A method for simulating flow of a viscoelastic liquid film at moderate reynolds number

Abstract

The application discloses a kind of medium Reynolds number viscoelastic liquid film flow simulation method, based on the control equation of liquid film flow and UCM constitutive equation, carry out dimensionless and simplify, the normal stress and shear stress balance condition of liquid film surface under the action of gravity, gas flow shear force and evaporation effect are deduced, and according to liquid film surface boundary condition and wall no slip boundary condition, on the basis of liquid film velocity expression without gas flow shear force, the expression of liquid film velocity under the action of gas flow shear force and evaporation effect is introduced.The differential equation set that liquid film thickness and flow rate evolve with time and flow direction is derived according to boundary layer integration method, this differential equation set can be used to study the influencing factors of liquid film flow characteristics;Time is dispersed using Runge-Kutta method, and space is dispersed using finite difference format, so that the variation law of liquid film thickness with time and flow direction is obtained, and the influence law of gas flow shear force and evaporation effect on the variation of liquid film thickness is discussed.

Description

Technical Field

[0001] This invention belongs to the field of fluid mechanics technology, and in particular relates to a method for simulating viscoelastic liquid film flow at medium Reynolds number. Background Technology

[0002] Liquid film flow is a widespread phenomenon in daily life, production, and technology, including in the biological field (such as the flow of human tissue fluid) and in industry. It also exists in the field of aircraft thermal protection. For silicon-based materials, which are heat-resistant materials whose primary change is melting and loss, under aerodynamic heating conditions, the solid material melts at a certain temperature, forming a molten state, and then flows under the influence of airflow shear force and gravity.

[0003] Research on liquid film flow began in the 1940s and 50s, with the Kapitza father and son first discovering the phenomenon experimentally and conducting theoretical studies. Since then, this topic has attracted considerable attention from scholars. They have used boundary layer integral methods and long-wavelength theory, based on governing equations, constitutive equations, and boundary conditions, to study Newtonian and viscoelastic liquid film flows. However, these studies have largely been limited to liquid film flows and wave transport driven by gravity. Research on liquid film flows driven by airflow shear forces and evaporation effects has mostly focused on experimental testing. For example, Budakli experimentally studied the flow and heat transfer of liquid films driven by gravity and airflow shear forces. Currently, theoretical and numerical studies on liquid film flows and wave transport influenced by airflow shear forces and evaporation effects are relatively lacking. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for simulating the flow of viscoelastic liquid films with medium Reynolds numbers, which solves the problem that the prior art cannot study the liquid film flow driven by airflow shear force and the influence of evaporation effect.

[0005] To address the aforementioned technical problems, this invention discloses a method for simulating viscoelastic liquid film flow at moderate Reynolds numbers, comprising:

[0006] S1, the parameters are dimensionless to obtain dimensionless parameters;

[0007] S2, for the flow of liquid film over an inclined rigid plate under gravity, airflow shear force and evaporation effect, the corresponding mass equation a, x-momentum equation a, y-momentum equation a, and UCM constitutive equation a describing viscoelastic fluid are given.

[0008] S3 provides the corresponding normal stress equilibrium condition a, shear stress equilibrium condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a under the influence of evaporation effect for the liquid film surface under the action of airflow shear force, gas pressure and evaporation effect.

[0009] S4. Based on dimensionless parameters, the mass equation a, x-momentum equation a, y-momentum equation a, UCM constitutive equation a, normal stress equilibrium condition a, shear stress equilibrium condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a are respectively dimensionlessized to obtain dimensionless mass equation b, x-momentum equation b, y-momentum equation b, UCM constitutive equation b, normal stress equilibrium condition b, shear stress equilibrium condition b, wall no-slip boundary condition b, and liquid film surface motion boundary condition b.

[0010] S5. Scale the capillary number Ca and Reynolds number Re so that the scaled capillary number and Reynolds number are on the order of 1. Substitute the scaled capillary number and Reynolds number into the x-axis momentum equation b, y-axis momentum equation b, normal stress equilibrium condition b, and shear stress equilibrium condition b, respectively. Use order of magnitude analysis to neglect small quantities to obtain the x-axis momentum equation c, y-axis momentum equation c, normal stress equilibrium condition c, and shear stress equilibrium condition c.

[0011] S6. Perform a magnitude analysis on the UCM constitutive equation b, neglecting small quantities, to obtain the UCM constitutive equation c.

[0012] S7, determine the velocity equation within the liquid film that satisfies the shear stress equilibrium condition c;

[0013] S8. Integrate both sides of the mass equation b and the x-direction momentum equation c from 0 to the liquid film thickness, and derive the differential equation system based on the calculus theory according to the wall no-slip boundary condition b, the liquid film surface motion boundary condition b, and the UCM constitutive equation c.

[0014] S9. The Runge-Ku method is used to discretize the differential equation system in the time direction and the differential discretization method is used in the spatial direction. Given the initial conditions of liquid film thickness and flow rate, and applying the wave boundary conditions and steady boundary conditions at the inlet respectively, numerical solutions are obtained to obtain the liquid film thickness and flow rate that vary with time and space.

[0015] S10, change the magnitude of the airflow shear force and evaporation effect in the differential equation system to obtain the calculation results under different airflow shear forces and evaporation effects; compare the calculation results obtained under the same time based on different airflow shear forces and evaporation effects to obtain the influence law of airflow shear force and evaporation effect on liquid film wave transmission, as well as the influence law of airflow shear force and evaporation effect on wave generation.

[0016] In the above simulation method for viscoelastic liquid film flow at medium Reynolds number, the parameters are dimensionlessly processed to obtain dimensionless parameters, including:

[0017] Introduce a small amount ε = h0 / l; where h0 represents the initial liquid film thickness, l represents the typical deformation wavelength of the liquid-gas interface, and ε << 1;

[0018] Introducing velocity to the undisturbed lower liquid layer surface Where ρ represents the density of the fluid in the liquid film, g represents the gravitational acceleration, and μ represents the viscosity at zero shear rate;

[0019] Introduce the Reynolds number Re = ρU0h0 / μ;

[0020] The capillary number Ca = μU0 / γ0 is introduced; where γ0 represents the surface tension coefficient of the liquid film.

[0021] Based on ε, U0, Re, and Ca, the coordinates of the liquid film flow direction x, thickness direction y, liquid film thickness h, and normal stress σ in the x-direction are considered. xx Normal stress σ in the y direction yy , shear stress σ xy airflow shear force τ g Liquid film internal pressure p, external gas pressure p g The velocity of the liquid film along the flow direction (u), the normal velocity of the liquid film (v), time (t), and the airflow velocity (U) g and liquid film surface velocity u s Dimensionless processing is performed to obtain dimensionless parameters:

[0022]

[0023] in, U gg and They are x, y, h, and σ, respectively. xx σ yy σ xy τ g p, p g u, v, t, U g and u s The corresponding dimensionless parameter.

[0024] In the above-mentioned simulation method for viscoelastic liquid film flow at medium Reynolds number,

[0025] The expression for the mass equation a is as follows:

[0026]

[0027] The expression for the x-axis momentum equation a is as follows:

[0028]

[0029] Where θ represents the angle between the direction of liquid film flow and the horizontal direction;

[0030] The expression for the y-axis momentum equation a is as follows:

[0031]

[0032] The expression for the UCM constitutive equation a is as follows:

[0033]

[0034] Where λ represents the relaxation time.

[0035] In the above-mentioned simulation method for viscoelastic liquid film flow at medium Reynolds number,

[0036] The expression for the normal stress equilibrium condition 'a' is as follows:

[0037]

[0038] Where J represents the mass jump flow rate of the liquid film caused by the interfacial phase transition; h t This represents the rate of change of the liquid film thickness with time t. h x This represents the rate of change of the liquid film thickness with respect to x. h xx This represents the second partial derivative of the liquid film thickness with respect to x.

[0039] The expression for the shear stress equilibrium condition 'a' is as follows:

[0040]

[0041] The expression for the no-slip boundary condition 'a' on the wall is as follows:

[0042] u = 0, v = 0 (y = 0)

[0043] The expression for the boundary condition 'a' for the motion of the liquid film surface is as follows:

[0044]

[0045] Where h(x,t) represents the rate of change of liquid film thickness along the flow direction with time.

[0046] In the above simulation method for viscoelastic liquid film flow at medium Reynolds number, the original expression for J is as follows:

[0047]

[0048] ξ=1 / (Ku·Pr), Ku=ΔH / (C p·ΔT), Pr=ν / a

[0049] Where k represents thermal conductivity, ΔH represents the latent heat of vaporization of the liquid, T represents the temperature inside the liquid film, Ku represents the Kutateladzes number, and C p ΔT represents the specific heat capacity of the fluid within the liquid film, ΔT represents the temperature change within the liquid film, Pr represents the Prandtl number, ν represents the kinematic viscosity coefficient, a represents the thermal diffusivity, and ξ represents the mass jump flow rate. A positive value of ξ indicates the condensation state, while a negative value indicates the evaporation state.

[0050] For the pneumatically heated surface of the material, we have:

[0051]

[0052] Therefore, the simplified expression for J is as follows:

[0053]

[0054] Where, q or This represents the heat flux density of the cold wall.

[0055] In the above-mentioned simulation method for viscoelastic liquid film flow at medium Reynolds number,

[0056] The expression for mass equation b is as follows:

[0057]

[0058] The expression for the x-axis momentum equation b is as follows:

[0059]

[0060] The expression for the y-axis momentum equation b is as follows:

[0061]

[0062] The expression for the UCM constitutive equation b is as follows:

[0063]

[0064] Where De represents the Deborah number, De = ελU0 / h0;

[0065] The expression for the boundary condition b for the liquid film surface motion is as follows:

[0066]

[0067] The expression for the normal stress equilibrium condition b is as follows:

[0068]

[0069] The expression for the shear stress equilibrium condition b is as follows:

[0070]

[0071] The expression for the no-slip boundary condition b on the wall is as follows:

[0072]

[0073] Among them, J A and J B For evaporation effect parameters,

[0074] In the above simulation method for viscoelastic liquid film flow at intermediate Reynolds number, the capillary number Ca and Reynolds number Re are scaled as follows:

[0075]

[0076] in, and represents the scaled number of capillaries and Reynolds number, respectively, and O(1) indicates that the order of magnitude is 1.

[0077] In the above-mentioned simulation method for viscoelastic liquid film flow at medium Reynolds number,

[0078] The expression for the x-axis momentum equation c is as follows:

[0079]

[0080] The expression for the y-axis momentum equation c is as follows:

[0081]

[0082] The expression for the normal stress equilibrium condition c is as follows:

[0083]

[0084] The expression for the shear stress equilibrium condition c is as follows:

[0085]

[0086] The expression for the UCM constitutive equation c is as follows:

[0087]

[0088] In the above simulation method for viscoelastic liquid film flow at medium Reynolds number, the velocity equation within the liquid film satisfying the shear stress equilibrium condition c is expressed as follows:

[0089]

[0090] Where q represents the flow rate and,

[0091] In the above simulation method for viscoelastic liquid film flow at moderate Reynolds numbers, the system of differential equations is expressed as follows:

[0092]

[0093] The present invention has the following advantages:

[0094] Current methods for calculating liquid film flow only consider flow under gravity through vertical or inclined rigid or flexible plates, pipes, etc. For viscoelastic liquid film flow under the influence of airflow shear force and evaporation effect, most studies are conducted experimentally, lacking theoretical and numerical research. This invention, with aircraft thermal protection as its background, considers the liquid film flow characteristics under the influence of gravity, airflow shear force, and evaporation effect. It modifies and improves traditional research methods, enabling the analysis of liquid film flow under these conditions. Attached Figure Description

[0095] Figure 1 This is a flowchart of a method for simulating the flow of a viscoelastic liquid film with a medium Reynolds number, as described in an embodiment of the present invention.

[0096] Figure 2 This is a schematic diagram of a physical model in an embodiment of the present invention;

[0097] Figure 3 This is a schematic diagram illustrating the change in liquid film thickness under different airflow shear forces in an embodiment of the present invention;

[0098] Figure 4 This is a schematic diagram illustrating the change in liquid film thickness under different evaporation effects in an embodiment of the present invention. Detailed Implementation

[0099] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed herein will be described in further detail below with reference to the accompanying drawings.

[0100] Based on the current research status of liquid film flow, this invention addresses the shortcomings of existing liquid film flow research, which rarely considers the influence of airflow shear force and evaporation effects. It modifies existing velocity estimation formulas within the liquid layer, deriving a velocity estimation formula that considers airflow shear force and evaporation effects. Using the integral boundary layer method, it derives a set of differential equations for the evolution of liquid film thickness and flow rate with time and flow direction. Applying initial conditions and inlet boundary conditions to the differential equations, and performing temporal and spatial difference discretization, it obtains the liquid layer thickness distribution along the flow direction at a certain moment. By changing the dimensionless airflow shear force and evaporation effect parameters, it obtains the liquid layer thickness distribution under different airflow shear force and evaporation effect conditions.

[0101] Reference Figures 1-2 In this embodiment, the method for simulating the flow of a moderate Reynolds number viscoelastic liquid film includes:

[0102] S1, the parameters are dimensionless to obtain dimensionless parameters.

[0103] In this embodiment, the dimensionless processing procedure for the parameters is as follows:

[0104] Introduce a small amount ε = h0 / l. Where h0 represents the initial liquid film thickness, l represents the typical deformation wavelength of the liquid-gas interface, and ε << 1.

[0105] Introducing velocity to the undisturbed lower liquid layer surface Where ρ represents the density of the fluid in the liquid film, g represents the gravitational acceleration, and μ represents the viscosity at zero shear rate.

[0106] Introduce the Reynolds number Re = ρU0h0 / μ.

[0107] Introduce the capillary number Ca = μU0 / γ0. Where γ0 represents the surface tension coefficient of the liquid film.

[0108] Based on ε, U0, Re, and Ca, the coordinates of the liquid film flow direction x, thickness direction y, liquid film thickness h, and normal stress σ in the x-direction are considered. xx Normal stress σ in the y direction yy , shear stress σ xy airflow shear force τ g Liquid film internal pressure p, external gas pressure p g The velocity of the liquid film along the flow direction (u), the normal velocity of the liquid film (v), time (t), and the airflow velocity (U) g and liquid film surface velocity u s Dimensionless processing is performed to obtain dimensionless parameters:

[0109]

[0110] in, U gg and They are x, y, h, and σ, respectively. xx σ yy σ xy τ g p, p g u, v, t, U g and u s The corresponding dimensionless parameter.

[0111] S2, for the flow of liquid film over an inclined rigid plate under gravity, airflow shear force and evaporation effect, gives the corresponding mass equation a, x-momentum equation a, y-momentum equation a, and UCM constitutive equation a describing viscoelastic fluid.

[0112] In this embodiment, the expression for mass equation a is as follows:

[0113]

[0114] The expression for the x-axis momentum equation a is as follows:

[0115]

[0116] Where θ represents the angle between the direction of liquid film flow and the horizontal direction.

[0117] The expression for the y-axis momentum equation a is as follows:

[0118]

[0119] The expression for the UCM constitutive equation a is as follows:

[0120]

[0121] Where λ represents the relaxation time.

[0122] S3 provides the corresponding normal stress equilibrium condition a, shear stress equilibrium condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a under the influence of evaporation effect for the liquid film surface under the action of airflow shear force, gas pressure, and evaporation effect.

[0123] In this embodiment, the expression for the normal stress equilibrium condition 'a' is as follows:

[0124]

[0125] Where J represents the mass jump flow rate of the liquid film caused by the interfacial phase transition; h t This represents the rate of change of the liquid film thickness with time t. h x This represents the rate of change of the liquid film thickness with respect to x. h xx This represents the second partial derivative of the liquid film thickness with respect to x.

[0126] The expression for the shear stress equilibrium condition 'a' is as follows:

[0127]

[0128] The expression for the no-slip boundary condition 'a' on the wall is as follows:

[0129] u = 0, v = 0 (y = 0)

[0130] The expression for the boundary condition 'a' for the motion of the liquid film surface is as follows:

[0131]

[0132] Where h(x,t) represents the rate of change of liquid film thickness along the flow direction with time.

[0133] The preferred, known expression for J is as follows:

[0134]

[0135] ξ=1 / (Ku·Pr), Ku=ΔH / (C p ·ΔT), Pr=ν / a

[0136] Where k represents thermal conductivity, ΔH represents the latent heat of vaporization of the liquid, T represents the temperature inside the liquid film, Ku represents the Kutateladzes number, and C p ΔT represents the specific heat capacity of the fluid within the liquid film, ΔT represents the temperature change within the liquid film, Pr represents the Prandtl number, ν represents the kinematic viscosity coefficient, a represents the thermal diffusivity, and ξ represents the mass jump flow rate. A positive value of ξ indicates the condensation state, while a negative value indicates the evaporation state.

[0137] For the pneumatically heated surface of the material, we have:

[0138]

[0139] Therefore, the mass jump flow rate can be expressed as:

[0140]

[0141] Where, q or This represents the heat flux density of the cold wall.

[0142] S4. Based on the dimensionless parameters, the mass equation a, x-momentum equation a, y-momentum equation a, UCM constitutive equation a, normal stress equilibrium condition a, shear stress equilibrium condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a are respectively dimensionlessized to obtain dimensionless mass equation b, x-momentum equation b, y-momentum equation b, UCM constitutive equation b, normal stress equilibrium condition b, shear stress equilibrium condition b, wall no-slip boundary condition b, and liquid film surface motion boundary condition b. In this embodiment, the expression of the mass equation b obtained after dimensionlessization is as follows:

[0143]

[0144] The expression for the x-axis momentum equation b is as follows:

[0145]

[0146] The expression for the y-axis momentum equation b is as follows:

[0147]

[0148] The expression for the UCM constitutive equation b is as follows:

[0149]

[0150] Where De represents the Deborah number, De = ελU0 / h0. The expression for the boundary condition b for the liquid film surface motion is as follows:

[0151]

[0152] The expression for the normal stress equilibrium condition b is as follows:

[0153] The expression for the shear stress equilibrium condition b is as follows:

[0154]

[0155] The expression for the no-slip boundary condition b on the wall is as follows:

[0156]

[0157] Among them, J A and J B For evaporation effect parameters,

[0158] S5. Scale the capillary number Ca and Reynolds number Re so that the scaled capillary number and Reynolds number are on the order of 1. Substitute the scaled capillary number and Reynolds number into the x-axis momentum equation b, y-axis momentum equation b, normal stress equilibrium condition b, and shear stress equilibrium condition b, respectively. Use order of magnitude analysis to neglect small quantities to obtain the x-axis momentum equation c, y-axis momentum equation c, normal stress equilibrium condition c, and shear stress equilibrium condition c.

[0159] In this embodiment, the capillary number Ca and Reynolds number Re are scaled in the following manner:

[0160]

[0161] in, and represents the scaled number of capillaries and Reynolds number, respectively, and O(1) indicates that the order of magnitude is 1.

[0162] Preferred, based on and What was obtained:

[0163] The expression for the x-axis momentum equation c is as follows:

[0164]

[0165] The expression for the y-axis momentum equation c is as follows:

[0166]

[0167] The expression for the normal stress equilibrium condition c is as follows:

[0168]

[0169] The expression for the shear stress equilibrium condition c is as follows:

[0170]

[0171] S6. Perform a magnitude analysis on the UCM constitutive equation b, neglecting minor quantities, to obtain the UCM constitutive equation c.

[0172] In this embodiment, the expression for the UCM constitutive equation c is as follows:

[0173]

[0174] S7, determine the velocity equation within the liquid film that satisfies the shear stress equilibrium condition c.

[0175] In this embodiment, based on the updated liquid surface boundary conditions after magnitude analysis, the known velocity equation within the liquid film that does not consider airflow shear force is modified to propose a new velocity equation within the liquid film under the action of airflow shear force. That is, an airflow shear force driving term is added to the known velocity equation within the liquid film that does not consider airflow shear force, and it is made to satisfy the wall no-slip boundary condition and the shear stress equilibrium condition. Moreover, the added term conforms to physical laws, and the velocity equation within the liquid film that satisfies the shear stress equilibrium condition c is expressed as follows:

[0176]

[0177] Where q represents the flow rate and,

[0178] S8. Integrating both sides of the mass equation b and the x-direction momentum equation c from 0 to the liquid film thickness, and based on the wall no-slip boundary condition b, the liquid film surface motion boundary condition b, and the UCM constitutive equation c, the differential equation system is derived using calculus theory.

[0179] In this embodiment, the resulting system of differential equations is as follows:

[0180]

[0181] S9 uses Runge-Ku method to discretize the differential equation system in the time direction and differential discretization in the spatial direction. Given the initial conditions of liquid film thickness and flow rate, and applying wave boundary conditions and steady boundary conditions at the inlet respectively, numerical solutions are obtained to obtain the liquid film thickness and flow rate that vary with time and space.

[0182] S10, change the magnitude of the airflow shear force and evaporation effect in the differential equation system to obtain the calculation results under different airflow shear forces and evaporation effects; compare the calculation results obtained under the same time based on different airflow shear forces and evaporation effects to obtain the influence law of airflow shear force and evaporation effect on liquid film wave transmission, as well as the influence law of airflow shear force and evaporation effect on wave generation.

[0183] In this embodiment, given U gg =10.0, J A =0.0, J B =0.0, changing the magnitude of the airflow shear force in the differential equation system, and calculating for the same amount of time, compare the influence of the airflow shear force on the liquid film wave transmission. For example, the dimensionless airflow shear forces are 0.01, 0.05, 0.1, and 0.15, and the liquid film thickness is as follows. Figure 3 As shown. Furthermore, given τ g =0.0, J A =J B By changing the magnitude of the evaporation effect in the differential equations and calculating the same time interval, the influence of the evaporation effect on the transport of liquid film fluctuations can be compared. For example, the dimensionless evaporation effects are 0.01, 0.05, 0.1, and 0.5, and the liquid film thickness is as follows: Figure 4 As shown.

[0184] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0185] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for simulating flow in a viscoelastic liquid film with a moderate Reynolds number, characterized in that, include: S1, the parameters are dimensionless to obtain dimensionless parameters; S2, for the flow of liquid film over an inclined rigid plate under gravity, airflow shear force and evaporation effect, the corresponding mass equation a, x-momentum equation a, y-momentum equation a, and UCM constitutive equation a describing viscoelastic fluid are given. S3 provides the corresponding normal stress equilibrium condition a, shear stress equilibrium condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a under the influence of evaporation effect for the liquid film surface under the action of airflow shear force, gas pressure and evaporation effect. S4. Based on dimensionless parameters, the mass equation a, x-momentum equation a, y-momentum equation a, UCM constitutive equation a, normal stress equilibrium condition a, shear stress equilibrium condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a are respectively dimensionlessized to obtain dimensionless mass equation b, x-momentum equation b, y-momentum equation b, UCM constitutive equation b, normal stress equilibrium condition b, shear stress equilibrium condition b, wall no-slip boundary condition b, and liquid film surface motion boundary condition b. S5. Scale the capillary number Ca and Reynolds number Re so that the scaled capillary number and Reynolds number are on the order of 1. Substitute the scaled capillary number and Reynolds number into the x-axis momentum equation b, y-axis momentum equation b, normal stress equilibrium condition b, and shear stress equilibrium condition b, respectively. Use order of magnitude analysis to neglect small quantities to obtain the x-axis momentum equation c, y-axis momentum equation c, normal stress equilibrium condition c, and shear stress equilibrium condition c. S6. Perform a magnitude analysis on the UCM constitutive equation b, neglecting small quantities, to obtain the UCM constitutive equation c. S7, determine the velocity equation within the liquid film that satisfies the shear stress equilibrium condition c; S8. Integrate both sides of the mass equation b and the x-direction momentum equation c from 0 to the liquid film thickness, and derive the differential equation system based on the calculus theory according to the wall no-slip boundary condition b, the liquid film surface motion boundary condition b, and the UCM constitutive equation c. S9. The Runge-Ku method is used to discretize the differential equation system in the time direction and the differential discretization method is used in the spatial direction. Given the initial conditions of liquid film thickness and flow rate, and applying the wave boundary conditions and steady boundary conditions at the inlet respectively, numerical solutions are obtained to obtain the liquid film thickness and flow rate that vary with time and space. S10, change the magnitude of the airflow shear force and evaporation effect in the differential equation system to obtain the calculation results under different airflow shear forces and evaporation effects; compare the calculation results obtained under the same time based on different airflow shear forces and evaporation effects to obtain the influence law of airflow shear force and evaporation effect on liquid film wave transmission, as well as the influence law of airflow shear force and evaporation effect on wave generation.

2. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 1, characterized in that, The parameters are dimensionless to obtain dimensionless parameters, including: Introduce a small amount ε = h0 / l; where h0 represents the initial liquid film thickness, l represents the typical deformation wavelength of the liquid-gas interface, and ε << 1; Introducing velocity to the undisturbed lower liquid layer surface Where ρ represents the density of the fluid in the liquid film, g represents the gravitational acceleration, and μ represents the viscosity at zero shear rate; Introduce the Reynolds number Re = ρU0h0 / μ; The capillary number Ca = μU0 / γ0 is introduced; where γ0 represents the surface tension coefficient of the liquid film. Based on ε, U0, Re, and Ca, the coordinates of the liquid film flow direction x, thickness direction y, liquid film thickness h, and normal stress σ in the x-direction are considered. xx Normal stress σ in the y direction yy , shear stress σ xy airflow shear force τ g Liquid film internal pressure p, external gas pressure p g The velocity of the liquid film along the flow direction (u), the normal velocity of the liquid film (v), time (t), and the airflow velocity (U) g and liquid film surface velocity u s Dimensionless processing is performed to obtain dimensionless parameters: in, U gg and They are x, y, h, and σ, respectively. xx σ yy σ xy τ g p, p g u, v, t, U g and u s The corresponding dimensionless parameter.

3. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 2, characterized in that, The expression for the mass equation a is as follows: The expression for the x-axis momentum equation a is as follows: Where θ represents the angle between the direction of liquid film flow and the horizontal direction; The expression for the y-axis momentum equation a is as follows: The expression for the UCM constitutive equation a is as follows: Where λ represents the relaxation time.

4. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 3, characterized in that, The expression for the normal stress equilibrium condition 'a' is as follows: Where J represents the mass jump flow rate of the liquid film caused by the interfacial phase transition; h t This represents the rate of change of the liquid film thickness with time t. h x This represents the rate of change of the liquid film thickness with respect to x. h xx This represents the second partial derivative of the liquid film thickness with respect to x. The expression for the shear stress equilibrium condition 'a' is as follows: The expression for the no-slip boundary condition 'a' on the wall is as follows: u = 0, v = 0 (y = 0) The expression for the boundary condition 'a' for the motion of the liquid film surface is as follows: Where h(x,t) represents the rate of change of liquid film thickness along the flow direction with time.

5. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 4, characterized in that, The original expression for J is as follows: ξ=1 / (Ku·Pr),Ku=ΔH / (C p ·ΔT),Pr=ν / a Where k represents thermal conductivity, ΔH represents the latent heat of vaporization of the liquid, T represents the temperature inside the liquid film, Ku represents the Kutateladzes number, and C p ΔT represents the specific heat capacity of the fluid within the liquid film, ΔT represents the temperature change within the liquid film, Pr represents the Prandtl number, ν represents the kinematic viscosity coefficient, a represents the thermal diffusivity, and ξ represents the mass jump flow rate. A positive value of ξ indicates the condensation state, while a negative value indicates the evaporation state. For the pneumatically heated surface of the material, we have: Therefore, the simplified expression for J is as follows: Where, q or This represents the heat flux density of the cold wall.

6. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 5, characterized in that, The expression for mass equation b is as follows: The expression for the x-axis momentum equation b is as follows: The expression for the y-axis momentum equation b is as follows: The expression for the UCM constitutive equation b is as follows: Where De represents the Deborah number, De = ελU0 / h0; The expression for the boundary condition b for the liquid film surface motion is as follows: The expression for the normal stress equilibrium condition b is as follows: The expression for the shear stress equilibrium condition b is as follows: The expression for the no-slip boundary condition b on the wall is as follows: Among them, J A and J B For evaporation effect parameters, 7. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 6, characterized in that, The capillary number Ca and Reynolds number Re are scaled as follows: in, and represents the scaled number of capillaries and Reynolds number, respectively, and O(1) indicates that the order of magnitude is 1.

8. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 7, characterized in that, The expression for the x-axis momentum equation c is as follows: The expression for the y-axis momentum equation c is as follows: The expression for the normal stress equilibrium condition c is as follows: The expression for the shear stress equilibrium condition c is as follows: The expression for the UCM constitutive equation c is as follows:

9. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 8, characterized in that, The velocity equation within the liquid film that satisfies the shear stress equilibrium condition c is expressed as follows: Where q represents the flow rate and, 10. The method for simulating the flow of a viscoelastic liquid film with a moderate Reynolds number according to claim 9, characterized in that, The system of differential equations is represented as follows:

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