Water drop shielding area and water drop concentration enhancement area simulation method based on Lagrangian method

Abstract

The invention relates to a method for simulating a water drop shielding area and a water drop concentration enhancement area based on a Lagrange method. The method comprises the following steps of: carrying out geometric modeling and grid division on a simulated aircraft part; solving an air flow field according to working conditions; establishing a water drop stress motion equation under a Lagrange framework; water drops are released from a far field at fixed intervals in the direction perpendicular to the incoming flow speed of the airflow; solving the stress motion equation of each water drop on the air flow field, and recording the water drop collection quantity of the space grid; solving motion tracks of all released water drops, traversing all space grids, and calculating a space water drop collection coefficient of each space grid; and distinguishing a water drop shielding area and a water drop concentration enhancing area according to the spatial water drop collection coefficient. The Lagrangian method can accurately track the water drop movement process, the problem that the Euler method cannot accurately simulate the convergence or intersection phenomenon after water drop deflection is solved, and meanwhile, the water drop characteristic space field distribution rule is obtained from the water drop movement track through the definition solution of the space water collection coefficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft icing and anti-icing, and particularly relates to a simulation method for water droplet shielding area and water droplet concentration enhancement area based on the Lagrangian method, which can be used for the selection of installation positions of devices such as aircraft pitot tubes, icing detectors, antennas, etc., as well as the design and power distribution of their anti-icing systems. Background Art

[0002] During the flight of an aircraft, supercooled water droplets in the air hit the aircraft surface and cause icing. Aircraft icing on the windward surface is an important factor endangering flight safety. It can damage the aircraft's aerodynamic shape, affect the aircraft's maneuverability, and even lead to air disasters. As the core component of the aircraft anti-icing system, the icing detection system can effectively reduce flight safety hazards by real-time monitoring of icing signals, automatically triggering anti-icing devices or prompting the crew to manually activate protective measures.

[0003] In the design of the icing detection system, the installation position of the detector directly affects its detection efficiency. Research shows that there are two special regions around the windward surface of the aircraft: one is the water droplet shielding area formed by the separation or circumfluence of the airflow, where the collision rate of liquid water droplets is significantly reduced or even approaches zero; the other is the water droplet concentration enhancement area, where the liquid water content is higher than the environmental average. To ensure that the detection system accurately reflects the icing state of the aircraft, it is necessary to ensure that the icing detector extends out of the water droplet shielding area and the water droplet concentration enhancement area to achieve accurate monitoring and early warning of icing risks.

[0004] In addition, the identification of the water droplet shielding area and the water droplet concentration enhancement area can also be applied to the selection of installation positions of aircraft external accessories. For example, as the core sensor for measuring flight speed, icing on the surface of the pitot tube will cause blockage of the static pressure hole or distortion of the dynamic pressure measurement. Arranging the pitot tube, antenna, etc. in the water droplet shielding area can avoid interference of excessive icing on the measurement accuracy. When there is water droplet impact on the installation positions of devices such as the pitot tube and antenna, the identification of the water droplet shielding area and the water droplet concentration enhancement area is also helpful for the design of the anti-icing systems of these devices. Based on the spatial distribution of the water droplet concentration enhancement area, the distribution of anti-icing power can be optimized, increasing the heating power in the area with a large amount of water droplet impact; reducing the heating power in the water droplet shielding area, reducing energy consumption while ensuring the anti-icing effect.

[0005] The simulation of the water droplet shielding area and the water droplet concentration enhancement area is usually carried out by the Eulerian method. The Eulerian method calculates the local water droplet LWC local or the relative volume fraction α local , and the far-field parameters LWC ∞ or α ∞Comparisons are made to obtain the positions of the two regions. However, the formation of the water droplet shielding region is due to the flow around the air flow field near the component wall surface. Due to their large mass and inertia, the water droplets deviate from the air streamlines, and some of them hit the component surface, while the water droplets that do not hit deviate from the component and move backward, creating a water droplet-free region at the rear of the component. After the water droplets deviate, they may converge and cross paths. Through the analysis of the Lagrangian method and the Eulerian method, it can be seen that the Eulerian method cannot capture the convergence and crossing of the water droplet trajectories. Therefore, there are errors in the Eulerian method when calculating the water droplet shielding region and the water droplet concentration enhancement region. The core idea of the Lagrangian method is to track the motion trajectories of water droplets. Based on the air flow field, with the water droplets as the center, the force and motion equations of the water droplets are established according to Newton's second law. By solving the force and motion equations of the water droplets, the motion trajectories of the water droplets can be obtained, and then it can be determined whether the aircraft component surface is hit and the hitting position. By releasing a large number of particles at different positions, parameters such as the impact limit, total collection coefficient, and local collection coefficient can be obtained. However, only the qualitative analysis of the spatial distribution of water droplet concentration can be carried out based on the density of the water droplet motion trajectories, and it is difficult to accurately and quantitatively determine the specific water droplet shielding region and the water droplet concentration enhancement region. The present invention uses the Lagrangian method to analyze the motion and impact characteristics of water droplets, defines and calculates the spatial water droplet collection coefficient, and thereby distinguishes the water droplet shielding region from the concentration enhancement region. Summary of the Invention

[0006] The present invention proposes a simulation method for the water droplet shielding region and the water droplet concentration enhancement region based on the Lagrangian method.

[0007] There are two types of special regions around the windward surface of the aircraft: one is the water droplet shielding region formed due to air flow separation or flow around, where the collision rate of liquid water droplets is significantly reduced or even approaches zero; the other is the water droplet concentration enhancement region, where the liquid water content is higher than the environmental average. Simulating the water droplet shielding region and the water droplet concentration enhancement region can assist in determining the installation position of the ice detector, optimizing the installation of flight accessories such as the aircraft pitot tube and antenna, and has practical significance for the design and power distribution of the anti-icing system.

[0008] Based on the Lagrangian framework, the present invention proposes a simulation method for the water droplet shielding region and the water droplet concentration enhancement region. The main idea is to define the spatial water droplet collection coefficient to distinguish the water droplet shielding region from the concentration enhancement region. The method includes the following steps:

[0009] (1) Geometrically model the aircraft components used in the simulation, select the calculation region, and perform spatial grid division on the calculation region;

[0010] (2) Combine the operating conditions during flight, select the computational fluid dynamics model and set the air flow field boundary conditions of the calculation region, and solve the steady-state air flow field under the icing meteorological environment;

[0011] (3) Based on the steady-state air flow field, establish the equation of motion of water droplets under the Lagrangian framework;

[0012] (4) In the vertical direction y perpendicular to the air flow velocity direction, release n water droplets from a far-field position away from the surface of the aircraft component at a given spacing dy;

[0013] (5) Initialize the number of water droplets collected in each spatial grid to 0, solve the equation of motion of water droplets for each released water droplet, and whenever 1 water droplet flows through the spatial grid i, the number of water droplets collected in this grid N mes_i increases by 1;

[0014] (6) After solving all the water droplets, traverse all the spatial grids and calculate the spatial water droplet collection coefficient of each spatial grid according to the number of water droplets collected;

[0015] (7) Determine the water droplet shielding area and the water droplet concentration enhancement area according to the spatial water droplet collection coefficient.

[0016] Further, in step (4), set the y values (y 1 , y 2 ) of the far-field position endpoints and the number of water droplets n, and the given spacing is

[0017] Further, in step (6), the spatial water droplet collection coefficient of the spatial grid i is where Δy i is the projection of the spatial grid i in the y direction, that is, the difference between the highest y value and the lowest y value of the current spatial grid, and N mesh_i is the number of water droplets collected in the spatial grid i.

[0018] Further, in step (7), for the spatial grid where no water droplets flow through in the water droplet motion calculation domain, the number of water droplets collected N mesh_i and the spatial water droplet collection coefficient β cell_i are 0, which is the water droplet shielding area; while the area where the spatial water droplet collection coefficient β cell_i is greater than 1 is the water droplet concentration enhancement area.

[0019] Beneficial effects: The Lagrangian method can accurately track the motion process of water droplets, overcome the problem that the Eulerian method cannot accurately simulate the convergence or crossing phenomenon after the deflection of water droplets. At the same time, the definition and solution of the spatial water droplet collection coefficient realize the acquisition of the distribution law of the spatial field of water droplet characteristics from the water droplet motion trajectory, and can more accurately simulate the water droplet shielding area and the water droplet concentration enhancement area. Description of the Drawings

[0020] Figure 1 Schematic diagram of the simulation method flow of the water droplet shielding area and the water droplet concentration enhancement area based on the Lagrangian method.

[0021] Figure 2 NACA0012 and partial view of the grid.

[0022] Figure 3 Schematic diagram of the water droplet release method and parameters.

[0023] Figure 4 Distribution map of the spatial water droplet collection coefficient. Specific implementation manners

[0024] To make the objectives, technical solutions and advantages of the implementation of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific examples described herein are only used to explain the present invention and cannot be construed as limiting the present invention.

[0025] The simulation method for the water droplet shielding area and the water droplet concentration enhancement area based on the Lagrangian method of the present invention includes the following steps:

[0026] (1) Geometrically model the aircraft components used in the simulation, select the calculation area, and perform spatial grid division on the calculation area. For example, geometrically model the NACA0012 airfoil of the aircraft wing, select the space of 20 times the chord length around the airfoil as the calculation area, and perform grid division on the calculation area. Select structured O-type grids, and the divided grids are as Figure 2 shown.

[0027] (2) Combine the working conditions during flight, select a compressible, turbulent computational fluid dynamics model, and load the energy equation; set the air flow field boundary conditions of the calculation area, and set the wall boundary of the airfoil as an isothermal non-slip surface. Based on the computational fluid dynamics method (CFD) and the selected computational fluid dynamics model and boundary conditions, solve the N-S equation and the energy conservation equation to obtain the steady air flow field in the calculation area under the icing meteorological environment, including the air velocity distribution, pressure distribution, and temperature distribution.

[0028] (3) Based on the steady air flow field, establish the equation of motion of water droplets under the Lagrangian framework.

[0029] When selecting the initial velocity and position of the water droplets as input conditions and using the Lagrangian method to establish the water droplet motion trajectory equation, the following assumptions are made:

[0030] (a) The water droplets are spherical. During the movement, they neither coagulate nor decompose, and the water droplet size remains unchanged;

[0031] (b) The volume of the water droplets is very small, and the flow around them will not affect the nature of the flow field, that is, the influence of supercooled water droplets in the air on

[0032] the air flow field is not considered;

[0033] (c) The physical properties of the water droplets, such as temperature, viscosity, density, etc., remain unchanged throughout the process. The motion of the water droplets is determined by the magnitude and direction of the forces acting on them. For water droplets suspended in moving air, the forces acting on them include viscous drag pressure difference force gravity and buoyancy caused by the earth's gravitational force etc. The caused by the pressure gradient is very small and can be ignored; the main force affecting the motion of the water droplets is viscous drag Taking into account the gravity and buoyancy of the water droplets, according to Newton's first law, the equation of motion of the water droplets under force can be obtained:

[0034] That is:

[0035]

[0036] Among them, the mass of the water droplet the windward area of the water droplet C D is the drag coefficient, D is the diameter of the water droplet, V is the volume of the water droplet, is the acceleration due to gravity, ρ a and ρ d represent the density of air and water droplets respectively, and represent the velocity vectors of air and water droplets respectively, and t is the time variable. Divide both sides of the above equation by m d :

[0037]

[0038] Define Re as the Reynolds number with the relative velocity as the characteristic velocity:

[0039]

[0040] Among them, μ a is the dynamic viscosity of air. Substituting Re into it can be changed to:

[0041]

[0042] Define the intermediate variable K A , let

[0043]

[0044] Then the above equation can be rewritten as

[0045]

[0046] (4) In the vertical direction y perpendicular to the air flow velocity direction, release n water droplets from a far-field position away from the surface of the aircraft component at a given spacing dy. The schematic diagram is as shown in Figure 3 . Set the y values (y 1 , y 2 ) of the far-field position endpoints and the number of water droplets n. The given spacing is

[0047] (5) Initialize and set the number of water droplets collected in each spatial grid to 0. Solve the equation of motion of the water droplet under force for each released water droplet. Whenever 1 water droplet flows through spatial grid i, the number of water droplets collected N mes_i in this grid increases by 1.

[0048] Taking the two-dimensional plane water droplet motion as an example, calculate the water droplet motion trajectory using numerical methods. First, transform the equation of motion of the water droplet under force into a difference form

[0049]

[0050] Calculate each water droplet starting from the far-field release position away from the surface of the aircraft component, with the starting coordinates being (x0, y0). The initial conditions for solving the equation of motion of the water droplet under force are: at the starting moment in the far-field position, the water droplet and air velocities are equal, that is, k = 0. At time t0, (u d,x )0 = (u a,x )0, (u d,y )0 = (u a,y )0.

[0051] According to the relationship between displacement and velocity, when t = t k+1 , the water droplet coordinates become

[0052] x k+1 = x k + Δt(u d,x ) k

[0053] y k+1 = y k + Δt(u d,y ) k

[0054] Update the water droplet coordinates (x k+1 , y k+1 ) to determine the grid point where the water droplet is located, and obtain the values of (u a，x ), (u a,y ) k+1 , (u k+1 and at the new position through interpolation calculation of the air flow field results. Solve the difference form of the equation of motion of the water droplet under force to obtain the water droplet velocity (u d,x ) at the new position.k+1 , (u d,y ) k+1 . By this method, the position and velocity of the water droplet are calculated and updated in a loop until the water droplet collides with the surface of the aircraft component or the water droplet moves around the component to the outside of the calculation area, and then the movement trajectory of this water droplet can be obtained.

[0055] Solve the equation of motion of the water droplet under force for each released water droplet to obtain the movement trajectory of this water droplet. The position coordinates of the water droplet particle j at a certain moment are (x j , y j ), within the range of the area of the spatial grid i: If the position coordinates of the water droplet at the previous moment are not within the grid i, then the water droplet collection quantity N mesh_i of this grid is incremented by 1; if the position coordinates of the water droplet at the previous moment are already within the range of this grid area, then N mesh_i remains unchanged.

[0056] (6) Traverse all spatial grids and calculate the spatial water droplet collection coefficient β cell_i , where N mesh_i is the number of water droplets passing through the spatial grid i, that is, the spatial grid water droplet collection quantity, dy is the water droplet release spacing, and Δy i is the projection of the spatial grid i in the y direction, that is, the difference between the highest y value and the lowest y value of the spatial grid y value. The distribution of the obtained spatial water droplet collection coefficient is as Figure 4 shown.

[0057] (7) Judge the water droplet shielding area and the water droplet concentration enhancement area according to the spatial water droplet collection coefficient, as Figure 4 shown, that is, the spatial grid in the water droplet movement calculation domain where no water droplets flow through, and the spatial water droplet collection quantity N mesh_i and the spatial water droplet collection coefficient β cell_i are 0, then it is the water droplet shielding area; and the area where the spatial water droplet collection coefficient β cell_i is greater than 1 is the water droplet concentration enhancement area.

Claims

1. A method for simulating water droplet shielding areas and water droplet concentration enhancement areas based on Lagrangian method, characterized in that: The following steps are involved: (1) Geometric modeling of the aircraft components used in the simulation, selection of the calculation area, and spatial grid division of the calculation area; (2) Based on the flight conditions, the computational fluid dynamics model is selected and the air flow field boundary conditions of the calculation area are set to solve the steady-state air flow field in the icing meteorological environment; (3) Based on the steady-state air flow field, the force motion equation of the water droplet in the Lagrangian framework is established; (4) releasing n water droplets at a given spacing dy from a far-field position away from the surface of the aircraft component in a direction y perpendicular to the air flow velocity direction; (5) Initialize and set the number of water droplets collected in each spatial grid to 0. Solve the force motion equation for each released water drop. Whenever a water drop flows through spatial grid i, the number of water droplets collected in this grid N is mes_i Increase by 1; (6) After all water droplets are solved, all spatial grids are traversed, and the spatial water droplet collection coefficient of each spatial grid is calculated according to the number of water droplets collected; (7) Determine the water droplet shielding area and the water droplet concentration enhancement area based on the spatial water droplet collection coefficient.

2. The method for simulating water droplet shielding area and water droplet concentration enhancement area based on Lagrangian method according to claim 1, characterized in that: In step (4), set the y value of the far-field position endpoint (y 1 ,y 2 ) and the number of water droplets n, the given spacing is 3. The method for simulating water droplet shielding area and water droplet concentration enhancement area based on Lagrangian method according to claim 1, characterized in that: In step (6), the spatial droplet collection coefficient of spatial grid i is where Δy i is the projection of the spatial grid i in the y direction, that is, the difference between the highest y value point and the lowest y value point of the current spatial grid, N mesh_i is the number of water droplets collected in spatial grid i.

4. The method for simulating water droplet shielding area and water droplet concentration enhancement area based on Lagrangian method according to claim 1, characterized in that: Step (7), the spatial grid where no water droplets flow in the water droplet motion calculation domain, the number of water droplets collected N mesh_i and spatial droplet collection coefficient β cell_i is 0, which is the water droplet shielding area; and the spatial water droplet collection coefficient β cell_i The area where the value is greater than 1 is the area where the water droplet concentration is enhanced.

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