Method for determining volume evolution model of Newtonian fluid liquid film under action of shear airflow

Abstract

The invention relates to the technical field of fluid mechanics, and discloses a method for determining a volume evolution model of a Newtonian fluid liquid film under the action of shear airflow, and the method comprises the following steps: determining the thickness of the liquid film; determining an equilibrium equation based on set conditions; determining an expression of shear force of the liquid film surface according to the liquid film thickness and the liquid film surface speed; determining an expression of shearing force of the shearing airflow to the liquid film; substituting the two expressions into an equilibrium equation to obtain a liquid film surface velocity equation; determining a liquid membrane continuity equation and a liquid membrane internal velocity equation; substituting the liquid film internal velocity equation and the liquid film surface velocity equation into a liquid film continuity equation to solve the time evolution process of the liquid film, and obtaining differential equations of liquid film volume evolution under the action of uniformly accelerated shear airflow and uniform shear airflow, so as to construct a model; the model has high accuracy for the volume evolution rule of the Newtonian fluid membrane.

Description

Technical Field

[0001] This invention relates to the field of fluid mechanics, and in particular to a method for determining a Newtonian fluid liquid film volume evolution model under shear airflow. Background Technology

[0002] Liquid film flow under shear airflow is a crucial physical process in applications such as aircraft / engine icing, aircraft de-icing, and surface cleaning. Driven by shear forces, the liquid film flows along the surface, generating complex phenomena such as surface waves, film rupture, and splashing. The underlying physical mechanisms are not yet fully understood. Volume change of the liquid film is key to measuring its flow velocity and is fundamental to understanding the flow process. However, due to the surface waves caused by shear airflow, the flow process is too complex to be quantified. Furthermore, limitations in measurement technology hinder real-time, non-contact measurement of liquid film volume, and the evolution of liquid film volume in Newtonian fluids remains unclear. Summary of the Invention

[0003] The purpose of this invention is to provide a method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow. By applying digital projection technology, a quantitative measurement experiment of the volume of a Newtonian fluid liquid film under shear airflow is carried out. At the same time, a volume evolution model of a Newtonian fluid liquid film under shear airflow that can be used for engineering applications is established. By analyzing experimental data and combining theoretical analysis, the liquid film volume evolution model is obtained.

[0004] To achieve the above objectives, the following technical solution is adopted:

[0005] This invention provides a method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow, thereby determining the liquid film thickness;

[0006] Based on the set conditions, the equilibrium equation is determined; wherein, the set conditions are that the liquid film flows in the form of a uniform liquid film under the action of shear airflow, ignoring the surface waves caused by interface instability, and under the set conditions, the frictional force of the shear airflow on the liquid film should be balanced with the shear force on the surface of the liquid film.

[0007] When the flow velocity type within the liquid film is linear, the expression for the shear force on the liquid film surface is determined based on the liquid film thickness and the liquid film surface velocity.

[0008] When the air above the liquid film is a Blasius boundary layer, determine the expression for the shear force of the shear gas flow on the liquid film;

[0009] Substituting the expressions for the shear force on the liquid film surface and the shear force of the shearing airflow on the liquid film into the equilibrium equation, the velocity equation of the liquid film surface is obtained.

[0010] Determine the continuity equation of the liquid film and the velocity equation within the liquid film;

[0011] Substituting the velocity equations inside and on the surface of the liquid film into the continuity equation of the liquid film, the evolution of the liquid film over time is solved, and the differential equation of the volume evolution of the liquid film under uniformly accelerated shear airflow is obtained.

[0012] Based on the differential equation of liquid film volume evolution under the action of accelerated shearing airflow, the differential equation of liquid film volume evolution under the action of uniform shearing airflow is determined when the airflow is accelerated to a preset speed and then kept at a constant speed.

[0013] The differential equations for the evolution of liquid film volume under uniformly accelerated shear airflow and the differential equations for the evolution of liquid film volume under uniform shear airflow are combined side by side to form a Newtonian fluid liquid film volume evolution model under shear airflow.

[0014] Furthermore, the liquid film thickness is determined as follows:

[0015] When the reference surface is not covered by a liquid film, a target pattern is projected onto the reference plane by a projector, and the target pattern projected onto the reference plane is recorded by a camera. Any point in the projector is used as point N to represent the position of the projector, any point in the target pattern is used as point A to represent the position of the target pattern, and any point in the camera is used as point M to represent the position of the camera.

[0016] With the reference surface covered by a liquid film, the target pattern is projected onto the reference plane again by a projector, and the target pattern projected onto the reference plane is recorded by a camera. The position points D and C where the projected light from the projector first contacts the liquid film are determined, and point C is the lateral position point of point D recorded by the camera.

[0017] Based on the similarity between triangles ΔMDN and ΔADC, the relationship between line segment AC and liquid film thickness is determined, and the liquid film thickness is determined based on the relationship.

[0018] Furthermore, based on the similarity between triangles ΔMDN and ΔADC, the relationship between line segment AC and liquid film thickness is determined. The liquid film thickness is then determined based on this relationship, including:

[0019] Based on the similarity between triangle ΔMDN and triangle ΔADC, the first relationship between line segment AC and liquid film thickness is expressed as:

[0020]

[0021] in, Let AC be the length of line segment AC. Let be the length of line segment BD. Let be the length of line segment MN, and s be the distance from the projection plane to the reference plane. The projection plane is the plane where the projector is located.

[0022] The distance from the projector to the reference plane is much greater than the liquid film thickness. Based on formula (1), the second relationship between line segment AC and liquid film thickness is expressed as:

[0023]

[0024] Where h is the thickness of the liquid film and d is the distance between the camera and the projector.

[0025] Furthermore, based on the given conditions, the determined equilibrium equation is expressed as:

[0026]

[0027] Where, μ a μ l U a U l These represent air viscosity, liquid film viscosity, local air velocity, and local liquid film velocity, respectively; y represents the vertical distance.

[0028] Furthermore, when the flow velocity within the liquid film is linear, the expression for the shear force at the liquid film surface, determined based on the liquid film thickness and surface velocity, is as follows:

[0029]

[0030] Where h is the liquid film thickness, U e The velocity is the surface velocity of the liquid film.

[0031] Furthermore, when the air above the liquid film is a Blasius boundary layer, the expression for the shear force of the shear gas flow on the liquid film is determined as follows:

[0032]

[0033] Where U and f(0) are the free air velocity and the second derivative of the Blasius solution, respectively, and ρ a For air density, μ a denoted as air viscosity, and x as horizontal distance.

[0034] Furthermore, substituting the expressions for the shear force on the liquid film surface and the shear force of the shearing airflow on the liquid film into the equilibrium equation, the resulting liquid film surface velocity equation is expressed as:

[0035]

[0036] Furthermore, the liquid film continuity equation is expressed as:

[0037]

[0038] Among them, U l (x,y,t) is the spatial and temporal evolution function of the flow velocity within the liquid film, h(x,t) is the spatial and temporal evolution function of the liquid film thickness, and t is time;

[0039] The velocity equation within the liquid film is expressed as:

[0040]

[0041] Furthermore, substituting the velocity equations within and on the surface of the liquid film into the liquid film continuity equation to solve for the evolution of the liquid film over time, the differential equation for the volume evolution of the liquid film under uniformly accelerated shear airflow is obtained as follows:

[0042]

[0043] Where, β v ξ is a constant term for uniform airflow acceleration; ξ is the airflow acceleration.

[0044] Furthermore, based on the differential equation for the evolution of liquid film volume under the action of the accelerated shearing airflow, when the airflow is accelerated to a preset speed and then maintained at a constant speed, the differential equation for the evolution of liquid film volume under the action of a constant-speed shearing airflow is determined to be:

[0045]

[0046]

[0047] β c This is a constant term when the airflow velocity is constant.

[0048] The beneficial effects of this invention are reflected in:

[0049] This invention addresses the problem of volume evolution of Newtonian fluid films under shear airflow. By combining experimental research and theoretical analysis, it ultimately derives an experimental correlation for the volume evolution of Newtonian fluid films, which demonstrates high accuracy in understanding the volume evolution law of Newtonian fluid films. Attached Figure Description

[0050] Figure 1 A flowchart is shown below illustrating a method for determining a Newtonian fluid liquid film volume evolution model under shear airflow according to an embodiment of the present invention.

[0051] Figure 2 A flowchart illustrating the determination of liquid film thickness according to an embodiment of the present invention is shown;

[0052] Figure 3 A schematic diagram illustrating the principle of liquid film volume measurement according to an embodiment of the present invention is shown;

[0053] Figure 4 A schematic diagram illustrating the experimental principle of liquid film volume measurement according to an embodiment of the present invention is shown.

[0054] Figure 5 A diagram illustrating the liquid film mechanics analysis under shear gas flow according to an embodiment of the present invention is shown.

[0055] Figure 6 A flowchart illustrating the establishment of correlations for liquid film volume evolution experiments according to an embodiment of the present invention is shown.

[0056] Figure 7 A comparison diagram of the calculation model and experimental results under a wind speed of 10 m / s according to an embodiment of the present invention is shown;

[0057] Figure 8 A comparison diagram of the calculation model and experimental results under a wind speed of 15 m / s according to an embodiment of the present invention is shown;

[0058] Figure 9 A comparison diagram of the calculation model and experimental results under a wind speed of 20 m / s according to an embodiment of the present invention is shown. Detailed Implementation

[0059] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0060] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0061] This invention provides a method for determining a Newtonian fluid liquid film volume evolution model under shear airflow, such as... Figure 1 The diagram shows the overall flowchart of the method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow includes the following steps S10 to S90.

[0062] S10: Determine the liquid film thickness.

[0063] In some embodiments, such as Figure 2 As shown, the liquid film thickness is determined through the following steps S101-S103.

[0064] S101: When the reference surface is not covered by a liquid film, the target pattern is projected onto the reference plane by a projector, and the target pattern projected onto the reference plane is recorded by a camera. Any point in the projector is used as point N representing the position of the projector, any point in the target pattern is used as point A representing the position of the target pattern, and any point in the camera is used as point M representing the position of the camera.

[0065] It should be noted that the target pattern is a known pattern with obvious features to facilitate camera recognition. The camera can use existing target detection algorithms to identify the target pattern, and the geometric center of the target pattern is used as point A to represent its position. Alternatively, other points in the target pattern can be selected as point A. For example, a feature point can be preset in the target pattern for identification, and this feature point can be identified as point A. Point N represents the projector position and can be selected as the projector's geometric center or light output point. Point M represents the camera position and can be selected as the camera's geometric center or image acquisition point. The camera's image acquisition point refers to the location of the image sensor in the camera used to acquire image or video data. The selection of points A, N, and M as described above is merely exemplary and does not constitute a limitation of this application. In other embodiments, other points besides those listed above can be selected to represent the corresponding points, as long as they can represent the corresponding positions.

[0066] S102: With the reference surface covered by a liquid film, the target pattern is projected onto the reference plane again by the projector, and the target pattern projected onto the reference plane is recorded by the camera. The positions D and C where the projected light from the projector first contacts the liquid film are determined. Point C is the lateral position of point D recorded by the camera.

[0067] It should be noted that both point D and point C can be determined using images captured by the camera. Specifically, when the reference surface is covered by a liquid film, the upper boundary of the liquid film and the light emitted by the projector can be determined from the images captured by the camera. The point where the emitted light first contacts the upper boundary is determined as point D. Point C, on the other hand, is the position point used to characterize the target pattern when the reference surface is covered by a liquid film. Its determination method is the same as in step S101. The target pattern can be identified by a target detection algorithm, and any point in the target pattern can be selected for characterization. It should be noted that the method of selecting any point should be the same as the method of selecting point A. For example, the geometric center of the target pattern or a feature point in the target pattern can be selected. Point C is the lateral position point of point D recorded by the camera. Here, it should be understood as the position of the target pattern shifted by the liquid film when the projector projects the target pattern, and the shift begins from point D.

[0068] S103: Based on the similarity between triangles ΔMDN and ΔADC, determine the relationship between line segment AC and liquid film thickness, and determine the liquid film thickness based on the relationship.

[0069] In this embodiment, the surface liquid film thickness is measured using digital projection technology through the above steps S101-S103. The measurement principle is as follows: Figure 3 As shown. Specifically, first, a projector (point N) projects a known pattern with distinct features, i.e., the target pattern (point A), onto a reference surface, and a camera (point M) records the pattern projected onto the surface. After the reference surface is covered by a liquid film, the projector projects the pattern onto the liquid film surface. The projector light is scattered by the liquid film at point D and recorded by a high-precision camera. In camera M, the lateral position of point D is recorded at point C, while the corresponding pattern on the reference plane is at point A. Therefore, due to the presence of the liquid film, point A moves to point C. (Refer to...) Figure 1 Based on the similarity between triangle ΔMDN and triangle ΔADC, we can deduce the first relationship between line segment AC and liquid film thickness as shown in formula (1).

[0070]

[0071] in, Let AC be the length of line segment AC. Let be the length of line segment BD. Let be the length of line segment MN, and s be the distance from the projection plane to the reference plane. The projection plane is the plane where the projector is located.

[0072] Assuming the distance from the projector to the reference plane is much greater than the thickness of the liquid film, the relationship between the liquid film thickness and the length of line segment AC can be written as formula (2), which is the second relationship between line segment AC and liquid film thickness.

[0073]

[0074] Where h is the thickness of the liquid film and d is the distance between the camera and the projector.

[0075] By applying formula (2), the thickness of the liquid film at the corresponding point can be measured under the condition of displacement of the target pattern.

[0076] In one exemplary embodiment, such as Figure 4As shown, the thickness of the liquid film was determined through experiments. The experimental steps are as follows: 1) Place the truncated plate at the bottom of the wind tunnel test section to generate good boundary layer airflow. Use a high-precision projector to project a known pattern onto the reference plane and use a high-precision camera to photograph the projected pattern; 2) Move the plate up or down by a suitable distance and photograph the displacement change of the pattern on the plate. Use a classic binarization algorithm to locate the center position of the pattern and automatically identify the pattern displacement to clarify the linear relationship between height change and pattern displacement, and complete the calibration of digital projection technology; 3) Spread the liquid film evenly on the plate, then project the pattern onto the surface of the liquid film and accelerate the wind tunnel to a set speed. During this period, the high-precision camera continuously photographs the projected pattern; 4) Compare the difference between the pattern on the reference plane and the pattern on the liquid film using a cross-correlation algorithm, calculate the cross-correlation coefficient (R), determine the positions of the two patterns with the highest cross-correlation coefficients, and determine the displacement of the liquid film pattern. This method can automatically determine the displacement of all patterns.

[0077] After obtaining the displacement of the measured pattern, the thickness of the liquid film at the center of the pattern (x) can be determined based on the calibration curve. i The distribution of ), i.e., h(x) i The liquid film volume (V) at the instant of liquid film measurement can be obtained by adding the thickness distributions, as shown in formula (13).

[0078] V = ∑ i h(x i ,t) (13)

[0079] By applying DIP technology, the real-time thickness distribution of the liquid film can be calculated from captured images, thereby determining the evolution of the liquid film volume. Pitot tubes are used to simultaneously measure wind speed, obtaining the airflow acceleration in the wind tunnel, which is then used for theoretical calculations of the liquid film volume evolution process.

[0080] Given a fixed liquid film thickness, the following section will detail the process for establishing experimental correlations for liquid film volume evolution, using liquid film mechanics analysis under shear airflow. The process for establishing experimental correlations for liquid film volume evolution includes the following steps S20-S90.

[0081] S20: Determine the equilibrium equation based on the set conditions; wherein, the set conditions are that the liquid film flows in the form of a uniform liquid film under the action of shear airflow, ignoring the surface waves caused by interface instability, and under the set conditions, the frictional force of the shear airflow on the liquid film should be balanced with the shear force on the surface of the liquid film.

[0082] In this embodiment, as Figure 5As shown, the motion of the liquid film and the airflow is analyzed by force. It is assumed that the liquid film flows in the form of a uniform liquid film under the action of shear airflow, and the surface waves caused by interface instability are ignored. Under this assumption, the frictional force of shear airflow on the liquid film should be balanced with the shear force on the surface of the liquid film. Therefore, the equilibrium equation can be obtained, as shown in formula (3).

[0083]

[0084] Where, μ a μ l U a U l These represent air viscosity, liquid film viscosity, local air velocity, and local liquid film velocity, respectively; y represents the vertical distance.

[0085] S30: When the flow velocity type in the liquid film is linear, determine the expression for the shear force on the surface of the liquid film based on the liquid film thickness and the surface velocity of the liquid film.

[0086] In this embodiment, the liquid film thickness is relatively thin (approximately 1 mm). Therefore, applying the lubricating liquid film theory, the velocity gradient within the liquid film can be considered constant, i.e., the flow velocity type within the liquid film is linear. Thus, the expression for the shear force on the liquid film surface is shown in formula (4).

[0087]

[0088] Where h is the liquid film thickness, U e The velocity is the surface velocity of the liquid film.

[0089] S40: Determine the expression for the shear force of the shear flow on the liquid film when the air above the liquid film is a Blasius boundary layer.

[0090] In this embodiment, it is assumed that the air above the liquid film is a Blasius boundary layer with a known velocity profile. Therefore, the shear force of the shearing airflow on the liquid film can be expressed as formula (5).

[0091]

[0092] Where U and f(0) are the free air velocity and the second derivative of the Blasius solution, respectively, and ρ a For air density, μ l Let be the liquid density, and x be the horizontal distance.

[0093] S50: Substitute the expressions for the shear force on the liquid film surface and the shear force of the shearing airflow on the liquid film into the equilibrium equation to obtain the velocity equation of the liquid film surface.

[0094] In this embodiment, formulas (4) and (5) are substituted into formula (3) to obtain the expression for the surface velocity of the liquid film, i.e., the surface velocity equation of the liquid film, as shown in formula (6).

[0095]

[0096] S60: Determine the liquid film continuity equation and the velocity equation within the liquid film.

[0097] In this embodiment, the liquid film continuity equation can be written as formula (7).

[0098]

[0099] Among them, U l (x,y,t) is the spatial and temporal evolution function of the flow velocity within the liquid film, h(x,t) is the spatial and temporal evolution function of the liquid film thickness, and t is time.

[0100] The velocity within the liquid film is linear, therefore the velocity equation within the liquid film can be written as formula (8).

[0101]

[0102] S70: Substitute the velocity equations inside and on the surface of the liquid film into the continuity equation of the liquid film to solve for the evolution of the liquid film over time, and obtain the differential equation for the volume evolution of the liquid film under uniformly accelerated shearing airflow.

[0103] Substituting the velocity equations (8) inside the liquid film and (6) on the surface of the liquid film into the continuity equation (7) of the liquid film, the evolution of the liquid film over time can be solved, yielding the differential equation for the volume evolution of the liquid film under uniformly accelerated shear airflow, as shown in equation (9). The constant term β... v The constant term for uniform airflow acceleration is expressed in formula (10).

[0104]

[0105] Where ξ is the airflow acceleration.

[0106] S80: Based on the differential equation of liquid film volume evolution under accelerated shearing airflow, the differential equation of liquid film volume evolution under uniform shearing airflow is determined when the airflow is accelerated to a preset speed and then kept at a constant speed.

[0107] If the airflow accelerates to a predetermined speed and then maintains a constant speed, the differential equation for the evolution of the liquid film volume under the action of a uniform shear airflow is shown in equation (11). The constant term β c The constant term is expressed in formula (12) when the airflow velocity is constant.

[0108]

[0109] S90: The differential equations for the volume evolution of the liquid film under uniformly accelerated shear airflow and the differential equations for the volume evolution of the liquid film under uniform shear airflow are combined side by side to form a Newtonian fluid liquid film volume evolution model under shear airflow.

[0110] In formulas (10) and (12), the liquid film viscosity coefficient μ l It can be measured experimentally, but considering that the liquid film surface will generate waves under the action of shearing airflow, increasing the mass transport rate of the liquid film, this is equivalent to reducing μ. l The surface morphology and internal flow of the liquid film are quite complex, making it difficult to establish a theoretical model suitable for engineering applications. Therefore, this patent combines experimental data and theoretical analysis to determine the coefficient μ. l To determine the true volume evolution process of the liquid film.

[0111] Based on the experimental results, μ in the model l The fitting process is described in the flowchart below. Figure 6 As shown. First, the experimental conditions for each group of experiments, such as airflow velocity, temperature, initial liquid film thickness, and liquid film viscosity, are input into the program; the model is used to simulate the liquid film volume evolution process, obtaining the simulated liquid film volume evolution curve; the simulated liquid film volume evolution curve is compared with the experimental liquid film volume evolution curve over time, and the average relative error is calculated; according to the differential equation of liquid film volume evolution theory (Formula 9 or 11), μ is determined to minimize the relative error between the simulated and experimental liquid film volume evolution curves. l， The simulation and experimental results are in good agreement, see Figures 7-9 .

[0112] This embodiment presents an experimental study on a low-viscosity Newtonian fluid with a viscosity of 20 cp, and compares the results with simulation results (see [link]). Figures 7 to 9 The results show that no surface waves are generated on the liquid film surface when the wind speed is 10 m / s. Therefore, this model applies the liquid's intrinsic viscosity (μ). l =20cp) can effectively predict the evolution of liquid film volume. At wind speeds of 15 m / s and 20 m / s, due to the generation of surface waves, the liquid film volume decreases rapidly. Therefore, when μ l When the error is reduced to 12 cp, the simulation results with the smallest error are obtained, all within 8%. This demonstrates that the model constructed in this application has high accuracy in understanding the volume evolution of Newtonian fluid films.

[0113] The above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also fall within the scope of the present invention, and the patent protection scope of the present invention should be defined by the claims.

Claims

1. A method for determining a Newtonian fluid liquid film volume evolution model under shear airflow, characterized in that, include: Determine the liquid film thickness; Based on the set conditions, the equilibrium equation is determined; wherein, the set conditions are that the liquid film flows in the form of a uniform liquid film under the action of shear airflow, ignoring the surface waves caused by interface instability, and under the set conditions, the frictional force of the shear airflow on the liquid film should be balanced with the shear force on the surface of the liquid film. When the flow velocity type within the liquid film is linear, the expression for the shear force on the liquid film surface is determined based on the liquid film thickness and the liquid film surface velocity. When the air above the liquid film is a Blasius boundary layer, determine the expression for the shear force of the shear gas flow on the liquid film; Substituting the expressions for the shear force on the liquid film surface and the shear force of the shearing airflow on the liquid film into the equilibrium equation, the velocity equation of the liquid film surface is obtained. Determine the continuity equation of the liquid film and the velocity equation within the liquid film; Substituting the velocity equations inside and on the surface of the liquid film into the continuity equation of the liquid film, the evolution of the liquid film over time is solved, and the differential equation of the volume evolution of the liquid film under uniformly accelerated shear airflow is obtained. Based on the differential equation of liquid film volume evolution under the action of accelerated shearing airflow, the differential equation of liquid film volume evolution under the action of uniform shearing airflow is determined when the airflow is accelerated to a preset speed and then kept at a constant speed. The differential equations for the evolution of liquid film volume under uniformly accelerated shear airflow and the differential equations for the evolution of liquid film volume under uniform shear airflow are combined side by side to form a Newtonian fluid liquid film volume evolution model under shear airflow.

2. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 1, characterized in that, The liquid film thickness is determined as follows: When the reference surface is not covered by a liquid film, a target pattern is projected onto the reference plane by a projector, and the target pattern projected onto the reference plane is recorded by a camera. Any point in the projector is used as point N to represent the position of the projector, any point in the target pattern is used as point A to represent the position of the target pattern, and any point in the camera is used as point M to represent the position of the camera. With the reference surface covered by a liquid film, the target pattern is projected onto the reference plane again by a projector, and the target pattern projected onto the reference plane is recorded by a camera. The position points D and C where the projected light from the projector first contacts the liquid film are determined, and point C is the lateral position point of point D recorded by the camera. Based on the similarity between triangles ΔMDN and ΔADC, the relationship between line segment AC and liquid film thickness is determined, and the liquid film thickness is determined based on the relationship.

3. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 2, characterized in that, Based on the similarity between triangles ΔMDN and ΔADC, the relationship between line segment AC and liquid film thickness is determined. The liquid film thickness is then determined based on this relationship, including: Based on the similarity between triangle ΔMDN and triangle ΔADC, the first relationship between line segment AC and liquid film thickness is expressed as: in, Let AC be the length of line segment AC. Let be the length of line segment BD. Let be the length of line segment MN, and s be the distance from the projection plane to the reference plane. The projection plane is the plane where the projector is located. The distance from the projector to the reference plane is much greater than the liquid film thickness. Based on formula (1), the second relationship between line segment AC and liquid film thickness is expressed as: Where h is the thickness of the liquid film and d is the distance between the camera and the projector.

4. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow as described in claim 1, characterized in that, Based on the given conditions, the equilibrium equation is expressed as: Where, μ a μ l U a U l These represent air viscosity, liquid film viscosity, local air velocity, and local liquid film velocity, respectively; y represents the vertical distance.

5. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 4, characterized in that, When the flow velocity within the liquid film is linear, the expression for the shear force at the liquid film surface, based on the liquid film thickness and the surface velocity, is as follows: Where h is the liquid film thickness, U e The velocity is the surface velocity of the liquid film.

6. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 5, characterized in that, When the air above the liquid film is a Blasius boundary layer, the expression for the shear force of the shear gas flow on the liquid film is determined as follows: Where U and f(0) are the free air velocity and the second derivative of the Blasius solution, respectively, and ρ a Let be the air density, and x be the horizontal distance.

7. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 6, characterized in that, Substituting the expressions for the shear force on the liquid film surface and the shear force of the shearing airflow on the liquid film into the equilibrium equation, the resulting velocity equation for the liquid film surface is as follows:

8. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 7, characterized in that, The liquid film continuity equation is expressed as: Among them, U l (x,y,t) is the spatial and temporal evolution function of the flow velocity within the liquid film, h(x,t) is the spatial and temporal evolution function of the liquid film thickness, and t is time; The velocity equation within the liquid film is expressed as:

9. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow as described in claim 8, characterized in that, Substituting the velocity equations within and on the surface of the liquid film into the continuity equation of the liquid film, the evolution of the liquid film over time is solved, yielding the differential equation for the volume evolution of the liquid film under uniformly accelerated shear airflow: Where, β v ξ is a constant term for uniform airflow acceleration; ξ is the airflow acceleration.

10. The method for determining the volume evolution model of a Newtonian fluid liquid film under shear airflow according to claim 9, characterized in that, Based on the differential equation of liquid film volume evolution under the action of accelerated shearing airflow, when the airflow is accelerated to a preset speed and then maintained at a constant speed, the differential equation of liquid film volume evolution under the action of uniform shearing airflow is expressed as follows: β c This is a constant term when the airflow velocity is constant.

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