Numerical simulation method for researching influence of ultrasonic parameters on whole process of cavitation effect

Abstract

The invention discloses a numerical simulation method for researching the influence of ultrasonic parameters on the whole process of a cavitation effect, which comprises the following steps: constructing a two-dimensional model subjected to grid division in Fluent, the two-dimensional model being a model in which an ultrasonic transducer is immersed in water; adding a mixture model and a cavitation model based on a gas-liquid two-phase flow continuity equation into Fluent, and obtaining a simulation result of the influence of ultrasonic parameters on cavitation bubbles based on the mixture model and the cavitation model; and based on a Keller-Miksis equation, analyzing in Matlab to obtain a simulation result of the influence of the ultrasonic parameters on the growth and fracture of the cavitation bubbles. According to the numerical simulation method provided by the invention, the influence of the ultrasonic parameters on the whole process of the cavitation effect can be explained, the influence of the ultrasonic parameters from bubble nucleus generation to growth to collapse can be summarized relatively completely, and the relationship between the ultrasonic parameters and the cavitation effect can be known more clearly.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of numerical simulation, and particularly relates to a numerical simulation method for studying the influence of ultrasonic parameters on the whole process of cavitation effect. BACKGROUND

[0002] With the in-depth research of ultrasonic technology in the medical field, the ultrasonic technology has evolved from a simple image diagnosis auxiliary tool to a treatment platform with both diagnosis and intervention treatment functions. The cavitation effect and thermal effect generated by the propagation of ultrasonic waves in biological tissues enable the ultrasonic technology to exhibit significant clinical application value in the precision medical field such as tumor ablation and transdermal drug delivery system.

[0003] The ultrasonic cavitation effect has been repeatedly proven to be the main mechanism of transdermal drug delivery and thermal ablation treatment. The effect is essentially the dynamic behavior of micron-sized bubbles generated in a liquid medium under the action of acoustic pressure, including bubble nucleation, bubble oscillation, and bubble collapse three stages, and releases a large amount of energy in the process. According to the kinetic characteristics, cavitation can be divided into steady-state cavitation and transient cavitation: steady-state cavitation is characterized by the periodic oscillation of bubble nuclei around the equilibrium radius in the ultrasonic field, contraction in the positive half cycle of acoustic pressure, and expansion in the negative half cycle. When the acoustic pressure exceeds the critical threshold, inertial cavitation occurs, the bubble expands and contracts violently until it collapses, generating local high temperature and high pressure, and releasing a shock wave.

[0004] Existing clinical studies have shown that, compared with high-frequency ultrasound (>0.7MHz), low-frequency ultrasound (20kHz~0.7MHz) has higher cavitation yield and better transdermal drug delivery efficacy, but its mechanism is still theoretically flawed. One of the theoretical defects is the limitation of clinical evaluation methods. The evaluation of cavitation effect in clinical research mainly relies on the observation of treatment effect, and lacks real-time and quantitative characterization means, which makes many clinical researchers have a shallow understanding of how ultrasonic parameters affect the theoretical mechanism of cavitation effect; the second is the defect of the existing calculation model. The model based on Rayleigh-Plesset equation and its improved form mainly simulates the dynamic behavior of pre-existing bubbles, including radius evolution and cavitation threshold, but the modeling of the initial key link of nucleation phase transition is not perfect, which leads to the inability to completely reconstruct the whole cycle process from the initial bubble nucleation to the growth and collapse of cavitation. This seriously restricts the in-depth study of how ultrasonic parameters (such as frequency) affect cavitation effect.

[0005] Therefore, it has become an urgent problem to propose a numerical simulation method that can explain the influence of ultrasonic parameters on the whole process of cavitation effect. SUMMARY

[0006] In order to solve the above problems in the prior art, the present application provides a numerical simulation method for studying the influence of ultrasonic parameters on the whole process of cavitation effect. The present application provides a numerical simulation method for studying the influence of ultrasonic parameters on the whole process of cavitation effect, which comprises: A two-dimensional model of an ultrasonic transducer immersed in water is constructed in Fluent; A mixture model and a cavitation model based on the continuity equation of gas-liquid two-phase flow are added in Fluent, and simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles are obtained based on the mixture model and the cavitation model, wherein the amplitude set in Fluent is unchanged; Based on the Keller-Miksis equation, simulation results of the influence of ultrasonic parameters on the growth and rupture of cavitation bubbles are obtained by analysis in Matlab, wherein the amplitude set in Matlab is unchanged.

[0007] In an embodiment of the present application, the two-dimensional model of the ultrasonic transducer immersed in water is constructed in Fluent, comprising: A two-dimensional model of an ultrasonic transducer immersed in water is constructed, and the grid of the two-dimensional model is divided to obtain a two-dimensional model of the ultrasonic transducer immersed in water; The two-dimensional model of the ultrasonic transducer immersed in water is imported into Fluent.

[0008] In an embodiment of the present application, the mixture model and the cavitation model based on the continuity equation of gas-liquid two-phase flow are added in Fluent, and simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles are obtained based on the mixture model and the cavitation model, comprising: The mixture model based on the continuity equation of gas-liquid two-phase flow is added in Fluent, and the Zwart-Gerber-Belamri cavitation model is added in the model setting interface of Fluent; A user-defined function is added to the emitting surface of the ultrasonic transducer to set a dynamic grid, so as to simulate the action of ultrasonic on liquid by using the displacement change of the emitting surface of the ultrasonic transducer; Different frequencies are set based on the user-defined function, the continuity equation of gas-liquid two-phase flow is solved according to the Zwart-Gerber-Belamri cavitation model, so as to obtain simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles.

[0009] In an embodiment of the present application, the continuity equation of gas-liquid two-phase flow is solved according to the Zwart-Gerber-Belamri cavitation model, so as to obtain simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles, comprising: A volume fraction equation is obtained according to a gas phase continuity equation in a gas-liquid two-phase flow continuity equation, and the volume fraction equation is expressed as: + . =

[0010] wherein, is a speed of evaporation or condensation, is a volume fraction of a gas phase, is a speed of the gas phase, is a density of the gas phase, is time, is divergence; A final source term expression is obtained according to the volume fraction equation; Based on the final source term expression, a relationship between pressure and a saturated vapor pressure is used to obtain evaporation and condensation rates, so as to obtain a simulation result of an influence of an ultrasonic parameter on a cavitation bubble.

[0011] In an embodiment of the present application, the final source term expression is obtained according to the volume fraction equation, and the final source term expression includes: A microelement volume Inside, a first equation is obtained according to a total mass of a bubble, and the first equation is expressed as: =

[0012] wherein, is a bubble number density, is a mass of a single bubble; A first source term expression is obtained according to the first equation and the volume fraction equation, and the first source term expression is expressed as:

[0013] A second equation is obtained according to , and the second equation is expressed as: =

[0014] wherein, is a volume; A second source term expression is obtained according to the first source term expression and the second equation, and the second source term expression is expressed as:

[0015] The second source term expression and A final source term expression is obtained, which is expressed as:

[0016] wherein, is an empirical coefficient, is the density of the liquid phase, is the pressure, is the saturated vapor pressure.

[0017] In an embodiment of the present application, based on the final expression of the source term, the evaporation rate and the condensation rate are obtained according to the relationship between the pressure and the saturated vapor pressure , comprising: if the pressure is less than the saturated vapor pressure , evaporation is obtained to obtain the evaporation rate; if the pressure is greater than the saturated vapor pressure , condensation is obtained to obtain the condensation rate.

[0018] In an embodiment of the present application, the evaporation rate is expressed as:

[0019] wherein, is the evaporation rate, is the evaporation coefficient; the condensation rate is expressed as:

[0020] wherein, is the condensation rate, is the condensation coefficient.

[0021] In an embodiment of the present application, based on the Keller-Miksis equation, simulation results of the influence of ultrasonic parameters on the growth and rupture of cavitation bubbles are obtained by analysis in Matlab, comprising: in Matlab, the Keller-Miksis equation is established based on the radius of the bubble, the rate of change of the radius of the bubble with time and the acceleration of the change of the radius of the bubble with time; a first-order linear differential equation constructed according to the Keller-Miksis equation is used to obtain the relationship between the bubble radius ratio and time based on a preset condition, wherein the preset condition is that the bubble radius at the initial moment is the bubble initial radius and the bubble change rate is 0; in a preset time period, the relationship between the bubble radius ratio and time obtaining a maximum bubble radius ratio according to the relationship between the bubble initial radius and the maximum bubble radius ratio, and obtaining the cavitation threshold according to the maximum bubble radius ratio under the current pressure amplitude condition; obtaining a maximum bubble radius ratio according to the relationship between the bubble initial radius and the maximum bubble radius ratio, and obtaining the cavitation threshold according to the maximum bubble radius ratio under the current pressure amplitude condition;

[0022] In an embodiment of the present application, the Keller-Miksis equation is expressed as:

[0023] wherein, R is the radius of the bubble, is the rate of change of the bubble radius with respect to time, is the acceleration of the bubble radius with respect to time, c is the sound speed of the liquid, is the density of the liquid, is the external pressure of the bubble, is the time; The external pressure of the bubble is expressed as:

[0024] wherein, P is the hydrostatic pressure, R0 is the initial radius of the bubble, P0 is the saturated vapor pressure, K is a multi-party index, μ is a viscosity coefficient, is a tension coefficient of the liquid surface, is a time-varying pressure generated due to the action of ultrasound, , is the pressure amplitude, , is the frequency, is the amplitude.

[0025] In an embodiment of the present application, the cavitation threshold under the current pressure amplitude condition is obtained according to the maximum bubble radius ratio under the current pressure amplitude condition, comprising: judging the relationship between the maximum bubble radius ratio and a set value, if the maximum bubble radius ratio is greater than or equal to the set value, setting the current pressure amplitude as the cavitation threshold, if the maximum bubble radius ratio is less than the set value, updating the current pressure amplitude as , until the maximum bubble radius ratio is greater than or equal to the set value, obtaining the cavitation threshold.

[0026] Compared with the prior art, the present application has the following beneficial effects: The numerical simulation method provided by the application firstly constructs a two-dimensional model immersed in water for an ultrasonic transducer in Fluent, then adds a mixture model and a cavitation model based on the continuity equation of gas-liquid two-phase flow in Fluent, and obtains simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles based on the mixture model and the cavitation model, and then obtains simulation results of the influence of ultrasonic parameters on the growth and collapse of cavitation bubbles by analysis in Matlab based on the Keller-Miksis equation, wherein the amplitude set in Fluent and Matlab is unchanged. Therefore, the numerical simulation method provided by the application can explain the influence of ultrasonic parameters on the whole process of cavitation effect, can more completely summarize the influence of ultrasonic parameters (such as ultrasonic frequency) from bubble nucleation to growth to collapse, and is helpful for more clearly understanding the relationship between ultrasonic parameters and cavitation effect.

[0027] The application will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 is a flow chart of a numerical simulation method for studying the influence of ultrasonic parameters on the whole process of cavitation effect provided by an embodiment of the application; Figure 2 is a flow chart of another numerical simulation method for studying the influence of ultrasonic parameters on the whole process of cavitation effect provided by an embodiment of the application; Figure 3 is a flow chart of a method for solving a cavitation threshold provided by an embodiment of the application; Figure 4 is a situation and two-dimensional model grid division diagram provided by an embodiment of the application, Figure 4 wherein figure (a) is a single-frequency ultrasonic transducer emitting sound waves into water, and figure (b) is a two-dimensional model grid division diagram; Figure 5 is a gas phase volume fraction diagram provided by an embodiment of the application, Figure 5 wherein figure (a) is 80kHz 125μs, figure (b) is 400kHz 25μs, and figure (c) is 2MHz 5μs; Figure 6 is a mass transfer rate diagram provided by an embodiment of the application, Figure 6 wherein figure (a) is 80kHz 125μs, figure (b) is 400kHz 25μs, and figure (c) is 2MHz 5μs; Figure 7 is a diagram of bubble radius ratio changing with initial bubble radius under different ultrasonic frequencies provided by an embodiment of the application; Figure 8A graph showing the change of the cavitation threshold with the initial radius of the bubble under different ultrasonic frequencies is provided for the embodiment of the present application. DETAILED DESCRIPTION

[0029] In order to further illustrate the technical means and effects adopted by the present application to achieve the predetermined object, a numerical simulation method for researching the influence of ultrasonic parameters on the whole process of cavitation effect is described in detail below in combination with the drawings and specific embodiments.

[0030] The foregoing and other technical contents, features and effects of the present application can be clearly presented in the detailed description of the specific embodiments below in combination with the drawings. Through the description of the specific embodiments, the technical means and effects adopted by the present application to achieve the predetermined object can be understood more deeply and specifically. However, the accompanying drawings are provided for reference and illustration only, and are not used to limit the technical solutions of the present application.

[0031] Please refer to Figure 1 and Figure 2 , Figure 1 is a flowchart of a numerical simulation method for researching the influence of ultrasonic parameters on the whole process of cavitation effect provided by the embodiment of the present application, Figure 2 is a flowchart of another numerical simulation method for researching the influence of ultrasonic parameters on the whole process of cavitation effect provided by the embodiment of the present application. The present application proposes a numerical simulation method for researching the influence of ultrasonic parameters on the whole process of cavitation effect, which includes the following steps: Step 1, constructing a two-dimensional model divided by a grid in Fluent, wherein the two-dimensional model is a model of an ultrasonic transducer immersed in water.

[0032] In one specific embodiment, step 1 can include: Step 1.1, constructing a two-dimensional model of an ultrasonic transducer immersed in water, and dividing the grid of the two-dimensional model to obtain a two-dimensional model divided by a grid.

[0033] Here, the grid is in the form of a quadrilateral cell.

[0034] Here, the ultrasonic transducer is a single-frequency ultrasonic transducer.

[0035] Step 1.2, importing the two-dimensional model divided by a grid into Fluent.

[0036] Step 2, adding a mixture model and a cavitation model based on the continuity equation of two-phase flow in Fluent, and obtaining the simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles based on the mixture model and the cavitation model, wherein the amplitude set in Fluent is unchanged.

[0037] Here, the cavitation model is the Zwart-Gerber-Belamri cavitation model.

[0038] In one specific embodiment, step 2 can include: Step 2.1, adding a mixture model based on the two-phase flow continuity equation in Fluent and adding the Zwart-Gerber-Belamri cavitation model in the model setting interface in Fluent.

[0039] Here, the gas-liquid two-phase flow continuity equation is shown in formulas (1), (2) and (3): . (1) . (2) (3) wherein the source term is the speed of evaporation or condensation of a certain phase, is the volume fraction of the gas phase, is the density of the gas phase, is the speed of the gas phase, is the volume fraction of the liquid phase, is the density of the liquid phase, is the speed of the liquid phase, is the volume fraction of the gas-liquid mixed phase, is the density of the gas-liquid mixed phase, is the speed of the gas-liquid mixed phase, is time, is divergence.

[0040] The relationship between , is expressed by formula (4), and formulas (5) and (6) are respectively used to calculate the gas-liquid mixed phase density and the mixture viscosity : (4) (5) (6) In this embodiment, it is assumed in the Zwart-Gerber-Belamri cavitation model that all the bubbles in the system have the same radius.

[0041] Step 2.2, adding a user-defined function (UDF, User Defined Function) to the emitting surface of the ultrasonic transducer to set a dynamic mesh to simulate the effect of ultrasound on the liquid by using the displacement change of the emitting surface of the ultrasonic transducer.

[0042] Here, the displacement of the emitting surface of the ultrasonic transducer Over time The changes are shown in formula (7): (7) in, This refers to the amplitude, or displacement amplitude. For frequency, it can be changed by frequency The effect of simulated ultrasonic frequency on simulation results.

[0043] Step 2.3: Based on user-defined functions, set different frequencies and solve the two-phase flow continuity equation according to the Zwart-Gerber-Belamri cavitation model to obtain simulation results of the influence of ultrasonic parameters on cavitation bubble generation.

[0044] Specifically, when studying the effect of frequency on simulation results, the amplitude is kept constant, and then a frequency is set through a user-defined function. This allows us to obtain simulation results of the effect of a certain ultrasonic parameter frequency on the generation of cavitation bubbles. By adjusting the frequency in the user-defined function, we can obtain various simulation results and analyze the effect of frequency on the generation of cavitation bubbles.

[0045] Step 2.31: Obtain the volume fraction equation based on the gas phase continuity equation in the gas-liquid two-phase flow continuity equation.

[0046] Specifically, the volume fraction equation can be obtained from the continuity equation of the gas phase when there is interphase mass transfer. That is, by transforming the mass equation (i.e., Formula 1) in the continuity equation of gas-liquid two-phase flow, the volume fraction equation can be obtained.

[0047] + . = (8) Formula (8) is the volume fraction equation.

[0048] Step 2.32: Obtain the final source term expression based on the volume fraction equation.

[0049] Step 2.321, Infinite Element Volume The first equation is derived from the total mass of the bubbles.

[0050] Specifically, establishing the relationship from the microscopic to the macroscopic, in the micro-element volume. Inside, set If the mass of a single bubble is given, then the volume... The total mass of the gas phase is: , For infinitesimal volume The total number of bubbles inside, thus the first equation can be obtained, which is expressed as: (9) wherein, is the bubble number density, is the mass of a single bubble.

[0051] Step 2.322, the first source term expression is obtained according to the first equation and the volume fraction equation.

[0052] Specifically, the material derivative of the first equation is obtained as , and then is brought into the volume fraction equation to obtain the first source term expression.

[0053] (10) wherein, formula (10) is the first source term expression.

[0054] Step 2.323, the second equation is obtained according to .

[0055] In this embodiment, the simplified linear R-P (Rayleigh-Plesset) equation is used to obtain .

[0056] Specifically, the volume change rate , wherein, is the average value of the bubble radius, is the change rate of the bubble radius with time, that is, the derivative of the bubble radius at the current moment. Thus, the second equation is obtained according to .

[0057] = (11) wherein, formula (11) is the second equation.

[0058] Step 2.324, the second source term expression is obtained according to the first source term expression and the second equation.

[0059] (12) wherein, formula (12) is the second source term expression.

[0060] Step 2.325, the final source term expression is obtained according to the second source term expression and . ​​​​

[0061] Here, the final source term expression is expressed as: (13) where, is an empirical coefficient, is the pressure, the bubble pressure obtained by the simplified linear R-P, is the saturated vapor pressure.

[0062] Step 2.33, based on the final expression of the source term, the evaporation rate and condensation rate are obtained according to the relationship between the pressure and the saturated vapor pressure to obtain the simulation results of the influence of the ultrasonic parameters on the generation of cavitation bubbles.

[0063] Specifically, if the pressure is less than the saturated vapor pressure , evaporation (liquid phase to gas phase) occurs, and the evaporation rate is obtained, which is expressed as: (14) where, is the evaporation rate, is the evaporation coefficient.

[0064] If the pressure is greater than the saturated vapor pressure , condensation (gas phase to liquid phase) occurs, and the condensation rate is obtained, which is expressed as: (15) where, is the condensation rate, is the condensation coefficient.

[0065] Because the pressure is equal to the saturated vapor pressure , neither evaporation nor condensation occurs, it is easier to generate bubbles when the pressure is less than the saturated vapor pressure , and it is not easy to generate bubbles when the pressure is greater than the saturated vapor pressure . Therefore, when analyzing the influence of the frequency of ultrasound on the generation of cavitation bubbles, the amplitude is fixed, the frequency is adjusted, and the simulation of the generation of cavitation bubbles by ultrasound is realized by the change of the frequency. Therefore, the influence of the frequency on the generation of cavitation bubbles can be analyzed by comparing the results of different frequencies.

[0066] Through simulation, the gas volume fraction distribution, mass transfer rate, pressure and other factors at a certain moment can be obtained.

[0067] Step 3, based on the Keller-Miksis equation, simulation results of the influence of ultrasonic parameters on the growth and collapse of cavitation bubbles are obtained by analysis in Matlab, wherein the amplitude set in Matlab is unchanged.

[0068] In one specific embodiment, step 3 can include: Step 3.1, in Matlab, the Keller-Miksis equation is established based on the radius of the bubble, the rate of change of the radius of the bubble with time, and the acceleration of the change of the radius of the bubble with time.

[0069] Here, the Keller-Miksis equation is expressed as: (16) Wherein, R is the radius of the bubble, is the rate of change of the radius of the bubble with time, is the acceleration of the change of the radius of the bubble with time, c is the sound speed of the liquid, is the external pressure of the bubble, is obtained based on the improved R-P equation (Keller-Miksis).

[0070] Here, the external pressure of the bubble is expressed as: (17) Wherein, is the hydrostatic pressure, is the initial radius of the bubble, is the saturated vapor pressure, K is a multi-party index, μ is a viscosity coefficient, is a tension coefficient of the liquid surface, is a time-varying pressure generated due to ultrasonic action.

[0071] Here, the time-varying pressure generated due to ultrasonic action is expressed as: (18) Wherein, is the pressure amplitude.

[0072] Here, the pressure amplitude is expressed as: (19) In this embodiment, in order to ensure consistency with the Fluent simulation conditions of step 1 and step 2, the pressure amplitude The relationship between the frequency and the displacement amplitude A is shown in equation (19). When the effect of the frequency on the growth and collapse of the bubble needs to be determined, the amplitude in Matlab is set to be constant.

[0073] Step 3.2, based on a preset condition, a first-order linear differential equation is constructed according to the Keller-Miksis equation to obtain the relationship between the bubble radius ratio and time , wherein the preset condition is that the bubble radius at the initial moment is the initial bubble radius , and the bubble change rate is 0.

[0074] Specifically, in this step, the Keller-Miksis equation shown in equation (4) is converted into the form of a first-order linear differential equation, as shown in equations (20) and (21) in the following formula, and the preset condition is set, as shown in equation (22). Equations (20), (21) and (22) are respectively represented as: (20) (21) (22) wherein is a variable, and is a bubble radius change rate, represents a function about , and .

[0075] Based on equations (17), (18) and (19), the ordinary differential equation solver (ode45) is used to solve equations (20), (21) and (22), so as to obtain the relationship between the bubble radius ratio and time at the current moment, the bubble radius ratio is the ratio of the bubble radius to the initial radius , that is, .

[0076] Step 3.3, based on the relationship between all bubble radius ratios and time in a preset time period, the maximum bubble radius ratio is obtained, and the cavitation threshold is obtained according to the maximum bubble radius ratio under the current pressure amplitude condition (the cavitation threshold referred to hereinafter refers to the inertial cavitation threshold).

[0077] Specifically, at the initial moment, an initial pressure amplitude is set, which is a small value, for example, 1e4. According to step 3.2, the relationship between all bubble radius ratios and time in a preset time period can be obtained, and then the maximum bubble radius is found to obtain the maximum bubble radius ratio, that is Finally, under the current pressure amplitude condition, the cavitation threshold under the current sound pressure condition is obtained according to the maximum bubble radius ratio.

[0078] It should be noted that the preset time period is not specifically limited in this embodiment, and can be set according to specific needs by those skilled in the art, for example, the preset time period is set to 1s.

[0079] In a specific embodiment, under the current pressure amplitude condition, the cavitation threshold under the current sound pressure condition is obtained according to the maximum bubble radius ratio, including: Under the current pressure amplitude condition, the relationship between the maximum bubble radius ratio and the set value is judged, if the maximum bubble radius ratio is greater than or equal to the set value, the current pressure amplitude is set as the cavitation threshold, if the maximum bubble radius ratio is less than the set value, the current pressure amplitude is updated as Then return to step 3.1 until the obtained maximum bubble radius ratio is greater than or equal to the set value, until the cavitation threshold is obtained, and the specific process is as shown in Figure 3

[0080] Optionally, the set value is 2.

[0081] Step 3.5, based on different frequencies, the relationship between the maximum bubble radius ratio and the bubble initial radius and the plurality of cavitation thresholds are obtained to obtain the simulation results of the influence of the ultrasonic parameters on the growth and rupture of cavitation bubbles.

[0082] Specifically, when analyzing the influence of frequency on the growth and rupture of cavitation bubbles, the amplitude in Matlab is set to be unchanged, then by setting different frequencies, the relationship between the maximum bubble radius ratio and the bubble initial radius and the cavitation threshold under different frequencies are obtained, thereby analyzing the simulation results of the influence of different frequencies on the growth, oscillation and rupture of cavitation bubbles. According to the change of the maximum bubble radius ratio, the influence of frequency on the degree of bubble oscillation can be analyzed, the greater the maximum bubble radius ratio, the more violent the bubble oscillation; the higher the cavitation threshold, the more difficult it is to occur inertial cavitation and the more difficult it is to make the bubble rupture, thereby according to the size of the cavitation threshold, the influence of different ultrasonic frequencies on the rupture of bubbles in the later cavitation is analyzed, for example, the cavitation thresholds obtained by two different frequencies are compared, the party with the high cavitation threshold is difficult to occur inertial cavitation to make the bubble rupture, and the party with the low cavitation threshold is easy to occur inertial cavitation to make the bubble rupture.

[0083] The application will be further described in combination with specific examples.

[0084] Figure 4 ​Figures and two-dimensional model grid diagrams in the scenario of exploring the influence of ultrasonic frequency on cavitation bubbles in the embodiments of the present application, wherein CD, DE, EF are the boundaries of the ultrasonic transducer in contact with water, and DE is the emission surface of the ultrasonic transducer. The multiphase flow model is set to Mixture, the cavitation model is set to Zwart-Gerber-Belamri model, and the viscosity model is set to standard k-epsilon (2 eqn) model. The fixed displacement amplitude is 5 um, the same amplitude is imported, the frequency f of the displacement function source file is respectively 80 kHz, 400 kHz, and 2 MHz, the dynamic mesh is set on the emission surface DE of the ultrasonic transducer and the displacement function is imported, the appropriate solver is selected, the standard initialization is performed, and the cloud diagram such as the gas phase volume fraction distribution and the mass transfer rate is set in advance in the result. The time step is defined as T / 25 (2e-8s, 1e-7s, and 2e-6s corresponding to 20 kHz, 400 kHz, and 2 MHz respectively), the time step number is 250 steps (running for 10 cycles), and the maximum iteration number / time step is set to 30.

[0085] Figure 5 Figure 6 The gas phase volume fraction and mass transfer rate under different frequencies are calculated. Figure 5 Figures (a), (b), and (c) in Figure 6 Figures (a), (b), and (c) inThe gas phase volume fraction distribution range from large to small: 2MHz > 400kHz > 80kHz, and the mass transfer rate range and intensity from large to small: 2MHz > 400kHz > 80kHz. Thus, it can be concluded that when the displacement amplitude is consistent, within a certain frequency range, the greater the frequency, the more intense the reaction from liquid phase to gas phase, which is more conducive to the generation of bubble nucleus.

[0086] Regarding the influence of ultrasonic frequency on bubble growth and rupture, the Keller-Miksis equation is constructed in Matlab, the frequency f is selected to be 80 kHz, 400 kHz, and 2 MHz respectively, and the ratio of is 1:5:25. The ode45 solver is called for calculation. Figure 7 is the calculated relationship diagram of the maximum bubble radius ratio with the change of the initial bubble radius under different frequencies. From Figure 7 Within a certain range, when the initial bubble radius is the same, the lower the frequency, the greater the change of the bubble radius.

[0087] The relationship between the cavitation threshold and the initial bubble radius under different frequencies is calculated based on the bubble radius ratio-time relationship diagram, as shown in Figure 8It can be seen that, in a certain initial radius range, the cavitation threshold of 400 kHz is slightly smaller than that of 80 kHz in most cases, but the difference is not large; compared with the two, the cavitation threshold of 2 MHz is much larger, which also shows that, under the same conditions, it is more difficult for high-frequency ultrasound to cause inertial cavitation, and low-frequency ultrasound is more suitable for cavitation.

[0088] From the simulation, it can be concluded that, in a certain frequency range, when the displacement amplitude is the same (the excitation voltage is the same), the higher the ultrasonic frequency, the more bubbles are generated, but it is not conducive to the growth and collapse of bubbles in the later stage; and the lower the ultrasonic frequency, although the bubble generation is not as good as that of high-frequency ultrasound, the growth of bubbles is more violent, and cavitation is more likely to occur.

[0089] The present application provides a numerical simulation method for studying the influence of ultrasonic parameters (including but not limited to ultrasonic frequency) on cavitation effect, which first explores the influence of ultrasonic on the generation of cavitation bubbles based on the Zwart-Gerber-Belamri cavitation model, and then analyzes the influence of ultrasonic on the growth and collapse of pre-existing cavitation bubbles in combination with the Keller-Miksis equation. The combination of the two can more completely summarize the influence of ultrasonic parameters (such as frequency) on the whole process of cavitation effect (from bubble nucleus generation to growth and collapse), and also enables clinical researchers to have a deeper understanding of the ultrasonic cavitation effect and its influencing parameters, which has certain scientific significance and application value for the application of ultrasonic cavitation effect in clinical medical treatment.

[0090] It should be noted that the terms "first", "second", and the like are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the application described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the above exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are only examples of devices and methods consistent with some aspects of the present application.

[0091] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" means that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present application.

[0092] Although the present application has been described in connection with the various embodiments thereof, those of ordinary skill in the art will understand and appreciate the modifications and / or additions which can be made thereto without departing from the scope of the present application as set forth in the appended claims. In the description of the present application, the word "comprising" does not exclude other components or steps, the word "a" or "an" does not exclude a plurality, and the word "one" does not exclude a plurality, unless expressly stated otherwise. Furthermore, it is understood that where the description indicates certain acts might be performed in different embodiments, this does not necessarily mean they are mutually exclusive.

[0093] The above description is further detailed in connection with specific preferred embodiments of the present application, and it is not to be construed that the specific implementation of the present application is limited to these descriptions. For those of ordinary skill in the art, without departing from the concept of the present application, a number of simple deductions or replacements can be made, which should be considered as falling within the protection scope of the present application.

Claims

1. A numerical simulation method for studying the influence of ultrasonic parameters on the entire process of cavitation, characterized in that, The numerical simulation method includes: A meshed two-dimensional model is constructed in Fluent, which is a model of an ultrasonic transducer immersed in water; Add a mixture model and a cavitation model based on the gas-liquid two-phase flow continuity equation in Fluent, and obtain simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles based on the mixture model and the cavitation model, wherein the amplitude set in Fluent remains unchanged. Based on the Keller-Miksis equation, simulation results of the influence of ultrasonic parameters on the growth and collapse of cavitation bubbles were obtained through analysis in Matlab, where the amplitude was kept constant in Matlab.

2. The numerical simulation method according to claim 1, characterized in that, Building a meshed 2D model in Fluent includes: A two-dimensional model of an ultrasonic transducer immersed in water is constructed, and the two-dimensional model is meshed to obtain a meshed two-dimensional model. Import the meshed 2D model into Fluent.

3. The numerical simulation method according to claim 1, characterized in that, Add a mixture model and a cavitation model based on the gas-liquid two-phase flow continuity equation in Fluent, and obtain simulation results of the influence of ultrasonic parameters on cavitation bubble generation based on the mixture model and the cavitation model, including: Add a mixture model based on the gas-liquid two-phase flow continuity equation in Fluent and add a Zwart-Gerber-Belamri cavitation model in the model settings interface in Fluent. Add a user-defined function to the emitting surface of the ultrasonic transducer to set a dynamic mesh, so as to simulate the effect of ultrasound on liquid by utilizing the displacement change of the emitting surface of the ultrasonic transducer; By setting different frequencies based on the user-defined function, and solving the gas-liquid two-phase flow continuity equation according to the Zwart-Gerber-Belamri cavitation model, simulation results of the influence of ultrasonic parameters on cavitation bubble generation are obtained.

4. The numerical simulation method according to claim 3, characterized in that, The continuity equation for the gas-liquid two-phase flow was solved using the Zwart-Gerber-Belamri cavitation model to obtain simulation results of the influence of ultrasonic parameters on the generation of cavitation bubbles, including: The volume fraction equation is derived from the gas-phase continuity equation in the gas-liquid two-phase flow continuity equation, and is expressed as follows: + . = in, The rate of evaporation or condensation. This represents the volume fraction of the gas phase. For the velocity of the gas phase, The density of the gas phase. For time, For divergence; The final source term expression is obtained from the volume fraction equation; Based on the final expression of the source term, according to pressure and saturated vapor pressure The relationship between evaporation rate and condensation rate was obtained to simulate the effect of ultrasonic parameters on cavitation bubble generation.

5. The numerical simulation method according to claim 4, characterized in that, The final expression for the source term is obtained from the volume fraction equation, including: Infinite element volume Within this equation, based on the total mass of the bubbles, we obtain the first equation, which is expressed as: = in, The bubble number density, The mass of a single bubble; Based on the first equation and the volume fraction equation, the first source term expression is obtained, which is expressed as: according to We obtain the second equation, which is expressed as: = in, For volume; Based on the first source term expression and the second equation, the second source term expression is obtained, which is expressed as follows: According to the second source term expression and The final source term expression is obtained, which is represented as: in, This is an empirical coefficient. The density of the liquid phase, For pressure, It is the saturated vapor pressure.

6. The numerical simulation method according to claim 5, characterized in that, Based on the final expression of the source term, according to pressure and saturated vapor pressure The relationship between evaporation rate and condensation rate is used to obtain the following: If the pressure Less than the saturated vapor pressure If the evaporation occurs, the evaporation rate is obtained. If the pressure Greater than the saturated vapor pressure If condensation occurs, the condensation rate is obtained.

7. The numerical simulation method according to claim 6, characterized in that, The evaporation rate is expressed as: in, Evaporation rate The coefficient of evaporation; The condensation rate is expressed as: in, For condensation rate, The coefficient of condensation.

8. The numerical simulation method according to claim 1, characterized in that, Based on the Keller-Miksis equation, simulation results of the influence of ultrasonic parameters on the growth and collapse of cavitation bubbles were obtained through analysis in Matlab, including: In Matlab, the Keller-Miksis equation is established based on the bubble radius, the rate of change of the bubble radius over time, and the acceleration of the bubble radius over time. Based on preset conditions, the bubble radius ratio and time are obtained from the first-order linear differential equation constructed according to the Keller-Miksis equation. The relationship is that the preset condition is that the bubble radius at the initial moment is the bubble initial radius. The rate of change of bubbles is 0; Within a preset time period, based on all bubble radius ratios and time... The relationship is used to obtain the maximum bubble radius ratio, and under the current pressure amplitude condition, the cavitation threshold is obtained based on the maximum bubble radius ratio; Based on different frequencies, the relationship between the maximum bubble radius ratio and the initial bubble radius, as well as multiple cavitation thresholds, were obtained to simulate the influence of ultrasonic parameters on the growth and collapse of cavitation bubbles.

9. The numerical simulation method according to claim 8, characterized in that, The Keller-Miksis equation is expressed as: in, Where is the radius of the bubble. This represents the rate of change of the bubble radius over time. Let be the acceleration of the bubble radius as a function of time. c The speed of sound in a liquid. The density of the liquid, The external pressure of the bubble. For time; The external pressure of the bubble is expressed as: in, For hydrostatic pressure, Let be the initial radius of the bubble. It is the saturated vapor pressure. K For multiple indices, μ The viscosity coefficient is... The surface tension coefficient of the liquid is denoted as . The time-varying pressure caused by ultrasonic action. , For pressure amplitude, , For frequency, The amplitude is denoted as .

10. The numerical simulation method according to claim 8, characterized in that, Under the current pressure amplitude conditions, the cavitation threshold under the current pressure amplitude conditions is obtained based on the maximum bubble radius ratio, including: The relationship between the maximum bubble radius ratio and a set value is determined. If the maximum bubble radius ratio is greater than or equal to the set value, the current pressure amplitude is set to the cavitation threshold. If the maximum bubble radius ratio is less than the set value, the current pressure amplitude is updated to [the set value]. The process continues until the maximum bubble radius ratio is greater than or equal to the set value, at which point the cavitation threshold is obtained.

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