Small Reynolds number liquid film flow simulation method

Abstract

The invention discloses a small Reynolds number liquid film flow simulation method, which comprises the following steps of: deducing normal stress, shear stress balance conditions and motion boundary conditions on the surface of a liquid film under the action of gravity, airflow shear force and evaporation effect according to a flow physical model; non-dimensionalization and simplification are carried out on the non-slip boundary condition of the wall surface, the mass equation and momentum equation of the flow and the boundary condition of the surface of the liquid film; for small Reynolds number flow, derivation is carried out based on a long wave theory method, and a differential equation of liquid film thickness evolving along with time and space under the synergistic influence of gravity, airflow shear force and evaporation effect is obtained; carrying out weak nonlinear evolution analysis of fluctuation on the differential equation to obtain a change relation of the instability growth rate of the fluctuation along with gravity, airflow shear force and evaporation effect, and giving a change image of the influence of the airflow shear force and the evaporation effect on the instability growth rate of the liquid film fluctuation.

Description

Technical Field

[0001] The invention belongs to the technical field of fluid mechanics, and in particular relates to a small Reynolds number 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 phenomenon began in the 1940s and 1950s. Kapitza and his son first discovered the liquid film flow phenomenon in experiments and conducted theoretical research on it. Since then, the subject 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 the liquid film flow phenomenon, 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 small Reynolds number liquid film flow simulation method, and solves the deficiency of the prior art that the liquid film flow under the influence of gravity-airflow shear force-evaporation effect cannot be studied simultaneously.

[0005] In order to solve the above technical problems, the present invention discloses a small Reynolds number liquid film flow simulation method, 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, give the corresponding mass equation a and momentum equation a;

[0008] S3, for the liquid film surface under the action of gravity, 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, momentum equation a, normal stress balance condition a, shear stress balance condition a, wall no-slip boundary condition a and liquid film surface motion boundary condition a are respectively dimensionless processed to obtain the dimensionless mass equation b, momentum equation b, normal stress balance condition b, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b;

[0010] S5, scaling the Weber number We so that the scaled Weber magnitude is 1, substituting the scaled Weber number into the normal stress equilibrium condition b, and using magnitude analysis to ignore small quantities, obtaining the normal stress equilibrium condition c;

[0011] S6, expand the dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film and the pressure inside the liquid film respectively with a small amount ε, retain the zero-order and first-order quantities, substitute them into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, simplify them, and obtain the zero-order solution and first-order solution of the velocity of the liquid film along the flow direction; where ε<<1;

[0012] S7, integrating the mass equation b along the direction of the liquid film thickness, combining the wall no-slip boundary condition b and the liquid film surface motion boundary condition b, and substituting the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 into the equation, to obtain a differential equation for the evolution of the liquid film thickness;

[0013] S8, based on differential equations, weak nonlinear evolution analysis of fluctuations is performed to obtain the variation law of disturbance instability growth rate with tilt angle, evaporation effect, air flow shear force, Reynolds number and Weber number;

[0014] S9, changing the magnitude of the evaporation effect and the airflow shear force in step S8, obtaining a curve of the change in the instability growth rate, and determining the influence of the evaporation effect and the airflow shear force on the growth rate of the instability of the liquid film wave transmission.

[0015] In the above-mentioned small Reynolds number liquid film flow simulation method, the parameters are dimensionally processed to obtain dimensionless parameters, including:

[0016] Introduce a small amount ε = h 0 / l; where h 0 represents the initial liquid film thickness, l represents the typical liquid-gas interface deformation wavelength;

[0017] The velocity of the surface of the undisturbed liquid layer is introduced 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;

[0018] Introducing Reynolds number Re = ρU0 h 0 / μ;

[0019] Introduction of Weber number Among them, γ 0 It represents the surface tension coefficient of the liquid film;

[0020] Based on ε, U 0 , Re and We, the flow direction coordinate x of the liquid film, the thickness direction coordinate y, the liquid film thickness h, the 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 dimensional processing to obtain dimensionless parameters:

[0021]

[0022] 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.

[0023] In the above-mentioned small Reynolds number liquid film flow simulation method,

[0024] The expression of the mass equation a is as follows:

[0025]

[0026] The expression of momentum equation a is as follows:

[0027]

[0028] Among them, θ represents the angle between the liquid film flow direction and the horizontal direction;

[0029] The expression of normal stress equilibrium condition a is as follows:

[0030]

[0031] 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, hxx represents the second partial differential of the film thickness with respect to x, u x represents the partial differential of the velocity of the liquid film along the stream direction with respect to x, u y represents the partial differential of the velocity of the liquid film along the stream direction with respect to y,

[0032] The expression of shear stress equilibrium condition a is as follows:

[0033]

[0034] The expression of the wall no-slip boundary condition a is as follows:

[0035]

[0036] The expression of the boundary condition a of the liquid film surface motion is as follows:

[0037]

[0038] Where h(x,t) represents the rate of change of the liquid film thickness along the flow direction with time.

[0039] In the above-mentioned small Reynolds number liquid film flow simulation method, the original expression of J is as follows:

[0040]

[0041] ξ=1 / (Ku·Pr), Ku=ΔH / (C p ·ΔT), Pr=ν / a

[0042] 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;

[0043] For the material pneumatic heating surface, there are:

[0044]

[0045] Then, the simplified expression of J is as follows:

[0046]

[0047] Among them, q or represents the cold wall heat flux.

[0048] In the above-mentioned small Reynolds number liquid film flow simulation method,

[0049] The expression of mass equation b is as follows:

[0050]

[0051] The expression of momentum equation b is as follows:

[0052]

[0053] The expression of normal stress equilibrium condition b is as follows:

[0054]

[0055] The expression of shear stress equilibrium condition b is as follows:

[0056]

[0057] The expression of the wall no-slip boundary condition b is as follows:

[0058]

[0059] The expression of the boundary condition b of the liquid film surface motion is as follows:

[0060]

[0061] Among them, J A and J B is the evaporation effect parameter, In the above-mentioned small Reynolds number liquid film flow simulation method, the Weber number We is scaled as follows:

[0062]

[0063] in, represents the scaled Weber number, and O(1) means the magnitude is 1.

[0064] In the above-mentioned small Reynolds number liquid film flow simulation method, the expression of the normal stress equilibrium condition c is as follows:

[0065]

[0066] In the above-mentioned small Reynolds number liquid film flow simulation method, the dimensionless liquid film velocity along the stream direction, the normal velocity of the liquid film and the pressure inside the liquid film are expanded with a small amount ε, respectively, and after retaining the zero-order and first-order quantities, they are substituted into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, and simplified to obtain the zero-order solution and first-order solution of the liquid film velocity along the stream direction, including:

[0067] The dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film, and the pressure inside the liquid film are expanded by a small amount ε:

[0068]

[0069] in, represents the dimensionless zero-order liquid film velocity along the stream direction, the normal velocity of the liquid film, and the pressure inside the liquid film. represents the dimensionless first-order liquid film velocity along the stream direction, the normal velocity of the liquid film, and the pressure inside the liquid film. O(ε 2 ) indicates the magnitude is ε 2 A small amount;

[0070] Will and Substitute into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, and perform the following simplification:

[0071]

[0072] in, express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of

[0073] Based on equation (15), the zero-order solution of the velocity of the liquid film along the flow direction is obtained: and the first-order solution

[0074]

[0075] in, express right The differential of express right The mixed differential of express right The third differential of .

[0076] In the above-mentioned small Reynolds number liquid film flow simulation method, the mass equation b is integrated along the liquid film thickness direction, combined with the wall no-slip boundary condition b and the liquid film surface motion boundary condition b, and the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 are substituted, and the differential equation for the evolution of the liquid film thickness is obtained, including:

[0077] Integrating the mass equation b along the thickness direction of the liquid film yields:

[0078]

[0079] q represents the flow rate:

[0080]

[0081] Substituting the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 into formula (18), we obtain:

[0082]

[0083] Substituting formula (19) into formula (17), we obtain the differential equation for the evolution of liquid film thickness:

[0084]

[0085] in, express right The fourth differential of .

[0086] In the above-mentioned small Reynolds number liquid film flow simulation method, based on the differential equation, the weak nonlinear evolution analysis of the fluctuation is carried out, and the variation law of the growth rate of disturbance instability with the inclination angle, evaporation effect, air flow shear force, Reynolds number and Weber number is obtained, including:

[0087] make Substitute into the differential equation, ignoring O(ε 2 )get:

[0088]

[0089] Among them, η represents the thickness of the liquid film after substitution, Represents η The differential of Represents η The differential of Represents η The second derivative of Represents η The fourth differential of

[0090] Make a substitution: represents the dimensionless liquid film flow direction coordinate after substitution, represents the dimensionless time after substitution, then:

[0091]

[0092] in, Represents η The differential of Represents η The differential of Represents η The second derivative of Represents η The fourth differential of

[0093] Considering the plate solution, that is, η≡0, we have:

[0094]

[0095] Given: Wherein, H<<1, i represents the imaginary unit, k represents the wave number, and ω represents the angular frequency;

[0096] Then we have:

[0097]

[0098] Then, the real part of ω is:

[0099]

[0100] Among them, ω r represents the real part of ω, which is used to characterize the instability growth rate.

[0101] The present invention has the following advantages:

[0102] The current calculation methods for liquid film flow only consider the flow through vertical or inclined rigid or flexible plates, pipes, etc. under the force of gravity. There is still a lack of theoretical and numerical research on the problem of small Reynolds number liquid film flow under the synergistic influence of gravity, airflow shear force, and evaporation effect. The present invention takes aircraft thermal protection as the background, considers the small Reynolds number liquid film flow law under the synergistic influence of gravity, airflow shear force, and evaporation effect, improves the traditional long wave theoretical research method to consider more factors affecting liquid film flow, and has the ability to analyze small Reynolds number liquid film flow under the synergistic influence of gravity, airflow shear force and evaporation effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 is a flow chart of a method for simulating a small Reynolds number liquid film flow in an embodiment of the present invention;

[0104] Figure 2 is a schematic diagram of a physical model in an embodiment of the present invention;

[0105] Figure 3 Schematic diagram of the effect of air flow shear force on the growth rate of liquid film fluctuation instability in an embodiment of the present invention;

[0106] Figure 4 It is a schematic diagram of the influence of an evaporation effect on the growth rate of liquid film fluctuation instability in an embodiment of the present invention. DETAILED DESCRIPTION

[0107] 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.

[0108] According to the current research status of liquid film flow, in view of the shortcomings of current liquid film flow that rarely considers the influence of gravity, airflow shear force trend and evaporation effect at the same time, for small Reynolds number liquid film flow, the long wave theory method is used to derive the differential equation describing the spatial evolution of liquid film thickness with time, and the weak nonlinear evolution analysis method of wave is used to analyze it, and the influence of airflow shear force, evaporation effect, Reynolds number, Weber number, etc. on the growth rate of wave instability is obtained.

[0109] Reference Figures 1-2 In this embodiment, the small Reynolds number liquid film flow simulation method includes:

[0110] S1, perform dimensionless processing on the parameters to obtain dimensionless parameters.

[0111] In this embodiment, the dimensionless processing flow of the parameters is as follows:

[0112] Introduce a small amount ε = h 0 / l. Among them, h 0 represents the initial liquid film thickness, and l represents the typical liquid-gas interface deformation wavelength.

[0113] The velocity of the surface of the undisturbed liquid layer is introduced 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.

[0114] Introducing Reynolds number Re = ρU 0 h 0 / μ.

[0115] Introduction of Weber number Among them, γ0 Represents the surface tension coefficient of the liquid film.

[0116] Based on ε, U 0 , Re and We, the flow direction coordinate x of the liquid film, the thickness direction coordinate y, the liquid film thickness h, the 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 dimensional processing to obtain dimensionless parameters:

[0117]

[0118] 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.

[0119] S2, for the flow of liquid film over an inclined rigid plate under the effects of gravity, air flow shear force and evaporation, give the corresponding mass equation a and momentum equation a.

[0120] In this embodiment, the expression of the mass equation a is as follows:

[0121]

[0122] The expression of momentum equation a is as follows:

[0123]

[0124] Where θ represents the angle between the liquid film flow direction and the horizontal direction.

[0125] S3, for the liquid film surface under the action of gravity, 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.

[0126] In this embodiment, the expression of the normal stress equilibrium condition a is as follows:

[0127]

[0128] Where J represents the mass jump flow rate of the liquid film caused by the interface phase change; ht 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, u x represents the partial differential of the velocity of the liquid film along the stream direction with respect to x, u y represents the partial differential of the velocity of the liquid film along the stream direction with respect to y,

[0129] The expression of shear stress equilibrium condition a is as follows:

[0130]

[0131] The expression of the wall no-slip boundary condition a is as follows:

[0132] u=0,v=0(y=0)···(5)

[0133] The expression of the boundary condition a of the liquid film surface motion is as follows:

[0134]

[0135] Where h(x,t) represents the rate of change of the liquid film thickness along the flow direction with time.

[0136] Preferably, the expression of the known J is as follows:

[0137]

[0138] ξ=1 / (Ku·Pr), Ku=ΔH / (C p ·ΔT), Pr=ν / a

[0139] 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 of 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, when ξ takes a positive value, it represents the condensation state, and when ξ takes a negative value, it represents the evaporation state.

[0140] For the material pneumatic heating surface, there are:

[0141]

[0142] Then, the simplified expression of J is as follows:

[0143]

[0144] Among them, q or represents the cold wall heat flux.

[0145] S4, based on the dimensionless parameters, the mass equation a, momentum equation a, normal stress balance condition a, shear stress balance condition a, wall no-slip boundary condition a and liquid film surface motion boundary condition a are respectively dimensionlessly processed to obtain the dimensionless mass equation b, momentum equation b, normal stress balance condition b, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b.

[0146] In this embodiment, the expression of the mass equation b is as follows:

[0147]

[0148] The expression of momentum equation b is as follows:

[0149]

[0150] The expression of normal stress equilibrium condition b is as follows:

[0151]

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

[0153]

[0154] The expression of the wall no-slip boundary condition b is as follows:

[0155]

[0156] The expression of the boundary condition b of the liquid film surface motion is as follows:

[0157]

[0158] Among them, J A and J B is the evaporation effect parameter,

[0159] S5, scale the Weber number We so that the scaled Weber magnitude is 1, substitute the scaled Weber number into the normal stress equilibrium condition b, and use magnitude analysis to ignore small quantities to obtain the normal stress equilibrium condition c.

[0160] In this embodiment, the Weber number We can be scaled as follows:

[0161]

[0162] in, represents the scaled Weber number, and O(1) means the magnitude is 1.

[0163] Then, the expression of the normal stress equilibrium condition c obtained by ignoring the small amount in the magnitude analysis is as follows:

[0164]

[0165] S6. Expand the dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film and the pressure inside the liquid film by a small amount ε (ε<<1), retain the zero-order and first-order quantities, substitute them into the mass equation b, momentum equation b, normal stress equilibrium condition c, shear stress equilibrium condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, simplify them, and obtain the zero-order solution and first-order solution of the velocity of the liquid film along the flow direction.

[0166] In this embodiment, the process of solving the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction is as follows:

[0167] The dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film, and the pressure inside the liquid film are expanded by a small amount ε:

[0168]

[0169] in, represents the dimensionless zero-order liquid film velocity along the stream direction, the normal velocity of the liquid film, and the pressure inside the liquid film. represents the dimensionless first-order liquid film velocity along the stream direction, the normal velocity of the liquid film, and the pressure inside the liquid film. O(ε 2 ) indicates the magnitude is ε 2 A small amount.

[0170] Will and Substitute into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, and perform the following simplification:

[0171]

[0172] in, express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of .

[0173] Based on equation (15), the zero-order solution of the velocity of the liquid film along the flow direction is obtained: and the first-order solution

[0174]

[0175] in, express right The differential of express right The mixed differential of express right The third differential of .

[0176] S7, integrate the mass equation b along the direction of the liquid film thickness, combine the wall no-slip boundary condition b and the liquid film surface motion boundary condition b, and substitute the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 to obtain the differential equation for the evolution of the liquid film thickness.

[0177] In this embodiment, the process of determining the differential equation is as follows:

[0178] Integrating the mass equation b along the thickness direction of the liquid film yields:

[0179]

[0180] q represents the flow rate:

[0181]

[0182] Substituting the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 into formula (18), we obtain:

[0183]

[0184] Substituting formula (19) into formula (17), we obtain the differential equation for the evolution of liquid film thickness:

[0185]

[0186] in, express right The fourth differential of .

[0187] S8, based on differential equations, the weak nonlinear evolution analysis of fluctuations is carried out, and the variation law of the growth rate of disturbance instability with the inclination angle, evaporation effect, airflow shear force, Reynolds number and Weber number is obtained.

[0188] In this embodiment, the process of analyzing the weak nonlinear evolution of fluctuations is as follows:

[0189] make Substitute into the differential equation, ignoring O(ε 2 )get:

[0190]

[0191] Among them, η represents the thickness of the liquid film after substitution, Represents η The differential of Represents η The differential of Represents η The second derivative of Represents η The fourth differential of .

[0192] Make a substitution: represents the dimensionless liquid film flow direction coordinate after substitution, represents the dimensionless time after substitution, then:

[0193]

[0194] in, Represents η The differential of Represents η The differential of Represents η The second derivative of Represents η The fourth differential of .

[0195] Considering the plate solution, that is, η≡0, we have:

[0196]

[0197] Given: Wherein, H<<1, i represents the imaginary unit, k represents the wave number, and ω represents the angular frequency.

[0198] Then we have:

[0199]

[0200] Then, the real part of ω is:

[0201]

[0202] Among them, ω r represents the real part of ω, which is used to characterize the instability growth rate.

[0203] S9, changing the magnitude of the evaporation effect and the airflow shear force in step S8, obtaining a curve of the change in the instability growth rate, and determining the influence of the evaporation effect and the airflow shear force on the growth rate of the instability of the liquid film wave transmission.

[0204] In this embodiment, given: U gg =10.0, J A =J B = 1.0, changing the magnitude of the airflow shear force in the differential equation, we can obtain the variation of the fluctuation instability growth rate with k, such as Figure 3 As shown. Further, given: τ g =0.0, J A =J B = J, changing the size of the evaporation effect in the differential equation: 0.1, 0.5, 1.0, 2.0, we get the fluctuation instability growth rate as k changes as follows Figure 4 shown.

[0205] 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.

[0206] 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 small Reynolds number liquid film flow, 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, give the corresponding mass equation a and momentum equation a; S3, for the liquid film surface under the action of gravity, 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, momentum equation a, normal stress balance condition a, shear stress balance condition a, wall no-slip boundary condition a and liquid film surface motion boundary condition a are respectively dimensionless processed to obtain the dimensionless mass equation b, momentum equation b, normal stress balance condition b, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b; S5, scaling the Weber number We so that the scaled Weber magnitude is 1, substituting the scaled Weber number into the normal stress equilibrium condition b, and using magnitude analysis to ignore small quantities, obtaining the normal stress equilibrium condition c; S6, expand the dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film and the pressure inside the liquid film respectively with a small amount ε, retain the zero-order and first-order quantities, substitute them into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, simplify them, and obtain the zero-order solution and first-order solution of the velocity of the liquid film along the flow direction; where ε<<1; S7, integrating the mass equation b along the direction of the liquid film thickness, combining the wall no-slip boundary condition b and the liquid film surface motion boundary condition b, and substituting the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 into the equation, to obtain a differential equation for the evolution of the liquid film thickness; S8, based on differential equations, weak nonlinear evolution analysis of fluctuations is performed to obtain the variation law of the growth rate of disturbance instability with the tilt angle, evaporation effect, air flow shear force, Reynolds number and Weber number; S9, changing the magnitude of the evaporation effect and the airflow shear force in step S8, obtaining a curve of the change in the instability growth rate, and determining the influence of the evaporation effect and the airflow shear force on the growth rate of the instability of the liquid film wave transmission.

2. The small Reynolds number 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 quantity ε = h0 / l, where h0 represents the initial liquid film thickness and l represents the typical liquid-gas interface deformation wavelength; 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; Introduction of Weber number Where γ0 represents the surface tension coefficient of the liquid film; Based on ε, U0, Re and We, the flow direction coordinate x, thickness direction coordinate y, film thickness h, and air flow shear force τ of the liquid film are calculated. 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 dimensional 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 method for simulating small Reynolds number liquid film flow according to claim 2, characterized in that: The expression of the mass equation a is as follows: The expression of 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 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, u x represents the partial differential of the velocity of the liquid film along the stream direction with respect to x, u y represents the partial differential of the velocity of the liquid film along the stream direction with respect to y, 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)···(5) 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.

4. The method for simulating small Reynolds number liquid film flow according to claim 3, 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, a represents the thermal diffusion coefficient; ξ represents the mass jump flow rate, when ξ takes a positive value, it represents the condensation state, and when ξ takes a negative value, it represents the evaporation state; for the pneumatic heating surface of the material, there are: Then, the simplified expression of J is as follows: Among them, q or represents the cold wall heat flux.

5. The method for simulating small Reynolds number liquid film flow according to claim 4, characterized in that: The expression of mass equation b is as follows: The expression of momentum equation b 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: The expression of the boundary condition b of the liquid film surface motion is as follows: Among them, J A and J B is the evaporation effect parameter, 6. The method for simulating small Reynolds number liquid film flow according to claim 5, characterized in that: The Weber number We is scaled as follows: in, represents the scaled Weber number, and O(1) means the magnitude is 1.

7. The method for simulating small Reynolds number liquid film flow according to claim 6, characterized in that: The expression of normal stress equilibrium condition c is as follows:

8. The method for simulating small Reynolds number liquid film flow according to claim 7, characterized in that: The dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film, and the pressure inside the liquid film are expanded with a small amount ε, respectively. After retaining the zero-order and first-order quantities, they are substituted into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b, and liquid film surface motion boundary condition b. After simplification, the zero-order solution and first-order solution of the velocity of the liquid film along the flow direction are obtained, including: The dimensionless velocity of the liquid film along the flow direction, the normal velocity of the liquid film, and the pressure inside the liquid film are expanded by a small amount ε: in, represents the dimensionless zero-order liquid film velocity along the stream direction, the normal velocity of the liquid film, and the pressure inside the liquid film. represents the dimensionless first-order liquid film velocity along the stream direction, the normal velocity of the liquid film, and the pressure inside the liquid film. O(ε 2 ) indicates the magnitude is ε 2 A small amount; Will and Substitute into the mass equation b, momentum equation b, normal stress balance condition c, shear stress balance condition b, wall no-slip boundary condition b and liquid film surface motion boundary condition b, and perform the following simplification: in, express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of express right The differential of Based on equation (15), the zero-order solution of the velocity of the liquid film along the flow direction is obtained: and the first-order solution in, express right The differential of express right The mixed differential of express right The third differential of .

9. The method for simulating small Reynolds number liquid film flow according to claim 8, characterized in that: The mass equation b is integrated along the direction of the liquid film thickness, combined with the wall no-slip boundary condition b and the liquid film surface motion boundary condition b, and the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 are substituted into the differential equation for the evolution of the liquid film thickness, including: Integrating the mass equation b along the thickness direction of the liquid film yields: q represents the flow rate: Substituting the zero-order solution and the first-order solution of the velocity of the liquid film along the flow direction obtained in step S6 into formula (18), we obtain: Substituting formula (19) into formula (17), we obtain the differential equation for the evolution of liquid film thickness: in, express right The fourth differential of .

10. The method for simulating small Reynolds number liquid film flow according to claim 9, characterized in that: Based on differential equations, the weak nonlinear evolution analysis of fluctuations is carried out, and the variation law of the growth rate of disturbance instability with the tilt angle, evaporation effect, air flow shear force, Reynolds number and Weber number is obtained, including: make Substitute into the differential equation, ignoring O(ε 2 )get: Among them, η represents the thickness of the liquid film after substitution, Represents η The differential of Represents η The differential of Represents η The second derivative of Represents η The fourth differential of Make a substitution: represents the dimensionless liquid film flow direction coordinate after substitution, represents the dimensionless time after substitution, then: in, Represents η The differential of Represents η The differential of Represents η The second derivative of Represents η The fourth differential of Considering the plate solution, that is, η≡0, we have: Given: Wherein, H<<1, i represents the imaginary unit, k represents the wave number, and ω represents the angular frequency; Then we have: Then, the real part of ω is: Among them, ω r represents the real part of ω, which is used to characterize the instability growth rate.

Images