·S surf_He ·(1 / (1-r IR )) 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 capsule, 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 ) h ex The external convective heat transfer coefficient can be expressed as: Among them, h ex_force h is the external forced convection heat transfer coefficient. ex_natural h represents the external natural convection heat transfer coefficient and the external forced convection heat transfer coefficient. ex_force It can be represented as: Among them, Re atm k represents the atmospheric Reynolds number. atmh L0 represents the atmospheric thermal conductivity at an altitude of h, and L0 represents the characteristic length of the airship. Where D represents the characteristic diameter of the airship, υ atm ρ represents air velocity. atmh μ atmh and T atmh These represent the atmospheric density, atmospheric viscosity, and atmospheric temperature at a height h, respectively. External natural convection heat transfer coefficient h ex_natural It can be represented as Among them, Nu atm_natural L0 is the Nusselt number of the external atmosphere and L0 is the characteristic length of the airship. In the formula, Gr atmh and Pr atmh represent the atmospheric Grashof number and Prandtl number at an altitude of h, respectively; Pr atmh =0.804-3.25 10 -4 ·T atmh ; Step S3: Combining the wind speed and direction of the external wind field of the airship, and based on the above-mentioned stratospheric environment thermal model and stratospheric airship thermal model, the finite element method is used to solve the helium temperature field and the average helium temperature inside the airship. Step S4: Establish an external flow field model for the airship and solve for the aerodynamic pressure on the airship surface: Based on the airship simulation model established in Step 3, the Fluent software is used to calculate the aerodynamic pressure on the airship surface. A velocity inlet is selected at the front end of the computational domain, and a pressure outlet is selected at the rear end. The steady-state pressure basis is used to solve the continuity equation and the RANS equation. The Realizable model is selected for the turbulence model. The pressure and velocity coupling is performed using the SIMPLE algorithm, and a second-order upwind scheme is used for equation discretization. The calculation residual is set to 10. -4 ; Step S5: Establish a near-space airship structural deformation simulation model; import the airship geometric model established in Step 3 into Abaqus software, set the elastic modulus and Poisson's ratio of the skin according to the actual mechanical properties of the skin material, and set the constraint conditions as follows: constrain the displacement in the X, Y and Z directions of the airship head, constrain the displacement in the Y and Z directions of the airship tail, and do not constrain the displacement in the X direction. Step S6: Solve for the structural deformation under the airship flow-thermal-structural coupling effect according to the following steps: 1) Based on the average helium temperature T inside the airship calculated in step 3, calculate the internal pressure of the airship according to the ideal gas law: Where, m he R is the mass of helium inside the airship, R is the molar gas constant of helium, and V is the volume of the airship. 2) Based on the airship's current flight altitude h and the US standard atmospheric model, the atmospheric pressure outside the airship is calculated as follows: According to the internal pressure P of the airship in and external atmospheric pressure P atmh The internal and external pressure difference ΔP1 is obtained: 3) Based on the assumption that the expansion / contraction process of the airship is considered as isothermal expansion / contraction, the internal pressure P of the airship is... in External atmospheric pressure P atmh and the aerodynamic pressure distribution P on the airship surface calculated in step 4. w Import the Abaqus software and load it onto the airship skin surface. Use Abaqus software to calculate the airship structural deformation and the volume V after deformation. 4) Calculate the height h after balancing based on the buoyancy weight. The calculation method is as follows: The buoyancy force acting on the airship can be expressed as B = ρ atm (h)gV, where ρ atm (h) represents the atmospheric density at altitude h, g represents the acceleration due to gravity, and according to the American Standard Atmospheric Model, the atmospheric temperature T atm and air pressure P atm It can be represented as Therefore, atmospheric density ρ atm (h) can be represented as: Where R m_atm ρ is the molar gas constant of the atmosphere; the gravitational force on the airship is G = mg, where m is the mass of the airship; 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, where By combining the above formulas, the height h can be calculated; 5) Update the internal pressure P of the airship after deformation according to step 1). in ; 6) Update the atmospheric pressure P according to step 2). atmh And calculate the internal and external pressure difference ΔP2=|P in -P atmh |; 7) Assume aerodynamic pressure distribution P w The convergence condition ε is set without changing with the deformation of the airship structure. Generally, ε = 5 Pa can be taken. Under this premise, the following judgment is made: If |ΔP1-ΔP2|≤ε, then the airship deformation is considered to have reached stability, and the corresponding structural deformation cloud map, skin stress distribution cloud map, and deformed volume V are the final stable state. If |ΔP1-ΔP2|>ε, then the airship deformation has not reached a steady state. The airship volume V in this unsteady state is derived using Abaqus software, and the internal and external pressure difference is reset. Repeat steps 3) to 7) until |ΔP1-ΔP2|≤ε. At this point, the airship deformation is considered to have reached stability. The corresponding structural deformation cloud map, skin stress distribution cloud map, and deformed volume V are the final stable state.

2. The method for calculating the thermal-fluid coupling of a flexible airship according to claim 1, characterized in that, In step S3, the finite element method is used to analyze the helium temperature field and average helium temperature inside the airship: a geometric model of the airship is established in Space Claim software, with the airship coordinate system being a right-handed coordinate system, the airship axis being the X direction, and the altitude direction being the Z direction. Fluent Meshing is used for mesh generation, and Poly-Hexcore volume mesh is used for mesh generation. Based on the stratospheric environment thermal model established in step S1 and the airship thermal model established in step S2, an airship thermal model UDF program is written in Fluent software. The UDF program is used to accurately load the airship thermal environment model established in step S2 and the wind field and wind speed corresponding to the current airship altitude. The mass, momentum, and energy control equations are solved based on the finite volume method.

3. The method for coupled thermal and fluid structure calculation of a flexible airship according to claim 2, characterized in that, After thermal analysis using Fluent software and the UDF program, the helium temperature field was obtained. The average temperature of the helium was obtained using the volume averaging method. Some parameters were selected during the thermal analysis as follows: (1) Set the working conditions to an operating pressure of 5829 Pa and an operating temperature of 230 K. Assume that the helium inside the airship is an incompressible gas. Select the pressure-based solver, the steady state time type, and the absolute velocity format. (2) Open the energy equation; (3) The standard k-ε model is used for the turbulence model; (4) The radiation model selected is the S2S model; (5) Boundary condition selection: Mixed boundary conditions are selected for the wall conditions of the skin and solar cells; (6) Solution method selection: The Coupled method is selected as the solution method, PRESTO is selected for pressure, and the second-order upwind scheme is selected for momentum equation, turbulent kinetic energy equation, turbulent dissipation rate equation and energy equation. (7) Relaxation factor selection: Select pressure relaxation factor 0.5, momentum relaxation factor 0.5, density relaxation factor 1, body force relaxation factor 1, turbulent kinetic energy relaxation factor 0.75, turbulent dissipation rate relaxation factor 0.75, turbulent viscosity relaxation factor 1, and energy relaxation factor 0.

75. (8) Select standard initialization, reference temperature 220K.

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