An aero-engine water film thickness prediction method and system based on liquid film motion law

Abstract

The application belongs to the technical field of aero-engine in-wing cleaning, and discloses a water film thickness prediction method and system for aero-engine based on liquid film motion law. The method establishes a two-dimensional velocity profile equation of the water film along the blade; a liquid drop collection efficiency model is constructed; the gas-liquid interface shear force is calculated by using the interface friction coefficient; and a relationship curve of the water film thickness relative to the water-gas ratio and the airflow velocity is obtained according to the volume flow of the water film on the blade surface and the gas-liquid interface shear force; wherein the relationship curve of the water film thickness relative to the water-gas ratio and the airflow velocity is used to predict the water film thickness of the aero-engine in-wing cleaning, and then the process parameters of the aero-engine in-wing cleaning are adjusted. The prediction result of the application is in good agreement with the experimental data, and the relative error is 20%. The root mean square error of the model is 11.6%, and the average absolute percentage error is 9.15%.

Description

Technical Field

[0001] This invention belongs to the field of on-wing cleaning technology for aero-engines, and particularly relates to a method and system for predicting the thickness of water film in aero-engines based on the law of liquid film motion. Background Technology

[0002] During operation, aircraft engines inevitably accumulate scale on the compressor blades, leading to performance degradation and affecting reliability. During cold starts, atomized cleaning fluid is injected into the engine's internal ducts via nozzles to perform on-wing cleaning, effectively removing scale particles from the blade surfaces and restoring engine performance. The atomized droplets impacting the blade surface undergo droplet spreading, splashing, diffusion, and film formation; the thickness of this water film determines the effectiveness of on-wing cleaning. Therefore, understanding and accurately monitoring the changes in blade water film thickness is crucial for accurately predicting on-wing cleaning effectiveness and optimizing cleaning parameters.

[0003] The flow of cleaning fluid inside the compressor is highly complex. Droplets undergo movement and breakup under the influence of airflow, a phenomenon exacerbated by increased airflow pressure. Due to aerodynamic shear forces, droplets deposited on the blade surface form thin films, streams, or discrete droplets. While domestic and international scholars have evaluated the thickness and motion of the water film on the blade surface through simulation and experiments, a relationship between cleaning parameters and water film thickness has not yet been established, and an accurate model for effectively predicting the water film thickness on the blade surface is lacking. Poor on-wing cleaning performance for aero-engines negatively impacts their operational safety. Summary of the Invention

[0004] To overcome the problems existing in related technologies, the present invention discloses an embodiment of a method and system for predicting the water film thickness of an aero-engine based on the liquid film motion law.

[0005] The technical solution is as follows: A method for predicting the thickness of water film in an aero-engine based on the motion law of liquid film, the method comprising the following steps:

[0006] S1. Based on the boundary conditions of no slip on the wall and continuous shear force at the gas-liquid interface, a two-dimensional velocity profile equation for the water film along the blade is established.

[0007] S2. Based on the aerodynamic efficiency and deposition efficiency between the droplets that collide with the air mist and the blade surface, a droplet collection efficiency model is constructed.

[0008] S3, calculate the gas-liquid interface shear force using the interfacial friction coefficient;

[0009] S4. During the wing cleaning process of aero-engines, a volumetric flow rate model of water film on the blade surface is constructed based on the interaction between airflow velocity, impact blade area, and cleaning fluid flow rate and the processes of cleaning fluid droplet deposition, growth, aggregation, and shedding on the blade surface.

[0010] S5. Based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface, the relationship curve between the water film thickness and the water-air ratio and the airflow velocity is obtained. The relationship curve between the water film thickness and the water-air ratio and the airflow velocity is used to predict the water film thickness of the on-wing cleaning of the aero-engine, and then adjust the on-wing cleaning process parameters of the aero-engine.

[0011] In step S1, the two-dimensional velocity profile equation of the water film along the blade is established, and the expression is:

[0012]

[0013] In the formula, The water film is distributed along the tangential velocity. Represents the direction of the tangent. Represents the direction of the normal. The pressure inside the water film, The density of water, This is the tangential component of gravitational acceleration. The viscosity of the water film. For water film thickness, This refers to the shear force at the gas-liquid interface.

[0014] In step S2, a droplet collection efficiency model is constructed, with the following expression:

[0015]

[0016] In the formula, For droplet collection efficiency model, For aerodynamic efficiency. For deposition efficiency.

[0017] Furthermore, aerodynamic efficiency The fraction of droplets in the air mist that may collide with the blade surface depends on the blade pressure loss coefficient and drag coefficient; aerodynamic efficiency. The expression is:

[0018]

[0019] In the formula, This is the leaf shading coefficient. This is the blade pressure loss coefficient. This is the drag coefficient; , The area of ​​the leaf shadow. The total area of ​​the blade cascade passage; when the inlet Mach number of the blade cascade is less than 0.3, the blade pressure loss coefficient. Drag coefficient , The inlet airflow angle of the blade. The average airflow angle of the blades;

[0020] In an air-water mist stream, droplets are driven by airflow. When the air encounters the blades, it is deflected, and the droplets are deposited onto the blade surface due to inertia. The deposition efficiency is high. It is a Stokes function, and the formula is:

[0021]

[0022]

[0023] In the formula, For Stokes numbers, The density of water, Where is the droplet diameter, For airflow velocity, air viscosity, The characteristic width of the impact blade surface. For deposition efficiency.

[0024] In step S3, the gas-liquid interface shear force is calculated, including:

[0025] Ignoring the gas-liquid interface fluctuation velocity, the gas-liquid interface shear force is represented by the interfacial friction coefficient, and the expression is:

[0026]

[0027] In the formula, Indicates the interface shearing factor. Indicates air density, The coefficient of interfacial friction, air viscosity;

[0028] The interfacial shear factor is equal to the wall friction coefficient of the turbulent boundary layer. The calculation formula is:

[0029]

[0030] In the formula, For interface shearing factor, The friction coefficient of the turbulent boundary layer wall. The airflow Reynolds number; , For airflow velocity, For characteristic length, Equal to the height of the cascade test section, The viscosity is the viscosity of air motion.

[0031] In step S4, a water film volumetric flow rate model for the blade surface is constructed, including:

[0032] During the wing cleaning process of an aero-engine, the deposition, growth, aggregation, and detachment of cleaning droplets on the blade surface are related to airflow velocity, impact area of ​​the blade, and cleaning fluid flow rate. Based on the interaction mechanism between droplets and the blade surface, the volumetric flow rate model of the water film on the blade surface is expressed as:

[0033]

[0034] In the formula, This refers to the volumetric flow rate of the water film on the blade surface. For droplet collection efficiency, For airflow velocity, air density, For water-to-air ratio, This represents the area of ​​the leaf shadow.

[0035] In step S5, based on the water film volumetric flow rate on the blade surface and the gas-liquid interface shear force, the relationship curve between the water film thickness and the water-air ratio and the airflow velocity is obtained, including:

[0036] During the full development stage of the air-water mist flow at the wing of an aero-engine, the tangential change in air pressure is ignored. The formula for calculating the volumetric flow rate of the water film is obtained by integrating the water film velocity along the normal direction:

[0037]

[0038] For water film flowing in a horizontal two-dimensional cross section, the gravitational component The value is zero, which simplifies to obtain the water film thickness model:

[0039]

[0040] In the formula, This refers to the volumetric flow rate of the water film on the blade surface. For water film thickness, The water film is distributed along the tangential velocity. Represents the direction of the normal. The viscosity of the water film. The density of water, This is the tangential component of gravitational acceleration. This refers to the shear force at the gas-liquid interface.

[0041] In step S5, the relationship curve between water film thickness and water-to-air ratio and airflow velocity is used to predict the on-wing cleaning water film thickness of the aero-engine, including:

[0042] Based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface, the relationship curve between the water film thickness and the water-to-air ratio and the airflow velocity was obtained:

[0043]

[0044] In the formula, For droplet collection efficiency, air density, For water-to-air ratio, The characteristic width of the impact blade surface. The airflow Reynolds number, This represents the airflow velocity.

[0045] Another objective of this invention is to provide a water film thickness prediction system for aero-engines based on liquid film motion laws. This system implements the aforementioned water film thickness prediction method for aero-engines based on liquid film motion laws. The system includes:

[0046] The two-dimensional velocity profile equation establishment module is used to establish the two-dimensional velocity profile equation of the water film along the blade.

[0047] The droplet collection efficiency model building module is used to build droplet collection efficiency models;

[0048] The droplet collection efficiency model calculation module is used to calculate the gas-liquid interface shear force;

[0049] The water film volumetric flow rate model building module is used to build a water film volumetric flow rate model on the blade surface;

[0050] The on-wing cleaning process parameter adjustment module for aero-engines is used to obtain the relationship curve between water film thickness and water-air ratio and airflow velocity based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface. The relationship curve between water film thickness and water-air ratio and airflow velocity is used to predict the water film thickness during on-wing cleaning of aero-engines, and then adjust the on-wing cleaning process parameters of aero-engines.

[0051] Furthermore, the system is mounted on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor. When the processor executes the computer program, it implements the function of a method for predicting the water film thickness of an aero-engine based on the laws of liquid film motion.

[0052] Combining all the above technical solutions, the advantages and positive effects of this invention are as follows: This invention establishes a two-dimensional velocity profile equation for the water film along the blade; constructs a droplet collection efficiency model; calculates the gas-liquid interface shear force; constructs a water film volumetric flow rate model on the blade surface; and obtains the relationship curve between the water film thickness and the water-air ratio and airflow velocity based on the water film volumetric flow rate and the gas-liquid interface shear force, which is used to predict the water film thickness for on-wing cleaning of aero-engines, thereby adjusting the on-wing cleaning process parameters of aero-engines. Based on the relationship between the water film thickness and the water-air ratio and airflow velocity, the water film thickness under different water-air ratios and airflow velocities is predicted by the water film thickness model, and compared with the experimentally measured water film thickness. The model's prediction results are in good agreement with the experimental data, with a relative error of 20%. The root mean square error of the model is 11.6%, and the mean absolute percentage error is 9.15%. The relationship curve between the water film thickness and the water-air ratio and airflow velocity in this embodiment of the invention can predict the water film thickness well, thereby adjusting the on-wing cleaning process parameters of aero-engines. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure;

[0054] Figure 1 This is a diagram of the method and system for predicting water film thickness in aero-engines based on the motion law of liquid film, provided in an embodiment of the present invention.

[0055] Figure 2 This is a schematic diagram of water film flow during wing cleaning of an aero engine, provided in an embodiment of the present invention.

[0056] Figure 3 This is a schematic diagram of the two-dimensional water film velocity profile provided in an embodiment of the present invention;

[0057] Figure 4 These are curves showing the relationship between airflow velocity and water film thickness under different water film volume flow rates provided in this embodiment of the invention.

[0058] Figure 5 This is a comparison chart of the prediction results and experimental data of the model provided in this embodiment of the invention. Detailed Implementation

[0059] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0060] The innovation of the aero-engine water film thickness prediction method and system based on liquid film motion law provided in this invention is as follows: Based on the liquid film motion law, by considering aerodynamic effects, droplet deposition and growth and gas-liquid interface forces, an aero-engine water film thickness prediction method and system is proposed, which can be used to predict the on-wing cleaning water film thickness of aero-engines, and then adjust the on-wing cleaning process parameters of aero-engines.

[0061] Example 1, such as Figure 1 As shown, the method for predicting the water film thickness of an aero-engine based on the liquid film motion law provided in this embodiment of the invention includes:

[0062] S1. Based on the boundary conditions of no slip on the wall and continuous shear force at the gas-liquid interface, a two-dimensional velocity profile equation for the water film along the blade is established.

[0063] S2. Based on the aerodynamic efficiency and deposition efficiency between the droplets that collide with the air mist and the blade surface, a droplet collection efficiency model is constructed.

[0064] S3, calculate the gas-liquid interface shear force using the interfacial friction coefficient;

[0065] S4. During the wing cleaning process of aero-engines, a volumetric flow rate model of water film on the blade surface is constructed based on the interaction between airflow velocity, impact blade area, and cleaning fluid flow rate and the processes of cleaning fluid droplet deposition, growth, aggregation, and shedding on the blade surface.

[0066] S5. Based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface, the relationship curve between the water film thickness and the water-air ratio and the airflow velocity is obtained. The relationship curve between the water film thickness and the water-air ratio and the airflow velocity is used to predict the water film thickness of the on-wing cleaning of the aero-engine, and then adjust the on-wing cleaning process parameters of the aero-engine.

[0067] During the wing cleaning process of an aero-engine, the compressor blades are exposed to a mist of water vapor. Droplets enter the compressor under the influence of aerodynamic forces; some droplets impact and spread on the blade surface, forming a continuous water film, while the remaining droplets follow the airflow into the next stage blade. For example... Figure 2 As shown. The water film moves under the shear force of the airflow, as... Figure 3 As shown.

[0068] In step S1 of this embodiment of the invention, the two-dimensional velocity profile equation of the water film along the blade is established as follows:

[0069] The two-dimensional incompressible Navier-Stokes equations for a water film can be written as:

[0070] (1)

[0071] (2)

[0072] In the formula, This is the density of water, expressed in kg / m³. 3 ; The tangential velocity distribution of the water film is expressed in m / s. The velocity distribution of the water film along the normal direction is expressed in m / s. This refers to the pressure inside the water film, measured in Pa. The viscosity of water, in units of The components of gravitational acceleration in the tangential and normal directions are: and The unit is m / s 2 .

[0073] The mass balance equation for a two-dimensional steady-state incompressible flow in a water film is:

[0074] (3)

[0075] Water film thickness The size is on the micrometer scale, much smaller than the blade length. The water film moves along the tangential direction of the blade, and its normal velocity is negligible. Therefore, the normal velocity of the water film can be ignored in this invention. According to the law of conservation of mass, it can be derived that... .

[0076] Based on the above assumptions, the equation of motion for the water film can be simplified to:

[0077] (4)

[0078] (5)

[0079] Assuming that surface tension does not play a major role in water film flow, in this case, the gas-liquid interface shear force ( , The shear stress on the water film plays a dominant role. The shear stress within the water film is balanced by the shear force exerted by the airflow. The shear stress within the water film can be expressed as:

[0080] (6)

[0081] Based on the boundary conditions of no slippage on the wall and continuous shear force at the gas-liquid interface, this invention substitutes the above equation into equation (4) and integrates to obtain the velocity distribution within the water film as follows:

[0082]

[0083] In step S2 of this embodiment of the invention, constructing the droplet collection efficiency model includes:

[0084] This invention innovatively proposes that droplet collection efficiency can be expressed as:

[0085] (8)

[0086] In the formula, For droplet collection efficiency model, For aerodynamic efficiency. For deposition efficiency.

[0087] Aerodynamic efficiency represents the fraction of droplets in an air-water mist flow that may collide with the blade surface; it depends on the blade pressure loss coefficient and drag coefficient. This invention innovatively proposes that aerodynamic efficiency be given by the following formula:

[0088] (9)

[0089] In the formula, This is the leaf shading coefficient. This is the blade pressure loss coefficient. This is the drag coefficient; , The area of ​​the leaf shadow. The total area of ​​the blade cascade passage; when the inlet Mach number of the blade cascade is less than 0.3, the blade pressure loss coefficient. Drag coefficient , The inlet airflow angle of the blade. The average airflow angle of the blades;

[0090] In an air-to-water mist stream, droplets are driven by airflow. When the air encounters the blades, it is deflected, but the droplets, due to inertia, will deposit onto the blade surface. The deposition efficiency is a function of Stokes' law, given by the following equation:

[0091] (10)

[0092] (11)

[0093] In the formula, For Stokes numbers, The density of water, Where is the droplet diameter, For airflow velocity, air viscosity, The characteristic width of the impact blade surface. For deposition efficiency.

[0094] In step S3 of this embodiment of the invention, the calculation of the gas-liquid interface shear force is specifically as follows:

[0095] Ignoring the velocity of gas-liquid interface fluctuations, the gas-liquid interface shear force can be represented by the interfacial friction coefficient:

[0096] (12)

[0097] In the formula, Indicates the interface shearing factor. Indicates air density, The coefficient of interfacial friction, air viscosity;

[0098] This invention assumes that the interfacial shear factor is equal to the wall friction coefficient of the turbulent boundary layer. Then its calculation formula is:

[0099]

[0100] In the formula, For interface shearing factor, The friction coefficient of the turbulent boundary layer wall. The airflow Reynolds number; , For airflow velocity, For characteristic length, Equal to the height of the cascade test section, The viscosity is the viscosity of air motion.

[0101] In step S4 of this embodiment of the invention, constructing the volumetric flow rate model of the water film on the blade surface includes:

[0102] During the wing cleaning process of aero-engines, cleaning droplets deposit, grow, converge, and detach on the blade surface. These processes are related to airflow velocity, impact blade area, and cleaning fluid flow rate. Therefore, based on the interaction mechanism between droplets and the blade surface, this invention innovatively proposes a blade surface water film volumetric flow rate model, which can be expressed as:

[0103] (14)

[0104] In the formula, This refers to the volumetric flow rate of the water film on the blade surface. For droplet collection efficiency, For airflow velocity, air density, For water-to-air ratio, This represents the area of ​​the leaf shadow.

[0105] In step S5 of this embodiment of the invention, during the stage when the air-water mist flow is fully developed on the wing of the aero-engine, the change in air pressure along the tangential direction is negligible and can be considered as... Integrating the water film velocity along the normal direction yields the formula for calculating the water film volumetric flow rate:

[0106] (15)

[0107] For water film flowing in a horizontal two-dimensional cross section, the gravitational component If the value is zero, simplifying equation (15) yields the water film thickness model:

[0108] (16)

[0109] In the formula, This refers to the volumetric flow rate of the water film on the blade surface. For water film thickness, The water film is distributed along the tangential velocity. Represents the direction of the normal. The viscosity of the water film. The density of water, This is the tangential component of gravitational acceleration. This refers to the shear force at the gas-liquid interface.

[0110] In step S5 of this embodiment of the invention, the relationship curve between the water film thickness and the water-to-air ratio and the airflow velocity is obtained based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface:

[0111] (17)

[0112] In the formula, For droplet collection efficiency, air density, For water-to-air ratio, The characteristic width of the impact blade surface. The airflow Reynolds number, This refers to the airflow velocity.

[0113] The water film thickness depends on air velocity, gas-liquid ratio, blade shading coefficient, and droplet collection efficiency based on blade profile and Stokes number. For a given compressor blade profile, the blade shading coefficient and droplet collection efficiency based on blade profile and Stokes number are constant; therefore, the water film thickness during wing cleaning is only related to air velocity and gas-liquid ratio. The relationship curve between water film thickness and water-air ratio and airflow velocity can be used to predict the water film thickness during wing cleaning of aero-engines, thereby adjusting the wing cleaning process parameters.

[0114] As demonstrated by the above embodiments, this invention adjusts the on-wing cleaning effect of aero-engines by using the relationship curve between water film thickness and water-air ratio and airflow velocity. For each aircraft, a 1°C increase in EGTM (Enhanced Geological Scale) during on-wing cleaning is expected to save over 10 tons of fuel, resulting in fuel cost savings of 45,000 yuan. Air China's fleet size has reached 902 aircraft; through on-wing cleaning, a 1°C increase in EGTM can save the fleet over 9,000 tons of fuel, resulting in fuel cost savings of 40.59 million yuan. This invention provides a predictive water film thickness model that can effectively predict the relationship between water-air ratio, airflow velocity, and water film thickness, providing a theoretical basis for adjusting on-wing cleaning process parameters for aero-engines.

[0115] Example 2: The aero-engine water film thickness prediction system based on liquid film motion law provided in this embodiment of the invention includes:

[0116] The two-dimensional velocity profile equation establishment module is used to establish the two-dimensional velocity profile equation of the water film along the blade.

[0117] The droplet collection efficiency model building module is used to build droplet collection efficiency models;

[0118] The droplet collection efficiency model calculation module is used to calculate the gas-liquid interface shear force;

[0119] The water film volumetric flow rate model building module is used to build a water film volumetric flow rate model on the blade surface;

[0120] The on-wing cleaning process parameter adjustment module for aero-engines is used to obtain the relationship curve between water film thickness and water-air ratio and airflow velocity based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface. The relationship curve between water film thickness and water-air ratio and airflow velocity is used to predict the water film thickness during on-wing cleaning of aero-engines, and then adjust the on-wing cleaning process parameters of aero-engines.

[0121] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0122] The information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of the present invention. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0123] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments.

[0124] This invention also provides a computer device comprising: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, wherein the processor executes the computer program to implement the steps in any of the above method embodiments.

[0125] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps described in the various method embodiments above.

[0126] This invention also provides an information data processing terminal, which, when executed on an electronic device, provides a user input interface to implement the steps described in the above method embodiments. The information data processing terminal is not limited to mobile phones, computers, or switches.

[0127] This invention also provides a server that, when executed on an electronic device, provides a user input interface to implement the steps described in the above method embodiments.

[0128] This invention provides a computer program product that, when run on an electronic device, enables the electronic device to implement the steps described in the various method embodiments above.

[0129] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a photographing device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0130] To further illustrate the effects of the embodiments of the present invention, the following experiments were conducted: The variation of water film thickness under different water-to-air ratios and airflow velocities was tested using an experimental setup. With the gas velocity remaining constant, different water-to-air ratios were used for each water flow rate configuration. The water film thickness was tested when the airflow velocities were 4.98, 10.05, 14.95, 19.98, 25.03, and 29.98 m / s, and the water flow rates were 2, 3, 4, and 5 L / min. A schematic diagram of the relationship between airflow velocity and water film thickness under different water flow rates is shown below. Figure 4 As shown.

[0131] Based on the relationship between water film thickness and water-to-air ratio and airflow velocity, a water film thickness model was used to predict the water film thickness under different water-to-air ratios and airflow velocities. The predicted results were then compared with experimentally measured water film thicknesses. The model prediction results are as follows: Figure 5 As shown, the model's predictions agree well with the experimental data, with a relative error of 20%. The model's root mean square error is 11.6% and mean absolute percentage error is 9.15%.

[0132] In summary, the relationship curve between water film thickness and water-air ratio and airflow velocity in the embodiments of the present invention can better predict water film thickness, thereby adjusting the on-wing cleaning process parameters of aero-engines.

[0133] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the thickness of water film in an aero-engine based on the motion law of liquid film, characterized in that, The method includes the following steps: S1. Based on the boundary conditions of no slip on the wall and continuous shear force at the gas-liquid interface, a two-dimensional velocity profile equation for the water film along the blade is established. S2. Based on the aerodynamic efficiency and deposition efficiency between the droplets that collide with the air mist and the blade surface, a droplet collection efficiency model is constructed. S3, calculate the gas-liquid interface shear force using the interfacial friction coefficient; S4. During the wing cleaning process of aero-engines, a volumetric flow rate model of water film on the blade surface is constructed based on the interaction between airflow velocity, impact blade area, and cleaning fluid flow rate and the processes of cleaning fluid droplet deposition, growth, aggregation, and shedding on the blade surface. S5. Based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface, the relationship curve between the water film thickness and the water-air ratio and the airflow velocity is obtained. The relationship curve between the water film thickness and the water-air ratio and the airflow velocity is used to predict the water film thickness of the on-wing cleaning of the aero-engine, and then adjust the on-wing cleaning process parameters of the aero-engine. In step S5, based on the water film volumetric flow rate on the blade surface and the gas-liquid interface shear force, the relationship curve between the water film thickness and the water-air ratio and the airflow velocity is obtained, including: During the full development stage of the air-water mist flow at the wing of an aero-engine, the tangential change in air pressure is ignored. The formula for calculating the volumetric flow rate of the water film is obtained by integrating the water film velocity along the normal direction: ； In the formula, The water film is distributed along the tangential velocity. Represents the direction of the normal. For water film thickness, This refers to the shear force at the gas-liquid interface. The viscosity of the water film. The density of water, This is the tangential gravitational acceleration component; For water film flowing in a horizontal two-dimensional cross section, the gravitational component The value is zero, which simplifies to obtain the water film thickness model: ； The relationship curve between water film thickness and water-to-air ratio and airflow velocity is used to predict the on-wing cleaning water film thickness of aero-engines, including: Based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface, the relationship curve between the water film thickness and the water-to-air ratio and the airflow velocity was obtained: ； In the formula, For droplet collection efficiency, air density, For water-to-air ratio, The characteristic width of the impact blade surface. The airflow Reynolds number, This refers to the airflow velocity.

2. The method for predicting water film thickness in aero-engines based on liquid film motion law according to claim 1, characterized in that, In step S1, the two-dimensional velocity profile equation of the water film along the blade is established, and the expression is: ； In the formula, The water film is distributed along the tangential velocity. Represents the direction of the tangent. Represents the direction of the normal. The pressure inside the water film, The density of water, This is the tangential component of gravitational acceleration. The viscosity of the water film. For water film thickness, This refers to the shear force at the gas-liquid interface.

3. The method for predicting water film thickness in aero-engines based on liquid film motion laws according to claim 1, characterized in that, In step S2, a droplet collection efficiency model is constructed, with the following expression: ； In the formula, For droplet collection efficiency model, For aerodynamic efficiency. For deposition efficiency.

4. The method for predicting the water film thickness of an aero-engine based on the liquid film motion law according to claim 3, characterized in that, Aerodynamic efficiency The fraction of droplets in the air mist that may collide with the blade surface depends on the blade pressure loss coefficient and drag coefficient; aerodynamic efficiency. The expression is: ； In the formula, This is the leaf shading coefficient. This is the blade pressure loss coefficient. This is the drag coefficient; , The area of ​​the leaf shadow. The total area of ​​the blade cascade passageway; when the inlet Mach number of the blade cascade is less than 0.3, the blade pressure loss coefficient. ; drag coefficient , The inlet airflow angle of the blade. The average airflow angle of the blades; In an air-water mist stream, droplets are driven by airflow. When the air encounters the blades, it is deflected, and the droplets are deposited onto the blade surface due to inertia. The deposition efficiency is high. It is a Stokes function, and the formula is: ； ； In the formula, For Stokes numbers, The density of water, Where is the droplet diameter, For airflow velocity, air viscosity, The characteristic width of the impact blade surface. For deposition efficiency.

5. The method for predicting the water film thickness of an aero-engine based on the liquid film motion law according to claim 1, characterized in that, In step S3, the gas-liquid interface shear force is calculated, including: Ignoring the gas-liquid interface fluctuation velocity, the gas-liquid interface shear force is represented by the interfacial friction coefficient, and the expression is: ； In the formula, Indicates the interface shearing factor. Indicates air density, The coefficient of interfacial friction, air viscosity; The interfacial shear factor is equal to the wall friction coefficient of the turbulent boundary layer. The calculation formula is: ； In the formula, For interface shearing factor, The friction coefficient of the turbulent boundary layer wall. The airflow Reynolds number; , For airflow velocity, For characteristic length, Equal to the height of the cascade test section, The viscosity is the viscosity of air motion.

6. The method for predicting the water film thickness of an aero-engine based on the liquid film motion law according to claim 1, characterized in that, In step S4, a water film volumetric flow rate model for the blade surface is constructed, including: During the wing cleaning process of an aero-engine, the deposition, growth, aggregation, and detachment of cleaning droplets on the blade surface are related to airflow velocity, impact area of ​​the blade, and cleaning fluid flow rate. Based on the interaction mechanism between droplets and the blade surface, the volumetric flow rate model of the water film on the blade surface is expressed as: ； In the formula, This refers to the volumetric flow rate of the water film on the blade surface. For droplet collection efficiency, For airflow velocity, air density, For water-to-air ratio, This represents the area of ​​the leaf shadow.

7. A system for predicting the thickness of water film in an aero-engine based on the motion law of liquid film, characterized in that, The system implements the method for predicting the water film thickness of an aero-engine based on the liquid film motion law as described in any one of claims 1-6, and the system includes: The two-dimensional velocity profile equation establishment module is used to establish the two-dimensional velocity profile equation of the water film along the blade. The droplet collection efficiency model building module is used to build droplet collection efficiency models; The droplet collection efficiency model calculation module is used to calculate the gas-liquid interface shear force; The water film volumetric flow rate model building module is used to build a water film volumetric flow rate model on the blade surface; The on-wing cleaning process parameter adjustment module for aero-engines is used to obtain the relationship curve between water film thickness and water-air ratio and airflow velocity based on the volumetric flow rate of the water film on the blade surface and the shear force at the gas-liquid interface. The relationship curve between water film thickness and water-air ratio and airflow velocity is used to predict the water film thickness during on-wing cleaning of aero-engines, and then adjust the on-wing cleaning process parameters of aero-engines.

8. The aero-engine water film thickness prediction system based on liquid film motion law according to claim 7, characterized in that, The system is mounted on a computer device, which includes at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor. When the processor executes the computer program, it implements the function of a method for predicting the water film thickness of an aero-engine based on the laws of liquid film motion.

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