Calculation Method for Surface Temperature of Three-Dimensional Hot Gas Anti-Icing System Considering Periodic Boundaries

Abstract

The present invention discloses a method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries. First, the external flow field and water droplet field of the wing are calculated, and the results of the flow field and water droplet field are exported for standby. Then, the heat transfer of the hot gas flow inside the anti-icing cavity is calculated to obtain the heat transfer coefficient on the inner surface of the skin and export it for standby. Next, the heat conduction of the skin is iteratively solved. During each iteration step, the mass and energy conservation equations of the water film need to be calculated, and the external net heat flux result is loaded onto the outer surface of the skin. The inner surface of the skin is set as the third type of boundary condition according to the heat transfer result of the hot gas flow inside the anti-icing cavity. Finally, during the iterative process of the skin heat conduction calculation, the inner and outer boundary values of the skin are also constantly changing and updating. Until the heat conduction calculation converges and the boundaries basically no longer change, it is considered that the heat transfer coupling calculation between the inside and outside of the anti-icing system converges.

Description

Technical Field

[0001] The present invention relates to the monitoring of the surface temperature of the hot - air anti - icing system of an aircraft wing. More particularly, it refers to a method for calculating the surface temperature of a three - dimensional hot - air anti - icing system considering periodic boundaries. Background Art

[0002] When an aircraft flies in clouds containing supercooled water droplets, the supercooled water droplets in the environment impact the wing surface, and local icing may occur on the windward side. Ice formation on the leading edge of the wing will change the wing shape, disrupt the aerodynamic boundary layer, resulting in an increase in flight resistance, a decrease in lift, a decline in maneuverability and stability. In severe icing conditions, it may even lead to flight accidents. To prevent the impact of wing icing on flight safety, an anti - icing system is usually installed to prevent icing on the leading edge of the wing. The anti - icing systems mainly include hot - air anti - icing systems and electro - thermal anti - icing systems. Due to the simple principle and high reliability of the hot - air anti - icing system, most large - scale aircraft wings currently adopt the hot - air anti - icing method.

[0003] The research on the hot - air anti - icing system of the wing mainly includes experimental research and numerical simulation. Experimental research is time - consuming and laborious, and it is impossible to simulate all icing conditions in the flight envelope; while numerical simulation can relatively quickly predict the temperature distribution on the anti - icing surface, analyze the working state of the hot - air anti - icing system under any icing condition, and can provide certain guidance for experimental research. A large number of numerical simulation studies on the hot - air anti - icing system of the wing have been carried out at home and abroad to evaluate the performance of the hot - air anti - icing system and guide the design of the hot - air anti - icing system. Khalil studied the influence of different flute - tube distributions on the wing surface temperature and convective heat transfer. Li Yan et al. carried out a simulation calculation study on the performance of a three - dimensional hot - air anti - icing cavity based on the Euler wall - film model. Pellissier et al. used the FENSAP - ICE software to calculate the wing anti - icing surface temperature and overflow water distribution, and optimized the hot - air anti - icing system using the simulation results. Bu Xueqin et al. developed a three - dimensional hot - air anti - icing system based on FLUENT to conduct a numerical simulation study and performance evaluation on the surface temperature of the swept - wing hot - air anti - icing system. However, considering the limitation of computing resources, current research is all aimed at simulating the local hot - air anti - icing system of the wing, and simplified treatment is carried out on the boundary conditions, without considering the impact of the entire anti - icing surface on the calculation area. Summary of the Invention

[0004] A method for calculating the surface temperature of a three - dimensional hot - air anti - icing system considering periodic boundaries proposed by the present invention is to solve for the temperature and overflow water distribution results on the wing skin surface through the coupled heat transfer calculation inside and outside the skin based on the calculation of the external environmental flow field and the internal anti - icing cavity. Considering the influence of the overflow water in adjacent anti - icing areas on the calculated anti - icing area, a periodic overflow water boundary condition is proposed, which effectively improves the calculation result of the surface temperature of the three - dimensional hot - air anti - icing system and makes it more in line with the actual situation.

[0005] A method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries, in which the internal and external heat transfer coupling calculation unit (30) adopts a loose coupling calculation method;

[0006] The heat transfer loose coupling calculation of the internal and external heat transfer coupling calculation unit (30) includes a hot gas anti-icing surface heat flux term and water film mass and energy conservation equations;

[0007] The hot gas anti-icing surface heat flux term includes a convective heat transfer heat flux density, an evaporative heat dissipation heat flux density, and a heat flux density required to heat water;

[0008] The convective heat transfer heat flux density is characterized as:

[0009]

[0010]

[0011] The evaporative heat dissipation heat flux density is characterized as:

[0012]

[0013]

[0014]

[0015] The saturated water vapor pressure can be obtained from the following calculation formula:

[0016]

[0017] According to Dalton's partial pressure principle, the water vapor partial pressure at the outer boundary of the boundary layer is calculated as follows:

[0018]

[0019] The heat flux density required to heat water is characterized as:

[0020]

[0021]

[0022] The heat flux density converted by the kinetic energy of water droplets is characterized as:

[0023]

[0024] The mass conservation equation of the anti-icing surface is characterized as:

[0025]

[0026] The energy conservation equation of the anti-icing surface is characterized as:

[0027] According to the law of conservation of energy, the energy conservation equation for the anti-icing surface can be obtained:

[0028]

[0029] The advantages of the method for calculating the surface temperature of the three-dimensional hot-gas anti-icing system considering periodic boundaries in the present invention are as follows:

[0030] ① When performing iterative solution for the skin heat conduction, the mass and energy conservation equations of the water film need to be calculated at each iteration step, and the external net heat flux MD of the flow field and the water droplet field 10 is loaded onto the outer surface of the skin and used as the second-kind boundary condition of the outer surface of the skin. At the same time, the heat transfer coefficient MD on the inner surface of the skin 20 is set as the third-kind boundary condition of the inner surface of the skin.

[0031] ② The internal and external heat transfer coupling calculation unit 30 of the present invention adopts a loose coupling calculation method.

[0032] ③ The established mass conservation equation and energy conservation equation for the anti-icing surface utilize the fact that the mass flow rate of water flowing into the control volume is equal to the mass flow rate of water flowing out of the control volume. Description of the Drawings

[0033] Figure 1 is the flow chart of the method for calculating the surface temperature of the three-dimensional hot-gas anti-icing system considering periodic boundaries in the present invention.

[0034] Figure 2 is the schematic diagram for calculating the surface temperature of the hot-gas anti-icing system.

[0035] Figure 2A is the structural block diagram for calculating the surface temperature of the hot-gas anti-icing system.

[0036] Figure 3 is the heat flux flow direction diagram of the anti-icing surface.

[0037] Figure 4 is the schematic diagram of the mass and energy conservation of the control volume of the anti-icing surface.

[0038] Figure 5 is the schematic diagram of the surface overflow water boundary.

[0039] Figure 6 is the schematic diagram of the periodic overflow water boundary condition.

[0040] Figure 7 is the grid division diagram of the anti-icing area.

[0041] Figure 8 is the two-dimensional curve graph of the surface temperature; among which (a) is the two-dimensional curve graph of the surface temperature at position 1; (b) is the two-dimensional curve graph of the surface temperature at position 2.

[0042] Figure 9 It is a two-dimensional curve graph of the overflow water result; among which, (a) is the two-dimensional curve graph of the overflow water result at position 1; (b) is the two-dimensional curve graph of the overflow water result at position 2.

[0043] Figure 10 It is a contour map of the surface temperature distribution under wet anti-icing conditions; among which, (a) is the boundary map without adding periodic overflow water; (b) is the boundary map with adding periodic overflow water.

[0044] Figure 11 It is the surface temperature distribution map at position 1.

[0045] Figure 12 It is the overflow water distribution at position 1.

[0046] Figure 13 It is the surface temperature distribution map at position 2.

[0047] Figure 14 It is the overflow water distribution at position 2. Specific implementation manners

[0048] The present invention will be further described in detail below in conjunction with the drawings and embodiments.

[0049] In the present invention, as shown in Figure 1 、 2 、 Figure 2A The hot gas anti-icing surface temperature monitoring system is composed of an external flow field and water droplet field calculation unit 10, an internal anti-icing cavity flow and heat transfer calculation unit 20, and an internal and external heat transfer coupling calculation unit 30.

[0050] The calculation process is as follows: First, calculate the external flow field and water droplet field of the wing, and export the external net heat flux MD of the flow field and water droplet field for backup; then calculate the hot gas flow and heat transfer inside the anti-icing cavity to obtain the heat transfer coefficient MD 10 on the inner surface of the skin and export it for backup; then perform iterative solution for the skin heat conduction. During each iterative step, it is necessary to calculate the water film mass and energy conservation equations, and load the said MD 20 onto the outer surface of the skin and use it as the second type boundary condition of the outer surface of the skin. At the same time, set the said MD 10 as the third type boundary condition of the inner surface of the skin. Finally, during the iterative process of the skin heat conduction calculation, the inner and outer boundary values of the skin are also constantly changing and updating. Until the heat conduction calculation converges and the boundary basically no longer changes, it is considered that the internal and external heat transfer coupling calculation of the hot gas anti-icing surface temperature in the internal and external heat transfer coupling calculation unit 30 reaches convergence. The specific calculation flow is shown in 20 Figure 1 . In the present invention, the internal and external heat transfer coupling calculation unit 30 adopts a loose coupling calculation method.

[0051] Figure 1 See Figure 1The heat transfer loose coupling calculation of the internal and external heat transfer coupling calculation unit 30 shown includes the hot gas anti-icing surface heat flux term and the mass and energy conservation equations of the anti-icing surface.

[0052] (1) Hot gas anti-icing surface heat flux term

[0053] In the present invention, the hot gas anti-icing surface heat flux term includes the convective heat transfer heat flux density, the evaporative heat dissipation heat flux density, and the heat flux density required to heat the water, as Figure 2 , Figure 2A , Figure 3 shown.

[0054] The main idea of the internal and external coupling calculation of the skin is to add heat flux boundary conditions on the inner and outer surfaces of the skin respectively, and then calculate the balance of skin heat conduction. First, the water film flow and heat transfer state on the anti-icing surface need to be considered. The heat flux term on the outer surface of the anti-icing system is as Figure 3 shown, where the heat dissipation heat flux includes the convective heat transfer heat flux density, the evaporative heat dissipation heat flux density, and the heat flux density required to heat the collected water; the heating heat flux includes the heat flux density converted from the kinetic energy of water droplets and the aerodynamic heating heat flux density. Secondly, it is the hot gas heating heat flux inside the anti-icing system.

[0055] Convective heat transfer heat flux density

[0056] When the outside air flows around the wing wall surface, due to the temperature difference, convective heat transfer will occur; at the same time, when the gas stagnates on the wing surface, the gas kinetic energy becomes heat energy, and there is an aerodynamic heating heat flux. In heat transfer, convective heat transfer and aerodynamic heating are generally considered together. The convective heat transfer calculation formula is as follows:

[0057]

[0058]

[0059] is the convective heat transfer.

[0060] h s is the convective heat transfer coefficient.

[0061] T s is the wall temperature.

[0062] T rec is the recovery temperature.

[0063] T ∞ is the oncoming flow temperature.

[0064] r is the specific heat ratio, with a value of 1.4.

[0065] Ma is the Mach number.

[0066] Evaporative heat dissipation heat flux density

[0067] When the air flow passes over the wet surface, due to the surface temperature T s being higher than the temperature T e at the outer boundary of the boundary layer, the concentration of water vapor in the air layer close to the wet surface is higher than the concentration of water vapor in the air at the boundary of the boundary layer. This causes the water molecules to diffuse from the higher concentration to the lower concentration, forming the mass and energy exchange between the hot and wet surface and the external air flow.

[0068] The calculation formula for evaporation heat dissipation is as follows:

[0069]

[0070]

[0071]

[0072] is the evaporation heat dissipation energy.

[0073] is the evaporation mass flux density.

[0074] i lv is the latent heat of vaporization of water.

[0075] h s is the convective heat transfer coefficient.

[0076] c p，air is the specific heat capacity of air.

[0077] Pr is the Prandtl number.

[0078] Sc is the Schmidt number, and its physical meaning is the ratio of momentum diffusion to mass diffusion.

[0079] M v is the molecular mass of water vapor.

[0080] M air is the molecular mass of air.

[0081] p v，sat (T w ) is the saturation vapor pressure at the local overflow water temperature.

[0082] p v,e is the local water vapor pressure at the outer boundary of the boundary layer.

[0083] P e is the total air pressure at the outer boundary of the attachment layer.

[0084] v is the kinematic viscosity of air.

[0085] μ is the dynamic viscosity of air.

[0086] D is the diffusion coefficient.

[0087] ρ is the density of air.

[0088] In the present invention, the calculation of the evaporative cooling and the evaporative mass transfer on the object surface adopts the heat and mass transfer analogy, that is, the Chilton-Colburn analogy theory, and the mass flow rate of the evaporative mass transfer is calculated by formula (4).

[0089] In the present invention, the saturated water vapor pressure can be obtained from the following calculation formula:

[0090]

[0091] T is the surface temperature of the wing, with the unit of K.

[0092] According to the Dalton partial pressure principle, the water vapor partial pressure at the outer boundary of the boundary layer is calculated as follows:

[0093]

[0094] p v,e is the local water vapor pressure at the outer boundary of the attachment layer.

[0095] P e is the total air pressure at the outer boundary of the boundary layer.

[0096] p v,sat (T ∞ ) is the saturated vapor pressure at the oncoming flow temperature.

[0097] ρ ∞ is the relative humidity of the air.

[0098] is the far-field relative humidity, with a value of 1.

[0099] The heat flux density required to heat the water

[0100] The water hitting the wall surface is heated from the far-field ambient temperature to the anti-icing surface temperature, and the heat flux density required to heat the water is calculated as follows:

[0101]

[0102]

[0103] is the heat flux density required to heat the water.

[0104] is the flux density of the mass of the impinging water.

[0105] c p，w is the specific heat of water.

[0106] T s is the wall temperature.

[0107] T ∞ is the incoming flow temperature.

[0108] U ∞ is the incoming flow velocity.

[0109] LWC is the liquid water content.

[0110] β is the local collection coefficient of water droplets.

[0111] A is the impact area.

[0112] Heat flux density converted from the kinetic energy of water droplets

[0113] In the present invention, the heat flux density converted from the kinetic energy of water droplets is calculated as follows:

[0114]

[0115] is the heat flux density converted from the kinetic energy of water droplets.

[0116] is the mass flow rate of the impacting water.

[0117] U ∞ is the incoming flow velocity.

[0118] (II) Construct the mass conservation equation for the anti-icing surface;

[0119] For any control volume on the anti-icing surface, the mass flow rate of water flowing into the control volume is equal to the mass flow rate of water flowing out of the control volume. Considering the control volume of the anti-icing surface as shown in Figure 4 the following is the establishment of its mass conservation equation for the anti-icing surface:

[0120]

[0121] is the mass flow rate of water flowing into the control volume, with the unit of kg / s.

[0122] is the flux density of the mass of the impacting water.

[0123] Δs is the area of the control volume on the anti-icing surface.

[0124] is the evaporation mass flux density.

[0125] is the mass flow rate of water flowing out of the control volume, with the unit of kg / s.

[0126] is the flux density of the icing mass.

[0127] When the hot gas anti-icing surface temperature monitoring system is working, due to the heating effect, the surface temperature is generally higher than 273.15K, and overflow water is formed on the surface. That is, when When is lower than or equal to 273.15K, there may be overflow icing.

[0128] (3) Construct the energy conservation equation of the anti-icing surface;

[0129] According to the law of conservation of energy, the energy conservation equation of the anti-icing surface can be obtained:

[0130]

[0131] is the heat flux density converted from the kinetic energy of water droplets.

[0132] is the energy of the overflow water flowing into the control volume area.

[0133] is the heat flux of the skin conduction, which is balanced with the net heat flux outside the skin.

[0134] is the heat released by icing.

[0135] is the heat flux of the ice cooling and releasing heat.

[0136] is the convective heat transfer.

[0137] is the energy of evaporation heat dissipation.

[0138] is the heat flux density required to heat the collected water.

[0139] is the energy of the overflow water flowing out of the control volume area.

[0140] Periodic overflow water boundary condition

[0141] Considering the limitation of computing resources, the anti-icing area of the present invention is a section of wing length intercepted along the span direction of the wing, as shown in Figure 5 . In the traditional internal and external coupling calculation process of the anti-icing system, the influence of the overflow water at both sides of the span direction of the anti-icing cavity on the anti-icing state is ignored. It is considered that at the boundary of the anti-icing area, only overflow water is allowed to flow out, and no overflow water flows in, resulting in Figure 5The overflow water inflow at the left boundary shown is abnormal. Most airliner wings are swept-back wings, and the leading edge of the wing is not perpendicular to the oncoming flow direction. Under the action of aerodynamic force, Figure 5 overflow water will flow into the left boundary in the middle, and overflow water will flow out of the right boundary. Previous calculations ignored the inflow of overflow water at the left boundary, which does not conform to the actual situation.

[0142] In order to consider the influence of the overflow water in the upstream anti-icing area on the calculation results, when the span length of the anti-icing area is not too long, it can be assumed that the change of the overflow water in the span direction is not large. Therefore, the outflow value of the overflow water in the downstream anti-icing area is taken and assigned to the inflow value of the overflow water in the upstream anti-icing area, that is, the parameter of the size of the overflow water is processed periodically, which is called the periodic overflow water boundary condition. The schematic diagram is shown in Figure 6 . The influence of the periodic overflow water boundary condition on the anti-icing state will be discussed in detail below.

[0143] The anti-icing area calculation model is shown in Figure 7 , and a hexahedral structured grid is used for division, with a total of 162,000 grid cells. The outer surface of the skin is a heat flux boundary condition, and its value is updated in real time with the change of the surface temperature. The inner surface of the skin is set with a convective heat transfer boundary condition, and the remaining walls are all adiabatic walls. The surface temperatures of the anti-icing systems with and without considering the periodic overflow water boundary are calculated respectively. Figure 7 Position 1 in the middle is located in the impact area and is also directly opposite the jet hole, so the surface temperature is relatively high; position 2 is located in the overflow water area, and the surface temperature is relatively low. Positions 1 and 2 will be used for subsequent comparison and analysis of the anti-icing condition results.

[0144] Through the coupled heat transfer calculation inside and outside the anti-icing cavity, the distribution of the outer surface temperature of the skin, heat load, overflow water flow rate, etc. at the state point can be obtained, and the performance of the anti-icing system can be evaluated.

[0145] A. Dry-state anti-icing state simulation

[0146] Under the dry-state anti-icing condition, the droplets will completely evaporate in the impact area. The specific calculation conditions are: environmental temperature -4.7 °C, wing angle of attack 4.8°, flight speed 118.1 m / s, water droplet equivalent diameter 20 μm, liquid water content 0.54 g / m 3 .

[0147] The comparison of the surface temperature results with and without adding the periodic overflow water boundary condition is shown in Figure 8 . It can be found from the figure that adding or not adding the periodic overflow water boundary condition has little influence on both the impact area and the overflow area. Analyzing the reason, in the case of dry-state anti-icing, the impact water basically completely evaporates in the impact area, and almost no overflow water flows to the rear of the wing. As Figure 9 shown, the overflow water at positions 1 and 2 is zero, so the anti-icing surface temperatures in the two cases are very close.

[0148] B, wet anti-icing state simulation

[0149] Under wet anti-icing conditions, the droplets will not completely evaporate in the impact area, and some overflow water will flow backward or even outside the anti-icing area. The specific calculation conditions are: ambient temperature -12.7℃, wing attack angle 1.1°, flight speed 200.8m / s, droplet equivalent diameter 22μm, liquid water content 0.37g / m 3 .

[0150] The effect of adding periodic overflow water boundary conditions on the anti-icing surface temperature can be seen in Figure 10 , after considering the periodic overflow water boundary condition, the surface temperature in the overflow water area is significantly reduced (in the black circle in the figure). Because in the case of wet anti-icing, there is a lot of overflow water backward in the wing anti-icing area, and the evaporation of the overflow water will take away a lot of heat, causing the skin surface temperature to drop significantly. In order to intuitively compare the surface temperature distribution under the two calculation conditions, the surface temperature distribution and overflow water distribution at position 1 and position 2 are compared respectively.

[0151] Surface temperature and overflow water distribution at position 1 are shown in Figure 11 and Figure 12 .Depend on Figure 12 From the overflow water distribution, it can be seen that when the periodic overflow water boundary condition is not added, the overflow water inflow at the left boundary is zero, and there is overflow water outflow at the right boundary; after adding the periodic boundary condition, the overflow water inflow at the left boundary is equal to the overflow water outflow value at the right boundary, that is, the overflow water inflow at the left boundary increases the total overflow water volume on the skin surface, so the overall overflow water volume after adding the periodic overflow water boundary condition in the figure is greater than that without adding it. Figure 11 It can be noticed that the surface temperature difference between the two cases at position 1 is not much. This is because when the environment and bleed air parameters are the same, the amount of water that can be evaporated by the anti-icing cavity heating is not much different, that is, the external heat load is not much different, so the surface equilibrium temperature is basically the same, but the surface overflow water will be relatively larger after adding the periodic boundary.

[0152] Surface temperature and overflow water distribution at position 2 are shown in Figure 13 and Figure 14 .Depend on Figure 13 It can be seen that at position 2, the surface temperature obtained by considering the periodic overflow water boundary is quite different. After adding the periodic overflow water boundary condition, the upper surface temperature is reduced by 20K. Figure 14 It can be seen that when the periodic overflow water boundary condition is not added, there is no overflow water at position 2 on the skin surface, which means that all the overflow water has completely evaporated before reaching position 2; after adding the periodic overflow water boundary condition, it can be seen from the above analysis that the total overflow water amount of the skin will increase, and the overflow water at position 2 has not completely evaporated, and some overflow water still exists, which reduces the local surface temperature.

[0153] In summary, the calculation method with a periodic overflow water boundary is more consistent with the actual situation, so the result will be closer to the reality.

[0154] The present invention is a method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering a periodic boundary, aiming at the technical problem that the setting of the surface overflow water boundary condition in previous calculations is unreasonable and inconsistent with the actual situation. This method calculates by setting a periodic overflow water boundary condition and analyzes the result to illustrate the rationality of the result. The conclusion is drawn that the periodic overflow water boundary condition has little influence on the dry anti-icing working condition, but has a greater influence on the wet anti-icing working condition, and the surface temperature in the upper surface overflow water area is significantly reduced. The periodic overflow water boundary condition can effectively improve the inflow of the overflow water at the upstream boundary, be more in line with the actual situation, so the surface temperature result will be more consistent with the reality. Thus, the technical effects of improving the calculation speed and accuracy of the surface temperature of the aircraft wing anti-icing system are achieved.

Claims

1. A method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries, characterized in that: Step 1, calculate the external flow field of the wing and the water droplet field, and export the external net heat flux MD of the flow field and the water droplet field for backup; 10 ​ Step 2: Calculate the heat transfer of the hot air flow inside the anti-icing cavity to obtain the heat transfer coefficient MD on the inner surface of the skin 20 And export it for backup; Step 3, applying the MD in the hot gas anti-icing surface temperature monitoring system 10 and the MD 20 Complete the internal and external heat transfer coupling calculation of the hot gas anti-icing surface temperature; apply the MD 10 to the outer surface of the skin and use it as the second type of boundary condition for the outer surface of the skin; set the MD 20 as the third type of boundary condition for the inner surface of the skin; The internal and external heat transfer coupling calculation of the hot gas anti-icing surface temperature carried out in step three includes the following sub-steps; Step 31, calculate the convective heat transfer flux density as: is convective heat transfer; h s is the convective heat transfer coefficient; T s is the wall temperature; T rec is for restoring the temperature; T ∞ is the incoming flow temperature; r is the specific heat ratio; Ma is the Mach number; Step 32, calculate the evaporative heat dissipation flux density as: is the energy for evaporative heat dissipation; is the evaporation mass flux density; i lv is the latent heat of evaporation of water; c p，air is the specific heat capacity of air; P r is the Prandtl number; Sc is the Schmidt number, and its physical meaning is the ratio of momentum diffusion to mass diffusion; M v is the molecular mass of water vapor; M air is the molecular mass of air; p v，sat (T w ) is the saturated vapor pressure at the local overflow water temperature; p v,e is the local water vapor pressure at the outer boundary of the boundary layer; according to Dalton's law of partial pressures, the p v,sat (T ∞ ) is the saturated vapor pressure at the inlet flow temperature; ρ ∞ is the relative humidity of air; is the far-field relative humidity; P e is the total pressure of air at the outer boundary of the boundary layer; v is the kinematic viscosity of air; μ is the dynamic viscosity of air; D is the diffusion coefficient; ρ is the density of air; Step 33, calculate the saturated water vapor pressure as: T is the surface temperature of the wing, in units of K; Step 34, calculate the heat flux density required to heat water as: The heat flux density required to heat water; is the flux density of the mass of the impinging water; c p，w is the specific heat of water; U ∞ is the oncoming flow velocity; LWC is the liquid water content; β is the local water droplet collection coefficient; A is the impact area; Step 35, calculate the heat flux density converted from the kinetic energy of water droplets as: The heat flux density converted from the kinetic energy of water droplets; is the mass flow rate of the impinging water; Step 36, calculate the mass conservation on the anti-icing surface as: is the mass flow rate of the water flowing in for controlling the volume, in kg / s; is the flux density of the mass of the impinging water; Δs is the area of the control volume on the anti-icing surface; is the evaporation mass flux density; is the mass flow rate of the water flowing out for controlling the volume, in kg / s; is the flux density of the icing mass; Step 37, calculate the energy conservation on the anti-icing surface as: According to the law of conservation of energy, the energy conservation equation of the anti-icing surface can be obtained: is the energy of the overflow water flowing into Δs; is the skin conduction heat flux, which is in balance with the net heat flux outside the skin; Heat released by icing; Heat flow for cooling ice by heat release; is convective heat transfer; is the energy for evaporative heat dissipation; is the energy of the overflow water flowing out by Δs; Step 38, in the iterative process of skin heat conduction calculation, the internal and external boundary values of the skin are also constantly changing and updating. Until the heat conduction calculation converges and the boundary no longer changes, it is considered that the internal and external heat transfer coupling calculation of the hot gas anti-icing surface temperature reaches convergence.

2. The method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries according to claim 1, characterized in that: Iteratively solve the skin heat conduction, and during each iteration step, it is necessary to calculate the water film mass and energy conservation equations.

3. The method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries according to claim 1 or 2, characterized in that: When the hot gas anti-icing surface temperature monitoring system is working, due to the heating effect, the surface temperature is higher than 273.15K, and overflow water is formed on the surface, that is, set When is lower than or equal to 273.15K, there may be overflow icing.

4. The method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries according to claim 1 or 2, characterized in that: The anti-icing area refers to a section of wing length intercepted along the span direction of the wing.

5. The method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries according to claim 4, characterized in that: The anti-icing area is divided into multiple grid cells by structured grids of hexahedrons.

6. The method for calculating the surface temperature of a three-dimensional hot gas anti-icing system considering periodic boundaries according to claim 1 or 2, characterized in that: It is applicable to the wings of passenger aircraft.

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