Medium Reynolds number viscoelastic liquid film flow simulation method

Abstract

The invention discloses a medium Reynolds number viscoelastic liquid film flow simulation method, which is characterized in that nondimensionalization and simplification are carried out based on a liquid film flow control equation and a UCM constitutive equation, and normal stress and shear stress balance conditions on the surface of a liquid film under the action of gravity, airflow shear force and evaporation effect are deduced; and according to a liquid film surface boundary condition and a wall surface slippage-free boundary condition, on the basis of the airflow shear force-free liquid film speed expression, an expression of the liquid film speed under the action of the airflow shear force and the evaporation effect is extracted. Deriving according to a boundary layer integration method to obtain a differential equation set of liquid film thickness and flow evolved along with time and a flow direction, wherein the differential equation set can be used for researching influence factors of liquid film flow characteristics; time discretization is carried out by adopting a Runge-Kutta method, spatial discretization is carried out by adopting a finite difference scheme, so that the change rule of the liquid film thickness along with the time and the flowing direction is obtained, and the influence rule of the airflow shear force and the evaporation effect on the change of the liquid film thickness is discussed.

Description

Technical Field

[0001] The invention belongs to the technical field of fluid mechanics, and in particular relates to a medium Reynolds number viscoelastic liquid film flow simulation method. Background Art

[0002] Liquid film flow phenomenon is widely present in daily life, production and science and technology, such as in the biological field, including the flow of human tissue fluid and industrial field. Liquid film flow phenomenon also exists in the field of aircraft thermal protection. For silicon-based materials, it is a heat protection material with melting loss as the main change. Under the condition of aerodynamic heating, when a certain temperature is reached, the solid material will melt to form a molten state, and flow will occur under the influence of air flow shear force and gravity.

[0003] The study of liquid film flow phenomena began in the 1940s and 1950s. Kapitza and his son first discovered the phenomenon of liquid film flow in experiments and conducted theoretical research on it. Since then, the topic of liquid film flow has attracted the attention of many scholars. They used boundary layer integral method, long wave theory method and other methods based on control equations, constitutive equations and boundary conditions to study Newtonian flow and viscoelastic liquid film flow phenomena, but the above research is still limited to the study of liquid film flow and wave transmission under gravity. For the study of liquid film flow under the shear force of airflow and evaporation effect, most of them are only in experimental testing. For example, Budakli used experimental methods to study the flow and heat transfer of liquid film under gravity and airflow shear force. There is currently a lack of theoretical and numerical research on liquid film flow and wave transmission under the influence of airflow shear force and evaporation effect. Summary of the invention

[0004] The technology of the present invention solves the problem: overcomes the shortcomings of the prior art, provides a medium Reynolds number viscoelastic liquid film flow simulation method, and solves the shortcomings of the prior art that it is impossible to study the liquid film flow under the influence of airflow shear force trend and evaporation effect.

[0005] In order to solve the above technical problems, the present invention discloses a method for simulating viscoelastic liquid film flow with a medium Reynolds number, comprising:

[0006] S1, dimensionless processing is performed on the parameters to obtain dimensionless parameters;

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

[0008] S3, for the liquid film surface under the action of air flow shear force, gas pressure and evaporation effect, the corresponding normal stress balance condition a, shear stress balance condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a under the influence of evaporation effect are given;

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

[0010] S5, scale the capillary number Ca and the Reynolds number Re so that the scaled capillary number and Reynolds number are 1, substitute the scaled capillary number and Reynolds number into the x-direction momentum equation b, the y-direction momentum equation b, the normal stress balance condition b and the shear stress balance condition b, respectively, and use magnitude analysis to ignore small quantities to obtain the x-direction momentum equation c, the y-direction momentum equation c, the normal stress balance condition c and the shear stress balance condition c;

[0011] S6, conduct magnitude analysis on the UCM constitutive equation b, neglect the small amount, and obtain the UCM constitutive equation c;

[0012] S7, determining the velocity equation in 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 thickness of the liquid film, and derive the differential equations 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 differential equations are discretized in the time direction by Rungeku method and in the space direction by difference discretization. The initial conditions of liquid film thickness and flow rate are given, and the fluctuating boundary conditions and steady boundary conditions at the inlet are loaded respectively. The numerical solution is performed to obtain the liquid film thickness and flow rate that vary with time and space.

[0015] S10, changing the magnitude of the airflow shear force and the evaporation effect in the differential equation group, and obtaining the calculation results under different airflow shear forces and evaporation effects; comparing the calculation results based on different airflow shear forces and evaporation effects at the same time, and obtaining the influence of the airflow shear force and the evaporation effect on the liquid film wave transmission, as well as the influence of the airflow shear force and the evaporation effect on the wave generation.

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

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

[0018] The velocity of the liquid surface under undisturbed Among them, ρ represents the density of the fluid in the liquid film, g represents the acceleration due to gravity, and μ represents the viscosity at zero shear rate;

[0019] Introduce 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 coordinate x of the liquid film flow direction, the coordinate y of the thickness direction, the liquid film thickness h, and the normal stress σ in the x direction are calculated. xx , normal stress in the y direction σ yy , shear stress σ xy , air flow shear force τ g , the pressure inside the liquid film p, the external gas pressure p g , the velocity of the liquid film along the flow direction u, the normal velocity of the liquid film v, the time t, the air flow velocity U g and the liquid film surface velocity u s Perform dimensionless processing to obtain dimensionless parameters:

[0022]

[0023] in, U gg and are x, y, h, 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 medium Reynolds number viscoelastic liquid film flow simulation method,

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

[0026]

[0027] The expression of the x-direction momentum equation a is as follows:

[0028]

[0029] Among them, θ represents the angle between the liquid film flow direction and the horizontal direction;

[0030] The expression of the y-direction momentum equation a is as follows:

[0031]

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

[0033]

[0034] Here, λ represents the relaxation time.

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

[0036] The expression of 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 interface phase change; h t represents the rate of change of liquid film thickness with time t, h x represents the rate of change of liquid film thickness with x, h xx represents the second partial differential of the film thickness with respect to x,

[0039] The expression of shear stress equilibrium condition a is as follows:

[0040]

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

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

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

[0044]

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

[0046] In the above-mentioned medium Reynolds number viscoelastic liquid film flow simulation method, the original expression of 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, C p represents the specific heat capacity of the fluid in the liquid film, ΔT represents the change in temperature in the liquid film, Pr represents the Prandtl number, ν represents the kinematic viscosity coefficient, and a represents the thermal diffusion coefficient; ξ represents the mass jump flow rate, and a positive value of ξ represents the condensation state, and a negative value of ξ represents the evaporation state;

[0050] For the material pneumatic heating surface, there are:

[0051]

[0052] Then, the simplified expression of J is as follows:

[0053]

[0054] Among them, q or represents the cold wall heat flux.

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

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

[0057]

[0058] The expression of the x-direction momentum equation b is as follows:

[0059]

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

[0061]

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

[0063]

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

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

[0066]

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

[0068]

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

[0070]

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

[0072]

[0073] Among them, J A and J B is the evaporation effect parameter,

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

[0075]

[0076] in, and represent the scaled capillary number and Reynolds number respectively, and O(1) means the order of magnitude is 1.

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

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

[0079]

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

[0081]

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

[0083]

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

[0085]

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

[0087]

[0088] In the above-mentioned medium Reynolds number viscoelastic liquid film flow simulation method, the velocity equation in the liquid film that satisfies the shear stress balance condition c is expressed as follows:

[0089]

[0090] Where q represents the flow rate and,

[0091] In the above-mentioned medium Reynolds number viscoelastic liquid film flow simulation method, the differential equation system is expressed as follows:

[0092]

[0093] The present invention has the following advantages:

[0094] The current calculation methods for liquid film flow only consider the flow through vertical or inclined rigid or flexible plates, pipes, etc. under the action of gravity. For the problem of viscoelastic liquid film flow under the action of airflow shear force and evaporation effect, most of them are tested and studied from the experimental perspective, and there is still a lack of theoretical and numerical research. The present invention takes aircraft thermal protection as the background, considers the flow law of liquid film under the action of gravity, airflow shear force, and evaporation effect, and makes corresponding corrections and improvements to the traditional research methods, so as to have the ability to analyze the flow of liquid film under the action of gravity, airflow shear force and evaporation effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 is a flow chart of a method for simulating viscoelastic liquid film flow at a medium Reynolds number in an embodiment of the present invention;

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

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

[0098] Figure 4 It is a schematic diagram of the change of liquid film thickness under different evaporation effects in an embodiment of the present invention. DETAILED DESCRIPTION

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

[0100] According to the current research status of liquid film flow, the present invention aims at the shortcoming that the current liquid film flow rarely considers the influence of airflow shear force trend and evaporation effect. The existing velocity estimation formula in the liquid layer is corrected to derive the velocity estimation considering the airflow shear force and evaporation effect. The integral boundary layer method is used to derive the differential equation group of the evolution of liquid film thickness and flow rate with time and flow direction. The initial conditions and inlet boundary conditions are applied to the differential equation group, and time and space differential discretization is performed to obtain the liquid layer thickness distribution along the flow direction at a certain moment. The dimensionless airflow shear force and evaporation effect parameters are changed to obtain the liquid layer thickness distribution under different airflow shear force and evaporation effect conditions.

[0101] Reference Figures 1-2 In this embodiment, the medium Reynolds number viscoelastic liquid film flow simulation method includes:

[0102] S1, perform dimensionless processing on the parameters to obtain dimensionless parameters.

[0103] In this embodiment, the dimensionless processing flow of the parameters is as follows:

[0104] A small quantity ε=h0 / l is introduced, where h0 represents the initial liquid film thickness, l represents the typical liquid-gas interface deformation wavelength, and ε<<1.

[0105] The velocity of the liquid surface under undisturbed Where ρ represents the density of the fluid in the liquid film, g represents the acceleration due to gravity, and μ represents the viscosity at zero shear rate.

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

[0107] The capillary number Ca=μU0 / γ0 is introduced, where γ0 represents the surface tension coefficient of the liquid film.

[0108] Based on ε, U0, Re and Ca, the coordinate x of the liquid film flow direction, the coordinate y of the thickness direction, the liquid film thickness h, and the normal stress σ in the x direction are calculated. xx , normal stress in the y direction σ yy , shear stress σ xy , air flow shear force τ g , the pressure inside the liquid film p, the external gas pressure p g , the velocity of the liquid film along the flow direction u, the normal velocity of the liquid film v, the time t, the air flow velocity U g and the liquid film surface velocity u s Perform dimensionless processing to obtain dimensionless parameters:

[0109]

[0110] in, U gg and are x, y, h, 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, air flow shear force and evaporation effect, the corresponding mass equation a, x-direction momentum equation a, y-direction momentum equation a, and UCM constitutive equation a describing viscoelastic fluid are given.

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

[0113]

[0114] The expression of the x-direction momentum equation a is as follows:

[0115]

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

[0117] The expression of the y-direction momentum equation a is as follows:

[0118]

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

[0120]

[0121] Here, λ represents the relaxation time.

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

[0123] In this embodiment, the expression of 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 interface phase change; h t represents the rate of change of liquid film thickness with time t, h x represents the rate of change of liquid film thickness with x, h xx represents the second partial differential of the film thickness with respect to x,

[0126] The expression of shear stress equilibrium condition a is as follows:

[0127]

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

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

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

[0131]

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

[0133] Preferably, the known expression of 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, C p represents the specific heat capacity of the fluid in the liquid film, ΔT represents the change in temperature in the liquid film, Pr represents the Prandtl number, ν represents the kinematic viscosity coefficient, a represents the thermal diffusion coefficient; ξ represents the mass jump flow rate, a positive value of ξ represents the condensation state, and a negative value of ξ represents the evaporation state.

[0137] For the material pneumatic heating surface, there are:

[0138]

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

[0140]

[0141] Among them, q or represents the cold wall heat flux.

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

[0143]

[0144] The expression of the x-direction momentum equation b is as follows:

[0145]

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

[0147]

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

[0149]

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

[0151]

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

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

[0154]

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

[0156]

[0157] Among them, J A and J B is the evaporation effect parameter,

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

[0159] In this embodiment, the capillary number Ca and the Reynolds number Re are scaled as follows:

[0160]

[0161] in, and represent the scaled capillary number and Reynolds number respectively, and O(1) means the order of magnitude is 1.

[0162] Preferably, based on and What we get:

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

[0164]

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

[0166]

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

[0168]

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

[0170]

[0171] S6, perform magnitude analysis on the UCM constitutive equation b, neglect small quantities, and obtain the UCM constitutive equation c.

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

[0173]

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

[0175] In this embodiment, according to the liquid surface boundary conditions updated after the magnitude analysis, the known velocity equation in the liquid film without considering the airflow shear force is corrected, and a new velocity equation in the liquid film under the action of the airflow shear force is proposed, that is, the airflow shear force trending term is added to the known velocity equation in the liquid film without considering the airflow shear force, and it is made to meet the wall no-slip boundary condition and the shear stress balance condition, and the added term conforms to the physical law, and the velocity equation in the liquid film that meets the shear stress balance condition c is expressed as follows:

[0176]

[0177] Where q represents the flow rate and,

[0178] S8, integrate both sides of the mass equation b and the x-direction momentum equation c from 0 to the thickness of the liquid film, and derive the differential equations 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.

[0179] In this embodiment, the obtained differential equations are as follows:

[0180]

[0181] S9, the differential equations are discretized in the time direction by the Rungeku method and in the space direction by difference discretization. The initial conditions of the liquid film thickness and flow rate are given, and the fluctuating boundary conditions and steady boundary conditions at the inlet are loaded respectively. The numerical solution is performed to obtain the liquid film thickness and flow rate that vary with time and space.

[0182] S10, changing the magnitude of the airflow shear force and the evaporation effect in the differential equation group, and obtaining the calculation results under different airflow shear forces and evaporation effects; comparing the calculation results based on different airflow shear forces and evaporation effects at the same time, and obtaining the influence of the airflow shear force and the evaporation effect on the liquid film wave transmission, as well as the influence of the airflow shear force and the evaporation effect on the wave generation.

[0183] In this embodiment, given U gg =10.0, J A =0.0, J B = 0.0, change the magnitude of the airflow shear force in the differential equations, calculate the same time, and compare the influence of airflow shear force on the wave transmission of liquid film. For example, the dimensionless airflow shear force is 0.01, 0.05, 0.1, 0.15 respectively, and the liquid film thickness is Figure 3 As shown. Furthermore, given τ g =0.0, J A =J B , change the size of the evaporation effect in the differential equations, and calculate the influence of the evaporation effect on the wave transmission of the liquid film in the same time. For example, the dimensionless evaporation effect is 0.01, 0.05, 0.1, and 0.5 respectively, and the liquid film thickness is Figure 4 shown.

[0184] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0185] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A method for simulating viscoelastic liquid film flow with medium Reynolds number, characterized in that: include: S1, dimensionless processing is performed on the parameters to obtain dimensionless parameters; S2, for the flow of liquid film over an inclined rigid plate under gravity, air flow shear force and evaporation effect, the corresponding mass equation a, x-direction momentum equation a, y-direction momentum equation a, and UCM constitutive equation a describing viscoelastic fluid are given; S3, for the liquid film surface under the action of air flow shear force, gas pressure and evaporation effect, the corresponding normal stress balance condition a, shear stress balance condition a, wall no-slip boundary condition a, and liquid film surface motion boundary condition a under the influence of evaporation effect are given; S4, based on the dimensionless parameters, the mass equation a, the x-direction momentum equation a, the y-direction momentum equation a, the UCM constitutive equation a, the normal stress balance condition a, the shear stress balance condition a, the wall no-slip boundary condition a and the liquid film surface motion boundary condition a are dimensionless processed respectively to obtain the dimensionless mass equation b, the x-direction momentum equation b, the y-direction momentum equation b, the UCM constitutive equation b, the normal stress balance condition b, the shear stress balance condition b, the wall no-slip boundary condition b and the liquid film surface motion boundary condition b; S5, scale the capillary number Ca and the Reynolds number Re so that the scaled capillary number and Reynolds number are 1, substitute the scaled capillary number and Reynolds number into the x-direction momentum equation b, the y-direction momentum equation b, the normal stress balance condition b and the shear stress balance condition b, respectively, and use magnitude analysis to ignore small quantities to obtain the x-direction momentum equation c, the y-direction momentum equation c, the normal stress balance condition c and the shear stress balance condition c; S6, conduct magnitude analysis on the UCM constitutive equation b, neglect the small amount, and obtain the UCM constitutive equation c; S7, determining the velocity equation in 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 thickness of the liquid film, and derive the differential equations 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 differential equations are discretized in the time direction by Rungeku method and in the space direction by difference discretization. The initial conditions of liquid film thickness and flow rate are given, and the fluctuating boundary conditions and steady boundary conditions at the inlet are loaded respectively. The numerical solution is performed to obtain the liquid film thickness and flow rate that vary with time and space. S10, changing the magnitude of the airflow shear force and the evaporation effect in the differential equation group, and obtaining the calculation results under different airflow shear forces and evaporation effects; comparing the calculation results based on different airflow shear forces and evaporation effects at the same time, and obtaining the influence of the airflow shear force and the evaporation effect on the liquid film wave transmission, as well as the influence of the airflow shear force and the evaporation effect on the wave generation.

2. The medium Reynolds number viscoelastic liquid film flow simulation method according to claim 1, characterized in that: The parameters are dimensionless processed to obtain dimensionless parameters, including: Introduce a small amount ε=h0 / l; where h0 represents the initial liquid film thickness, l represents the typical liquid-gas interface deformation wavelength, ε<<1; The velocity of the liquid surface under undisturbed Among them, ρ represents the density of the fluid in the liquid film, g represents the acceleration due to gravity, and μ represents the viscosity at zero shear rate; Introduce 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 coordinate x of the liquid film flow direction, the coordinate y of the thickness direction, the liquid film thickness h, and the normal stress σ in the x direction are calculated. xx , normal stress in the y direction σ yy , shear stress σ xy , air flow shear force τ g , the pressure inside the liquid film p, the external gas pressure p g , the velocity of the liquid film along the flow direction u, the normal velocity of the liquid film v, the time t, the air flow velocity U g and the liquid film surface velocity u s Perform dimensionless processing to obtain dimensionless parameters: in, U gg and are x, y, h, 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 medium Reynolds number viscoelastic liquid film flow simulation method according to claim 2, characterized in that: The expression of the mass equation a is as follows: The expression of the x-direction momentum equation a is as follows: Among them, θ represents the angle between the liquid film flow direction and the horizontal direction; The expression of the y-direction momentum equation a is as follows: The expression of the UCM constitutive equation a is as follows: Here, λ represents the relaxation time.

4. The medium Reynolds number viscoelastic liquid film flow simulation method according to claim 3, characterized in that: The expression of normal stress equilibrium condition a is as follows: Where J represents the mass jump flow rate of the liquid film caused by the interface phase change; h t represents the rate of change of liquid film thickness with time t, h x represents the rate of change of liquid film thickness with x, h xx represents the second partial differential of the film thickness with respect to x, The expression of shear stress equilibrium condition a is as follows: The expression of the wall no-slip boundary condition a is as follows: u=0,v=0(y=0) The expression of the boundary condition a of the liquid film surface motion is as follows: Where h(x,t) represents the rate of change of the liquid film thickness along the flow direction with time.

5. The medium Reynolds number viscoelastic liquid film flow simulation method according to claim 4, characterized in that: The original expression of 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, C p represents the specific heat capacity of the fluid in the liquid film, ΔT represents the change in temperature in the liquid film, Pr represents the Prandtl number, ν represents the kinematic viscosity coefficient, and a represents the thermal diffusion coefficient; ξ represents the mass jump flow rate, and a positive value of ξ represents the condensation state, and a negative value of ξ represents the evaporation state; For the material pneumatic heating surface, there are: Then, the simplified expression of J is as follows: Among them, q or represents the cold wall heat flux.

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

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

9. The medium Reynolds number viscoelastic liquid film flow simulation method according to claim 8, characterized in that: The velocity equation in the liquid film that satisfies the shear stress balance condition c is expressed as follows: Where q represents the flow rate and, 10. The medium Reynolds number viscoelastic liquid film flow simulation method according to claim 9, characterized in that: The system of differential equations is expressed as follows:

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