Three-dimensional icing numerical simulation method considering influence of water film overflow and grid area

Abstract

The invention relates to a three-dimensional icing numerical simulation method considering water film overflow and grid area influence, which comprises the following steps: setting a criterion and a distribution mode of overflow water flow in a grid, and determining the actual outflow water quantity and the final icing quantity of each edge of the grid; calculating the icing height of each grid according to the final icing amount of each grid; determining the icing height at each common point based on the icing height of each grid; according to the area and the wall surface normal of each grid, determining the icing growth direction at each common point; and determining coordinates of each grid after icing according to the icing height and the wall surface unit normal vector at each common point. According to the invention, the icing process of the airplane can be simulated more accurately, the icing ice shape more conforming to the experiment is obtained, and the appearance of the airplane after icing is obtained under the condition that the cost is greatly reduced.

Description

Technical Field

[0001] The present application relates to the field of aircraft flight safety, and in particular, to a three-dimensional icing numerical simulation method that considers the effects of water film overflow and grid area. Background Art

[0002] Icing is a major threat to aircraft flight safety, with numerous aircraft accidents caused by icing each year. Accurate prediction of aircraft icing plays a crucial role. Currently, there are three main methods for studying aircraft icing: flight testing, wind tunnel testing, and numerical simulation. Flight testing involves simulating icing conditions during actual flight, either by artificially creating the desired icing environment or by flying an aircraft through clouds with icing conditions. Due to the unpredictability of the natural environment, flight testing may carry certain risks, but the results are the most reliable. Icing wind tunnels are essential ground-based testing equipment for studying aircraft icing characteristics and verifying the performance of anti-icing and de-icing systems. They not only accurately simulate icing weather conditions but also simulate high-altitude flight parameters, making them a crucial method for studying aircraft icing. Compared to flight testing, icing wind tunnel testing is less expensive, more feasible, and has shorter test cycles. However, due to the size limitations of icing wind tunnels, the research object often needs to be scaled down. Numerical simulation technology has experienced rapid development with the continuous improvement of computer performance. Compared with other methods, numerical simulation has the advantages of short research cycle, cost savings and easy implementation. In most cases, it can quickly and accurately reflect the actual freezing trend. Through mutual verification with freezing experiments, it helps to deeply understand the freezing process and freezing mechanism.

[0003] Several mature numerical simulation software packages for icing have been developed, but their specific implementation methods and detailed technical details are often difficult for users to understand. Currently, the main difficulties in three-dimensional icing lie in the distribution of overflow water and the reconstruction of ice shapes. Distributing water within the control unit and calculating the growth direction and thickness of ice at grid nodes are pressing issues to be addressed. Summary of the Invention

[0004] In order to overcome at least one deficiency in the prior art, the present application provides a three-dimensional icing numerical simulation method that takes into account the effects of water film overflow and grid area.

[0005] In a first aspect, a three-dimensional icing numerical simulation method is provided that considers the effects of water film overflow and grid area, including:

[0006] Step 1: Determine the air flow field and water droplet impact characteristics of the target area on the aircraft surface. The air flow field includes air pressure, air temperature, and air velocity; the water droplet impact characteristics include water volume and water droplet distribution.

[0007] Step 2: Divide the target area into N grids and determine the number of cycles.

[0008] Step 3: In the current cycle, assume that the icing state of each grid is clear ice. Calculate the water droplet evaporation amount of each grid according to the air flow field, and determine the water droplet impact amount of each grid according to the water droplet impact characteristics.

[0009] Based on the water droplet evaporation amount, water droplet impact amount, and inflow amount of each grid, calculate the assumed icing amount and assumed outflow amount of each grid based on the energy conservation equation and mass conservation equation.

[0010] Calculate the freezing coefficient f of each grid according to the assumed icing amount, inflow amount, and water droplet impact amount.

[0011] If the current cycle is the first cycle, the inflow amount of each grid is 0.

[0012] Step 4: For any grid, if 0 < f < 1, the grid contains ice-water mixture. Calculate the actual outflow amount of each side of the grid according to the assumed outflow amount; the assumed icing amount is used as the actual icing amount of the grid.

[0013] For any grid, if f ≥ 1, all the water in the grid freezes; the actual outflow amount of each side of the grid is 0; the actual icing amount of the grid is the sum of the water droplet impact amount and the inflow amount.

[0014] For any grid, if f ≤ 0, the grid is not iced; calculate the actual outflow amount of each side of the grid according to the assumed outflow amount; the actual icing amount of the grid is 0.

[0015] Step 5: Update the inflow amount of each grid according to the actual outflow amount of each side of each grid, return to Step 3, and perform the next cycle until the cycle termination condition is reached to obtain the final icing amount of each grid.

[0016] Step 6: Calculate the icing height of each grid according to the final icing amount of each grid; determine the icing height at each common point based on the icing height of each grid; determine the icing growth direction at each common point according to the area and wall normal of each grid; determine the coordinates of each grid after icing according to the icing height and wall unit normal vector at each common point.

[0017] Step 7: Based on the coordinates of each grid after icing, realize the reconstruction of the ice shape through the Fluent dynamic mesh function.

[0018] In one embodiment, the freezing coefficient f of each grid is calculated using the following formula:

[0019] [[ID=3​ is the assumed amount of ice, is the water drop impact volume, The inflow water volume.

[0021] In one embodiment, in step 4, calculating the actual outflow of water of each edge of the grid based on the assumed outflow of water includes:

[0022] Calculate the dot product of the air velocity and the normal vector of each edge;

[0023] Determine whether water flows out of each edge based on the dot product result;

[0024] Calculate the angle between the air velocity and the normal vector of each edge;

[0025] If there is only one edge with water outflow, the actual outflow of this edge is equal to the assumed outflow; if there are two edges with water outflow, the actual outflow of each edge is determined according to the following formula:

[0026]

[0027]

[0028] in, and are the actual outflow of water from the first and second edges, θ1 is the angle between the air velocity and the normal vector of the first edge, and θ2 is the angle between the air velocity and the normal vector of the second edge. is the assumed outflow volume.

[0029] In one embodiment, determining whether water flows out of each edge according to the dot product result includes:

[0030] If the dot product result is greater than 0, water flows out of the edge corresponding to the dot product result; otherwise, no water flows out of the edge corresponding to the dot product result.

[0031] In one embodiment, in step 6, the ice height at each common point is determined based on the ice height of each grid, using the following formula:

[0032]

[0033] Among them, h ice,node is the ice height at the common point, h i is the ice height of the i-th grid around the common point, A i is the area of ​​the i-th grid around the common point, and n is the number of grids around the common point.

[0034] In one embodiment, in step 6, the ice growth direction at each common point is determined based on the area of ​​each grid and the wall normal, using the following formula:

[0035]

[0036] in, is the ice growth direction at the common point, A i is the area of ​​the i-th grid around the common point, n is the number of grids around the common point, is the wall normal of the i-th grid around the common point.

[0037] In one embodiment, in step 6, the coordinates of each grid after freezing are determined based on the ice height at each common point and the wall unit normal vector using the following formula:

[0038] x′=x+h ice,node ·n node,x

[0039] y′=y+h ice,node ·n node,y

[0040] z′=z+h ice,node ·n node,z

[0041] Among them, (x, y, z) is the coordinate of the grid around the common point, (x′, y′, z′) is the coordinate of the grid with coordinates (x, y, z) around the common point after freezing, and h ice,node is the ice height at the common point, n node,x 、n node,y 、n node,z The ice growth direction at the common point The coordinates along the x, y, and z axes respectively.

[0042] In the second aspect, a three-dimensional icing numerical simulation device that takes into account the influence of water film overflow and grid area is provided, which is used to implement the above-mentioned three-dimensional icing numerical simulation method that takes into account the influence of water film overflow and grid area.

[0043] In a third aspect, a computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, it realizes the above-mentioned three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area.

[0044] In a fourth aspect, a computer program product is provided, comprising a computer program / instruction, which, when executed by a processor, implements the above-mentioned three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area.

[0045] Compared with the existing technology, the present application has the following beneficial effects: the present application sets the criteria and distribution method for the overflow water flow within the grid, and performs weighted calculation of the ice height and ice growth direction at the node according to the grid area, which can more accurately simulate the aircraft icing process, obtain the ice shape that is more consistent with the experiment, and obtain the appearance of the aircraft after iced while greatly reducing the cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present application may be better understood by referring to the following description in conjunction with the accompanying drawings, which together with the following detailed description are incorporated into and form a part of this specification. In the drawings:

[0047] Figure 1 The flowchart of the three-dimensional icing numerical simulation method considering the effects of water film overflow and grid area is shown;

[0048] Figure 2 A mass balance diagram of the grid is shown;

[0049] Figure 3 An energy balance diagram of the grid is shown;

[0050] Figure 4 Shows the adjacent grid map of the current grid;

[0051] Figure 5 Shows the air velocity and the normal vector of each edge Angle diagram of

[0052] Figure 6 A schematic diagram of the mesh and its wall normal around the common point is shown;

[0053] Figure 7 The ice shape of working condition 1 is shown;

[0054] Figure 8 The ice shape of working condition 2 is shown;

[0055] Figure 9 The ice shape of working condition 3 is shown;

[0056] Figure 10 The ice shape of working condition 4 is shown;

[0057] Figure 11 The ice shape of working condition 5 is shown;

[0058] Figure 12 The ice shape for Case 6 is shown. DETAILED DESCRIPTION

[0059] Exemplary embodiments of the present application are described below with reference to the accompanying drawings. For the sake of clarity and conciseness, not all features of actual embodiments are described in this specification. However, it should be understood that in the process of developing any such actual embodiment, many implementation-specific decisions may be made to achieve the developer's specific goals, and these decisions may vary from one implementation to another.

[0060] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, the accompanying drawings only show the device structure closely related to the solution according to the present application, while other details that are not closely related to the present application are omitted.

[0061] It should be understood that the present application is not limited to the described embodiments due to the following description with reference to the accompanying drawings. In this document, where feasible, the embodiments may be combined with each other, features between different embodiments may be replaced or borrowed, and one or more features may be omitted in one embodiment.

[0062] The present invention provides a three-dimensional icing numerical simulation method that takes into account the influence of water film overflow and grid area. Figure 1 The flow chart of the three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area is shown in Figure 1 , methods include:

[0063] Step 1: Determine the air flow field and water droplet impact characteristics of the target area on the aircraft surface. The air flow field includes air pressure, air temperature and air speed; the water droplet impact characteristics include water volume and water droplet distribution state.

[0064] The Euler method is used to calculate the impact characteristics of water droplets. This method is a computational method for air-water droplet two-phase flow, developed based on field theory. Compared to the Lagrangian method, the Euler method focuses on the changes in the mass and momentum of supercooled water droplets within the control volume. The Euler method treats water droplets as a continuous phase and introduces a droplet volume fraction to represent the proportion of supercooled water droplets in the air-water droplet two-phase flow field. By solving the droplet phase governing equations, the impact force and distribution of water droplets on the surface of the object are determined.

[0065] Step 2: Divide the target area into N grids and determine the number of loops. Here, Fluent can be used for grid division. The grids are triangular, each grid has three edges, the internal surface has three adjacent grids, and the boundary surface has two adjacent grids.

[0066] Step 3: In the current loop, assume that the frozen state of each grid is clear ice, that is, the equilibrium temperature of the grid after freezing is equal to 273.15K. Calculate the water droplet evaporation amount of each grid based on the air flow field, and determine the water droplet impact amount of each grid based on the water droplet impact characteristics;

[0067] According to the water drop evaporation amount, water drop impact amount and water inflow amount of each grid, based on the energy conservation equation and mass conservation equation, the hypothetical ice amount and hypothetical water outflow amount of each grid are calculated; Figure 2 A mass balance diagram of the grid is shown; Figure 3 An energy balance diagram of the grid is shown;

[0068] The mass conservation equation is:

[0069]

[0070] The energy conservation equation is:

[0071]

[0072] in, is the assumed amount of ice, is the water drop impact volume, is the inflow water volume, is the assumed outflow volume, is the amount of water droplet evaporation. For the inflow of energy, is the water drop impact energy, The energy released for freezing, In order to prevent ice heat flow, the wall is usually insulated during ice calculation. The energy taken away by the evaporation of water droplets, To outflow energy, The energy carried away by the heat is exchanged for convection.

[0073] Since there is a conversion relationship between mass and energy, the two equations above can be used to solve the assumed ice volume and the assumed water outflow volume.

[0074] Calculate the freezing coefficient f of each grid based on the assumed amount of ice, inflow water and water drop impact;

[0075] Specifically,

[0076]

[0077] in, is the assumed amount of ice, is the water drop impact volume, The inflow water volume.

[0078] If the current cycle is the first cycle, the water inflow into each grid is 0.

[0079] Step 4. For any grid, if 0 < f < 1, the assumption in Step 3 holds, the grid contains ice-water mixture, and the actual water outflow of each side of the grid is calculated according to the assumed water outflow; the assumed ice formation amount is used as the actual ice formation amount of the grid.

[0080] For any grid, if f ≥ 1, all the water in the grid freezes; the actual water outflow of each side of the grid is 0; the actual ice formation amount of the grid is the sum of the water droplet impact amount and the inflow amount.

[0081] For any grid, if f ≤ 0, the grid is not frozen; the actual water outflow of each side of the grid is calculated according to the assumed water outflow; the actual ice formation amount of the grid is 0.

[0082] Step 5. Update the inflow amount of each grid according to the actual water outflow of each side of each grid, return to Step 3, and perform the next cycle until the cycle termination condition is reached, and the final ice formation amount of each grid is obtained.

[0083] Here, after obtaining the actual water outflow of each side of the grid in Step 4, it is equivalent to determining the inflow amount flowing into other grids from each side. For any grid, calculate the sum of the actual inflow amounts of all sides as the inflow amount of the grid in the next cycle.

[0084] The cycle termination condition can be, for example, reaching the set number of cycles, or the error between the ice formation amount of the grid obtained in the current cycle and the ice formation amount of the grid in the previous cycle is less than the set value.

[0085] Step 6. Calculate the ice formation height of each grid according to the final ice formation amount of each grid; determine the ice formation height at each common point based on the ice formation height of each grid; determine the ice growth direction at each common point according to the area of each grid and the wall normal; determine the coordinates of each grid after icing according to the ice formation height and the wall unit normal vector at each common point.

[0086] Step 7. Based on the coordinates of each grid after icing, the reconstruction of the ice shape is realized through the Fluent dynamic mesh function.

[0087] In this embodiment, the criterion and distribution method for the overflow water flow in the grid are set, the actual water outflow of each side of the grid and the final ice formation amount are determined; the ice formation height and ice growth direction at the nodes are weighted and calculated according to the grid area, which can more accurately simulate the aircraft icing process, obtain an ice shape more consistent with the experiment, and obtain the external shape of the aircraft after icing with greatly reduced costs.

[0088] In one embodiment, in Step 4, calculating the actual water outflow of each side of the grid according to the assumed water outflow includes: <00First, calculate the air velocity The dot product with the normal vector of each edge; here, the air speed refers to the air speed of the first layer of mesh close to the ice surface; the positive direction of the normal vector of each edge points to the outside of the mesh. Figure 4 Shows the neighboring grids of the current grid.

[0090] Then, determine whether water flows out of each edge based on the dot product result;

[0091] Specifically, if the dot product result is greater than 0, water flows out of the edge corresponding to the dot product result; otherwise, no water flows out of the edge corresponding to the dot product result.

[0092] Then, calculate the air velocity and the normal vector of each edge The angle between Figure 5 Shows the air velocity and the normal vector of each edge Angle diagram.

[0093] Then, if there is only one edge with water outflow, the actual outflow of this edge is equal to the assumed outflow; if there are two edges with water outflow, the actual outflow of each edge is determined according to the following formula:

[0094]

[0095]

[0096] in, and are the actual outflow of water from the first and second edges, θ1 is the angle between the air velocity and the normal vector of the first edge, and θ2 is the angle between the air velocity and the normal vector of the second edge. is the assumed outflow volume.

[0097] In this embodiment, a criterion for the flow direction of water droplets within a grid and a specific distribution method are provided. The smaller the angle between the air velocity and the normal vector of the grid edge, the more water flows out from this edge.

[0098] In one embodiment, in step 6, the ice height at each common point is determined based on the ice height of each grid, using the following formula:

[0099]

[0100] Among them, h ice,node is the ice height at the common point, h i is the ice height of the i-th grid around the common point, A i is the area of ​​the i-th grid around the common point, and n is the number of grids around the common point. Here, in, is the amount of freezing, Δt is the freezing time, ρ ice is the density of ice.

[0101] In step 6, the ice growth direction at each common point is determined based on the area of ​​each grid and the wall normal, using the following formula:

[0102]

[0103] in, is the ice growth direction at the common point, A i is the area of ​​the i-th grid around the common point, n is the number of grids around the common point, is the wall normal of the i-th grid around the common point, where it is assumed that ice grows along the wall normal. Figure 6 A schematic diagram of the mesh and its wall normals around the common point is shown.

[0104] In step 6, the coordinates of each grid after freezing are determined based on the ice height at each common point and the wall unit normal vector using the following formula:

[0105] x′=x+h ice,node ·n node,x

[0106] y′=y+h ice,node ·n node,y

[0107] z′=z+h ice,node ·n node,z

[0108] Among them, (x, y, z) is the coordinate of the grid around the common point, (x′, y′, z′) is the coordinate of the grid with coordinates (x, y, z) around the common point after freezing, and h ice,node is the ice height at the common point, n node,x 、n node,y 、n node,z The ice growth direction at the common point The coordinates along the x, y, and z axes are respectively expressed in a Cartesian coordinate system.

[0109] In this embodiment, the ice growth takes into account the influence of the grid area. The larger the grid area, the greater the influence of the grid on the ice growth.

[0110] In order to further verify the effectiveness of the method of this application, the following experimental analysis was carried out.

[0111] The icing conditions of the three-dimensional straight-wing NACA0012 airfoil and the swept-wing MS-317 airfoil under different incoming flow conditions were calculated and compared with the experimental results and LEWICE calculation results. The working conditions are shown in Table 1.

[0112] Table 1

[0113]

[0114] Figure 7 The ice shape of working condition 1 is shown; Figure 8 The ice shape of working condition 2 is shown; Figure 9 The ice shape of working condition 3 is shown; Figure 10 The ice shape of working condition 4 is shown; Figure 11 The ice shape of working condition 5 is shown; Figure 12 The ice shape for Case 6 is shown.

[0115] Comparison shows that the upper and lower icing limits calculated by this application are consistent with the experimental ice shape, the ice angle positions are also relatively close, and the calculated maximum icing thickness is better than the LEWICE result. The main difference is that the icing value on the lower surface of the airfoil is relatively large, and some water overflows to the lower surface, which deviates from the experimental results. Overall, the calculation results of this application can well reflect the trend of water droplet overflow and the maximum icing thickness. The simulation accuracy is higher at lower temperatures. The simulation of clear ice needs to be improved in terms of icing limits, but the calculation method is relatively effective.

[0116] An embodiment of the present application also provides a three-dimensional icing numerical simulation device that takes into account the influence of water film overflow and grid area, which is used to implement the three-dimensional icing numerical simulation method that takes into account the influence of water film overflow and grid area in the above embodiment.

[0117] The three-dimensional icing numerical simulation device considering the influence of water film overflow and grid area in this embodiment has the same inventive concept as the three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area mentioned above. Therefore, the specific implementation method of the device can be seen in the embodiment part of the three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area mentioned above, and its technical effect corresponds to the technical effect of the above method, which will not be repeated here.

[0118] An embodiment of the present application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the above-mentioned three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area.

[0119] An embodiment of the present application provides a computer program product, including a computer program / instruction. When the computer program / instruction is executed by a processor, it implements the above-mentioned three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area.

[0120] The above descriptions are merely examples of various embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any modifications or substitutions that can be readily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included within the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area, characterized in that: Comprising: Step 1, determining the air flow field and water droplet impact characteristics of the target area on the aircraft surface, where the air flow field includes air pressure, air temperature, and air velocity; The water droplet impact characteristics include water quantity and water droplet distribution state; Step 2, dividing the target area into N grids and determining the number of cycles; Step 3, in the current cycle, assuming the icing state of each grid is clear ice, calculating the water droplet evaporation amount of each grid according to the air flow field, and determining the water droplet impact amount of each grid according to the water droplet impact characteristics; Based on the water droplet evaporation amount, water droplet impact amount, and inflow water amount of each grid, calculating the assumed icing amount and assumed outflow water amount of each grid based on the energy conservation equation and mass conservation equation; Calculating the freezing coefficient f of each grid according to the assumed icing amount, the inflow water amount, and the water droplet impact amount; If the current cycle is the first cycle, the inflow water amount of each grid is 0; Step 4, for any grid, if 0 < f < 1, the grid is in an ice-water mixture state, and calculating the actual outflow water amount of each side of the grid according to the assumed outflow water amount; the assumed icing amount is used as the actual icing amount of the grid; For any grid, if f ≥ 1, all the water in the grid freezes; the actual outflow water amount of each side of the grid is 0; the actual icing amount of the grid is the sum of the water droplet impact amount and the inflow water amount; For any grid, if f ≤ 0, the grid is not iced; Calculating the actual outflow water amount of each side of the grid according to the assumed outflow water amount; the actual icing amount of the grid is 0; Step 5, updating the inflow water amount of each grid according to the actual outflow water amount of each side of each grid, returning to Step 3 for the next cycle until the cycle termination condition is reached, and obtaining the final icing amount of each grid; Step 6, calculating the icing height of each grid according to the final icing amount of each grid; Determining the icing height at each common point based on the icing height of each grid; determining the icing growth direction at each common point according to the area of each grid and the wall normal; determining the coordinates of each grid after icing according to the icing height and wall unit normal vector at each common point; Step 7, based on the coordinates of each grid after icing, realizing the reconstruction of the ice shape through the Fluent dynamic mesh function.

2. The method according to claim 1, wherein The freezing coefficient f of each grid is calculated using the following formula: in, is the assumed amount of ice, is the water drop impact volume, The inflow water volume.

3. The method according to claim 1, wherein In Step 4, calculating the actual outflow water amount of each side of the grid according to the assumed outflow water amount includes: Calculating the dot product of the air velocity and the normal vector of each side; Determining whether there is water outflow from each side according to the dot product result; Calculating the angle between the air velocity and the normal vector of each side; If there is only one side with water outflow, the actual outflow water amount of this side is equal to the assumed outflow water amount; if there are two sides with water outflow, determining the actual outflow water amount of each side according to the following formula: in, and are the actual outflow of water from the first and second edges, θ1 is the angle between the air velocity and the normal vector of the first edge, and θ2 is the angle between the air velocity and the normal vector of the second edge. is the assumed outflow volume.

4. The method according to claim 3, wherein Where, Determining whether there is water outflow from each side according to the dot product result includes: If the dot product result is greater than 0, the side corresponding to the dot product result has water outflow, otherwise, the side corresponding to the dot product result has no water outflow.

5. The method according to claim 1, wherein In Step 6, determining the icing height at each common point based on the icing height of each grid uses the following formula: Among them, h ice,node is the ice height at the common point, h i is the ice height of the i-th grid around the common point, A i is the area of ​​the i-th grid around the common point, and n is the number of grids around the common point.

6. The method according to claim 1, wherein In step 6, the ice growth direction at each common point is determined based on the area of ​​each grid and the wall normal, using the following formula: in, is the ice growth direction at the common point, A i is the area of ​​the i-th grid around the common point, n is the number of grids around the common point, is the wall normal of the i-th grid around the common point.

7. The method according to claim 1, wherein In step 6, the coordinates of each grid after freezing are determined based on the ice height at each common point and the wall unit normal vector, using the following formula: x′=x+h ice,node ·n node,x y′=y+h ice,node ·n node,y z′=z+h ice,node ·n node,z Among them, (x, y, z) are the coordinates of the grid around the common point, (x ′ ,y ′ ,z ′ ) is the coordinate of the grid with coordinates (x, y, z) around the common point after freezing, h ice,node is the ice height at the common point, n node,x 、n node,y 、n node,z The ice growth direction at the common point The coordinates along the x, y, and z axes respectively.

8. A three-dimensional icing numerical simulation device considering the influence of water film overflow and grid area, characterized in that: A three-dimensional icing numerical simulation method considering the effects of water film overflow and grid area is used to implement any one of claims 1-7.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area as described in any one of claims 1 to 7.

10. A computer program product, characterized in that The invention comprises a computer program / instruction, which, when executed by a processor, implements the three-dimensional icing numerical simulation method considering the influence of water film overflow and grid area as described in any one of claims 1 to 7.

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