A numerical simulation method, device, equipment and medium for laser cavitation bubbles

Abstract

The present application discloses a method, device, equipment and medium for numerical simulation of laser cavitation bubbles, which relates to the field of laser cavitation technology, including: in the process of root canal washing using a jet generated by laser injection into a water body, using the current velocity vector of the fluid to update the current apparent density of the fluid; updating the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the current apparent density and the input energy of the laser; the mass flux is the mass flux of the fluid vaporized at high temperature due to laser injection into the water body; the current velocity vector, the current gas-liquid phase function and the current mass flux are input into a coupling relationship to update the current vortex vector, the current velocity vector and the current gas-liquid phase function of the fluid, so as to realize the numerical simulation of laser cavitation bubbles by combining the input energy of the laser, the mass flux of the fluid vaporized at high temperature due to laser injection into the water body, and the gas-liquid two-phase flow, thereby realizing the simulation and optimization of the root canal cleaning technology.

Description

Technical Field

[0001] The invention relates to the technical field of laser cavitation, and in particular to a numerical simulation method, device, equipment and medium for laser cavitation bubbles. Background Art

[0002] Regarding the root canal flushing problem, with the rapid development of laser cavitation technology in recent years, the principle of root canal flushing is to inject energy into the water body through high-frequency pulse laser, instantly generate high temperature, and locally vaporize the water body, thereby generating a large number of tiny bubbles. The bubble groups collide with each other, breaking and inducing jets, and then using the hydrodynamic force generated by the jet to clean the root canal. However, the laser cavitation problem involves laser energy injection and phase change of gas-liquid two-phase flow. In view of the traction of industrial demand, how to independently develop a numerical simulation method for laser cavitation bubbles and then realize the simulation of root canal cleaning technology is a problem that needs to be solved. Summary of the invention

[0003] In view of this, the purpose of the present invention is to provide a numerical simulation method, device, equipment and medium for laser cavitation bubbles, which can link the input energy of the laser, the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body, and the gas-liquid two-phase flow, realize the numerical simulation of laser cavitation bubbles, and then realize the simulation and optimization of root canal cleaning technology. The specific scheme is as follows:

[0004] In a first aspect, the present application provides a numerical simulation method for laser cavitation bubbles, comprising:

[0005] In the process of root canal flushing using the jet generated by laser injection into water, the current apparent density of the fluid is updated using the current velocity vector of the fluid to obtain an updated current apparent density;

[0006] The current mass flux is updated based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body;

[0007] The current velocity vector, the current gas-liquid phase function and the updated current mass flux are input into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and the current gas-liquid phase function is updated using the updated current mass flux and the updated current velocity vector to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function.

[0008] Optionally, the updating of the current apparent density of the fluid by using the current velocity vector of the fluid to obtain the updated current apparent density includes:

[0009] Determine the apparent density at the next moment by using the current velocity vector and the current displacement vector of the fluid and based on the apparent density of the fluid at the current moment, so as to update the current apparent density to obtain an updated current apparent density; wherein the apparent density at the initial moment is a density determined according to the density of water and water vapor and the current gas-liquid phase function;

[0010] And, the updated formula for the apparent density includes: ; t represents time, represents the apparent density, represents the displacement vector, represents the velocity vector; and the updated formula for the apparent density uses the Einstein summation convention, Indicates three different directions.

[0011] Optionally, the updating of the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux includes:

[0012] Using the law of conservation of energy and based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density, the input energy of the laser and the current mass flux, the current temperature of the fluid is updated to obtain the updated current temperature;

[0013] The current mass flux is updated using the updated current temperature and the apparent thermal conductivity of the fluid to obtain an updated current mass flux; wherein the apparent thermal conductivity is a thermal conductivity determined according to the thermal conductivity of water and water vapor and the current gas-liquid phase function.

[0014] Optional, temperature update formula, including:

[0015] ;

[0016] ; ;

[0017] in, represents the apparent density, T represents the temperature, t represents the time, represents the displacement vector, represents the velocity vector, represents the apparent specific heat capacity, p represents the fluid pressure, represents the gas-liquid phase function, represents the apparent thermal conductivity, represents the mass flux, It represents the energy injected by laser into water per unit volume and per unit time. Indicated in The pulse function is not zero at is a distance vector, representing any position in space, Indicated in The input energy at , R is the gas constant of water vapor, is the specific heat capacity of water, represents the specific heat capacity of water vapor;

[0018] And, the updated formula for mass flux includes: ; represents the latent heat of gas-liquid phase change; the updated formulas for temperature and mass flux both use the Einstein summation convention, Indicates three different directions.

[0019] Optionally, the current velocity vector, the current gas-liquid phase function and the updated current mass flux are input into a coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and the current gas-liquid phase function is updated using the updated current mass flux and the updated current velocity vector, including:

[0020] Inputting the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to determine the boundary vortex vector of the fluid at the root canal wall based on the boundary velocity of the fluid at the root canal wall of the root canal, and determining the complete current vortex vector of the fluid according to the boundary vortex vector, and then updating the current vortex vector using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid and the surface tension vector;

[0021] Determine a stream function vector based on a current displacement vector of the fluid and an updated current vortex vector, and determine a velocity potential function based on the current displacement vector, the current velocity vector and the updated current mass flux, so as to update a current velocity vector using the stream function vector and the velocity potential function;

[0022] The current gas-liquid phase function is updated using the current displacement vector, the updated current mass flux, and the updated current velocity vector.

[0023] Optionally, before the current vortex vector is updated using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid, and the surface tension vector, the method further includes:

[0024] Determining the apparent dynamic viscosity of the fluid according to the dynamic viscosity of water and water vapor and the current gas-liquid phase function, and determining the apparent kinematic viscosity of the fluid based on the ratio of the apparent dynamic viscosity to the updated current apparent density;

[0025] The gas-liquid interface normal vector is determined according to the current displacement vector and the current gas-liquid phase function, and the curvature coefficient is determined according to the gas-liquid interface normal vector and the current displacement vector, so as to determine the surface tension vector based on the gas-liquid interface normal vector, the curvature coefficient, the current displacement vector and the current gas-liquid phase function.

[0026] Optionally, the coupling relationship includes:

[0027] ;

[0028] ;

[0029] ; ;

[0030] ;

[0031] ;

[0032] Wherein, the coupling relation adopts the Einstein summation convention, and Indicates three different directions. Indicates three different directions. Indicates three different directions. represents the boundary vortex vector of the fluid at the root canal wall, represents the boundary velocity of the fluid at the root canal wall, are displacement vectors, represents the curl operator, Both represent the complete vortex vector, All represent velocity vectors, t represents time, represents the apparent kinematic viscosity, represents the apparent density, p represents the fluid pressure, represents the gas-liquid phase function, represents the surface tension vector, denotes the stream function vector, represents the velocity potential function, represents the mass flux, is the density of water vapor, Represents the density of water.

[0033] In a second aspect, the present application provides a numerical simulation device for laser cavitation bubbles, comprising:

[0034] A first updating module is used to update the current apparent density of the fluid using the current velocity vector of the fluid during root canal flushing using the jet generated by laser injection into the water body to obtain an updated current apparent density;

[0035] A second updating module is used to update the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body;

[0036] A numerical simulation module is used to input the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and to update the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector, so as to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function.

[0037] In a third aspect, the present application provides an electronic device, including:

[0038] Memory, used to store computer programs;

[0039] A processor is used to execute the computer program to implement the aforementioned numerical simulation method of laser cavitation bubbles.

[0040] In a fourth aspect, the present application provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the aforementioned numerical simulation method of laser cavitation bubbles.

[0041] In the present application, in the process of root canal flushing using a jet generated by laser injection into a water body, the current velocity vector of the fluid is used to update the current apparent density of the fluid to obtain an updated current apparent density; the current mass flux is updated based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain an updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body; the current velocity vector, the current gas-liquid phase function and the updated current mass flux are input into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and the current gas-liquid phase function is updated using the updated current mass flux and the updated current velocity vector to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function. It can be seen that the present application independently developed a numerical simulation device for laser cavitation bubbles by linking the input energy of the laser, the mass flux of the fluid caused by high-temperature vaporization due to the laser injection into the water body, and the gas-liquid two-phase flow. By gradually solving the apparent density, mass flux, vortex vector and gas-liquid phase function at each moment, the real-time numerical simulation of laser cavitation bubbles is realized, thereby realizing the simulation and optimization of root canal cleaning technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0043] Figure 1 A flow chart of a numerical simulation method for laser cavitation bubbles disclosed in this application;

[0044] Figure 2 This is a schematic diagram of the structure of a numerical simulation device for laser cavitation bubbles disclosed in this application;

[0045] Figure 3 This is a structural diagram of an electronic device disclosed in this application. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] The laser cavitation problem involves laser energy injection and phase change of gas-liquid two-phase flow. In view of the industrial demand, how to independently develop a numerical simulation method for laser cavitation bubbles and then realize the simulation of root canal cleaning technology is a problem that needs to be solved. To this end, the present application provides a numerical simulation method for laser cavitation bubbles, which realizes the numerical simulation of laser cavitation bubbles by linking the input energy of the laser, the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body, and the gas-liquid two-phase flow, thereby realizing the simulation and optimization of the root canal cleaning technology.

[0048] See also Figure 1 As shown, an embodiment of the present invention discloses a numerical simulation method of laser cavitation bubbles, comprising:

[0049] Step S11 , in the process of root canal irrigation using the jet generated by laser injection into water, the current apparent density of the fluid is updated using the current velocity vector of the fluid to obtain an updated current apparent density.

[0050] In this embodiment, during root canal irrigation using a jet generated by laser injection into a water body, the current apparent density of the fluid is first updated according to the current velocity vector and the current displacement vector of the fluid to obtain an updated current apparent density.

[0051] Specifically, in the process of root canal flushing using a jet generated by laser injection of water, the current velocity vector and the current displacement vector of the fluid are used to determine the apparent density at the next moment based on the apparent density of the fluid at the current moment, so as to update the current apparent density of the fluid to obtain an updated current apparent density; it should be noted that the updated current apparent density is the apparent density at the next moment.

[0052] Among them, the apparent density at the initial time is the density determined according to the density of water and water vapor and the current gas-liquid phase function, that is, ; represents the apparent density, represents the gas-liquid phase function, represents the density of water, Represents the density of water vapor.

[0053] And, the updated formula for the apparent density includes: ; t represents time, represents the apparent density, represents the displacement vector, represents the velocity vector; and the updated formula for the apparent density uses the Einstein summation convention, It should be noted that all vectors in this application are expressed in the form of Einstein indicators.

[0054] Step S12, updating the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain an updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body.

[0055] In this embodiment, after the current apparent density is updated, the current mass flux is updated based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density, and the input energy of the laser to obtain the updated current mass flux. The mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body.

[0056] Specifically, for the update of the current mass flux, the law of conservation of energy can be used to update the current temperature of the fluid based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density, the input energy of the laser and the current mass flux to obtain the updated current temperature; then the current mass flux can be updated using the updated current temperature and the apparent thermal conductivity of the fluid to obtain the updated current mass flux.

[0057] Among them, the apparent thermal conductivity of the fluid is the thermal conductivity determined according to the thermal conductivity of water and water vapor and the current gas-liquid phase function, that is, ; represents the apparent thermal conductivity, represents the gas-liquid phase function, is the thermal conductivity of water, Represents the thermal conductivity of water vapor.

[0058] And, the temperature update formula includes:

[0059] ;

[0060] ; ;

[0061] The temperature update formula uses the Einstein summation convention, Indicates three different directions; represents the apparent density, T represents the temperature, t represents the time, represents the displacement vector, represents the velocity vector, represents the apparent specific heat capacity, p represents the fluid pressure, represents the gas-liquid phase function, represents the apparent thermal conductivity, represents the mass flux, It represents the energy injected by laser into water per unit volume and per unit time. Indicated in The pulse function is not zero at is a distance vector, which means any position in space. Indicated in The input energy at , R is the gas constant of water vapor, is the specific heat capacity of water, Represents the specific heat capacity of water vapor.

[0062] It should be noted that It represents the rate of change of energy with time; represents the energy change due to convection; represents the energy change due to temperature gradient, which is also the heat diffusion term; represents the energy change due to phase change; It represents the laser beam into the water per unit volume and per unit time. The energy injected at the location; represents the energy change due to work done by pressure, usually considered in compressible fluids, but in this application: Indicates that when the current phase is liquid, since the fluid is liquid (water), the fluid is incompressible at this time, and the pressure effect can be ignored, and this item is zero; when When the current phase is gaseous, since the fluid represents gas (water vapor), the fluid is compressible at this time, and the pressure effect needs to be considered. This item is not zero. At this time, the pressure of the fluid, that is, the pressure of water vapor, is expressed by Calculated.

[0063] Furthermore, the updated formula for mass flux includes: ; represents the latent heat of gas-liquid phase change, T represents the temperature, represents the displacement vector, represents the apparent thermal conductivity, represents the mass flux; and the updated formula for the mass flux adopts the Einstein summation convention, Indicates three different directions.

[0064] More specifically, in the case of adopting the law of conservation of energy, the current gas-liquid phase function of the fluid, the current velocity vector, the current displacement vector, the updated current apparent density, the input energy of the laser, the current mass flux and the temperature at the next moment are determined based on the current moment temperature to update the current temperature of the fluid and obtain the updated current temperature; wherein the updated current temperature is the temperature at the next moment. Then, the current mass flux is updated using the gas-liquid phase change latent heat, the current displacement vector, the updated current temperature and the apparent thermal conductivity of the fluid to obtain the updated current mass flux.

[0065] Step S13, input the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and update the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector, so as to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function.

[0066] In this embodiment, the current velocity vector, the current gas-liquid phase function and the updated current mass flux are input into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to update the current vortex vector of the fluid based on the current velocity vector and the current gas-liquid phase function, and update the current velocity vector of the fluid based on the updated current vortex vector, and then update the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector, so as to perform numerical simulation of laser cavitation bubbles according to the updated current gas-liquid phase function, and further realize simulation and optimization of root canal cleaning technology.

[0067] Specifically, the current velocity vector, the current gas-liquid phase function and the updated current mass flux are input into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to determine the boundary vortex vector of the fluid at the root canal wall based on the boundary velocity of the fluid at the root canal wall of the root canal, and determine the complete current vortex vector of the fluid according to the boundary vortex vector, and then update the current vortex vector using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid and the surface tension vector; further, determine the stream function vector based on the current displacement vector of the fluid and the updated current vortex vector, and determine the velocity potential function based on the current displacement vector, the current velocity vector and the updated current mass flux, so as to update the current velocity vector using the stream function vector and the velocity potential function; finally, update the current gas-liquid phase function using the current displacement vector, the updated current mass flux and the updated current velocity vector, so as to realize the numerical simulation of laser cavitation bubbles according to the updated current gas-liquid phase function.

[0068] Among them, the coupling relationship between the velocity vector, vortex vector and gas-liquid phase function includes:

[0069] ;

[0070] ;

[0071] ; ;

[0072] ;

[0073] ;

[0074] It should be noted that the coupling relationship adopts the Einstein summation convention, and Indicates three different directions. Indicates three different directions. Indicates three different directions. represents the boundary vortex vector of the fluid at the root canal wall, represents the boundary velocity of the fluid at the root canal wall, are displacement vectors, represents the curl operator, Both represent the complete vortex vector, All represent velocity vectors, t represents time, represents the apparent kinematic viscosity, represents the apparent density, p represents the fluid pressure, represents the gas-liquid phase function, represents the surface tension vector, denotes the stream function vector, represents the velocity potential function, represents the mass flux, is the density of water vapor, Represents the density of water.

[0075] by Take the example of Einstein's summation convention:

[0076] .

[0077] In addition, this embodiment uses the Runge-Kutta third-order format (Runge-Kutta third-order format) coupled with the Crank-Nicolson second-order format (Crank-Nicholson second-order format) to numerically discretize the unsteady time term The nonlinear convection term is numerically discretized using a hybrid format of sixth-order compact differential coupling WENO5 (Weighted Essentially Non-Oscillatory) and convection splitting technology. , the dissipative term is numerically discretized using the second-order central difference scheme and vortex stretching term , using the second-order central difference format to discretize the curl term , the second-order derivative and Both use the second-order central difference format to discretize the curl term. and .

[0078] and It represents the effect of surface tension on vorticity transport. Laser cavitation bubbles affect the flow field through surface tension. represents a baroclinic fluid, usually considered in compressible fluids, in this application: When the current phase is liquid, since the fluid is liquid (water), the fluid is incompressible at this time, so this item can be ignored and is zero; when When the current phase is gaseous, since the fluid represents gas (water vapor), the fluid is compressible at this time, and this item needs to be considered, and this item is not zero. is the phase change volume flux, which represents the effect of phase change on the velocity potential at the interface. represents the volume change caused by phase change.

[0079] It should be noted that for the complete current vortex vector of the fluid, the boundary velocity of the fluid at the root canal wall of the root canal is first obtained, and based on the boundary velocity of the fluid at the root canal wall of the root canal, the curl operator and the current displacement vector of the fluid, the boundary vortex vector of the fluid at the root canal wall of the root canal is determined, and then the complete current vortex vector of the fluid is determined based on the boundary vortex vector of the fluid at the root canal wall of the root canal and the internal vortex vector of the fluid outside the root canal wall of the root canal.

[0080] It should also be noted that, for the update of the current vortex vector of the complete fluid, the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity and the surface tension vector of the fluid are used to determine the vortex vector at the next moment based on the vortex vector at the current moment, so as to update the current vortex vector of the complete fluid and obtain the updated current vortex vector; wherein the updated current vortex vector is the vortex vector at the next moment.

[0081] In addition, for the update of the current gas-liquid phase function, specifically, the current displacement vector, the updated current mass flux and the updated current velocity vector are used to determine the gas-liquid phase function at the next moment based on the gas-liquid phase function at the current moment, so as to update the current gas-liquid phase function and obtain the updated current gas-liquid phase function; wherein, the updated current gas-liquid phase function is the gas-liquid phase function at the next moment.

[0082] Before updating the current vortex vector using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid and the surface tension vector, it is necessary to first determine the apparent kinematic viscosity and the surface tension vector of the fluid. Among them, for determining the apparent kinematic viscosity of the fluid, the apparent kinematic viscosity of the fluid can be first determined based on the dynamic viscosity of water and water vapor and the current gas-liquid phase function, and then the apparent kinematic viscosity of the fluid is determined based on the ratio of the apparent kinematic viscosity of the fluid and the updated current apparent density. The formulas involved are as follows:

[0083] ;

[0084] represents the apparent density, represents the gas-liquid phase function, represents the apparent dynamic viscosity, represents the dynamic viscosity of water, represents the dynamic viscosity of water vapor, Indicates apparent kinematic viscosity.

[0085] To determine the surface tension vector of the fluid, the gas-liquid interface normal vector can be determined based on the current displacement vector and the current gas-liquid phase function, and the curvature coefficient can be determined based on the gas-liquid interface normal vector and the current displacement vector. Then, the surface tension vector can be determined based on the gas-liquid interface normal vector, the curvature coefficient, the current displacement vector and the current gas-liquid phase function. The formulas involved are as follows:

[0086] ;

[0087] ;

[0088] The above formulas all use the Einstein summation convention, and Indicates three different directions. represents the surface tension vector, represents the surface tension coefficient, represents the curvature coefficient, represents the displacement vector, represents the gas-liquid phase function, represents the normal vector of the air-liquid interface.

[0089] It can be seen that the present application independently developed a numerical simulation device for laser cavitation bubbles by linking the input energy of the laser, the mass flux of the fluid caused by high-temperature vaporization due to the laser injection into the water body, and the gas-liquid two-phase flow. By gradually solving the apparent density, mass flux, vortex vector and gas-liquid phase function at each moment, the real-time numerical simulation of laser cavitation bubbles is realized, thereby realizing the simulation and optimization of root canal cleaning technology.

[0090] See also Figure 2As shown, the embodiment of the present invention discloses a numerical simulation device for laser cavitation bubbles, comprising:

[0091] A first updating module 11 is used to update the current apparent density of the fluid using the current velocity vector of the fluid during root canal flushing using the jet generated by laser injection into the water body to obtain an updated current apparent density;

[0092] The second updating module 12 is used to update the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body;

[0093] The numerical simulation module 13 is used to input the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and to update the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector, so as to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function.

[0094] It can be seen that the present application independently developed a numerical simulation device for laser cavitation bubbles by linking the input energy of the laser, the mass flux of the fluid caused by high-temperature vaporization due to the laser injection into the water body, and the gas-liquid two-phase flow. By gradually solving the apparent density, mass flux, vortex vector and gas-liquid phase function at each moment, the real-time numerical simulation of laser cavitation bubbles is realized, thereby realizing the simulation and optimization of root canal cleaning technology.

[0095] In some specific embodiments, the first updating module 11 includes:

[0096] An apparent density updating unit, used to determine the apparent density at the next moment based on the apparent density of the fluid at the current moment by using the current velocity vector and the current displacement vector of the fluid, so as to update the current apparent density to obtain an updated current apparent density; wherein the apparent density at the initial moment is a density determined according to the density of water and water vapor and the current gas-liquid phase function;

[0097] And, the updated formula for the apparent density includes: ; t represents time, represents the apparent density, represents the displacement vector, represents the velocity vector; and the updated formula for the apparent density uses the Einstein summation convention, Indicates three different directions.

[0098] In some specific embodiments, the second updating module 12 includes:

[0099] a temperature updating unit, for updating the current temperature of the fluid by using the law of conservation of energy and based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density, the input energy of the laser and the current mass flux, so as to obtain the updated current temperature;

[0100] The mass flux updating unit is used to update the current mass flux using the updated current temperature and the apparent thermal conductivity of the fluid to obtain an updated current mass flux; wherein the apparent thermal conductivity is a thermal conductivity determined based on the thermal conductivity of water and water vapor and the current gas-liquid phase function.

[0101] In some specific embodiments, the numerical simulation module 13 includes:

[0102] a vortex vector updating unit, for inputting a current velocity vector, a current gas-liquid phase function and an updated current mass flux into a coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to determine a boundary vortex vector of the fluid at the root canal wall based on a boundary velocity of the fluid at the root canal wall of the tooth root canal, and to determine a complete current vortex vector of the fluid according to the boundary vortex vector, and then to update the current vortex vector using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid and the surface tension vector;

[0103] a velocity vector updating unit, configured to determine a stream function vector based on a current displacement vector of the fluid and an updated current vortex vector, and to determine a velocity potential function based on the current displacement vector, the current velocity vector and the updated current mass flux, so as to update a current velocity vector using the stream function vector and the velocity potential function;

[0104] The phase function updating unit is used to update the current gas-liquid phase function using the current displacement vector, the updated current mass flux and the updated current velocity vector.

[0105] In some specific embodiments, the numerical simulation device for laser cavitation bubbles further includes:

[0106] a kinematic viscosity determination unit, configured to determine the apparent dynamic viscosity of the fluid according to the dynamic viscosity of water and water vapor and the current gas-liquid phase function, and to determine the apparent kinematic viscosity of the fluid based on the ratio of the apparent dynamic viscosity to the updated current apparent density;

[0107] A tension vector determination unit is used to determine the gas-liquid interface normal vector according to the current displacement vector and the current gas-liquid phase function, and to determine the curvature coefficient according to the gas-liquid interface normal vector and the current displacement vector, so as to determine the surface tension vector based on the gas-liquid interface normal vector, the curvature coefficient, the current displacement vector and the current gas-liquid phase function.

[0108] Furthermore, the present application also discloses an electronic device. Figure 3 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content in the diagram cannot be regarded as any limitation on the scope of use of the present application.

[0109] Figure 3 A schematic diagram of the structure of an electronic device 20 provided in an embodiment of the present application. The electronic device 20 may specifically include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 is used to store a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the numerical simulation method of laser cavitation bubbles disclosed in any of the aforementioned embodiments. In addition, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0110] In this embodiment, the power supply 23 is used to provide working voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and the external device, and the communication protocol it follows is any communication protocol that can be applied to the technical solution of the present application, and is not specifically limited here; the input and output interface 25 is used to obtain external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs and is not specifically limited here.

[0111] In addition, the memory 22, as a carrier for storing resources, can be a read-only memory, a random access memory, a disk or an optical disk, etc. The resources stored thereon can include an operating system 221, a computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0112] The operating system 221 is used to manage and control the hardware devices and computer program 222 on the electronic device 20, and can be Windows Server, Netware, Unix, Linux, etc. In addition to the computer program that can be used to complete the numerical simulation method of laser cavitation bubbles performed by the electronic device 20 disclosed in any of the aforementioned embodiments, the computer program 222 can further include computer programs that can be used to complete other specific tasks.

[0113] Furthermore, the present application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, the numerical simulation method of laser cavitation bubbles disclosed above is implemented. The specific steps of the method can be referred to the corresponding contents disclosed in the above embodiments, and will not be repeated here.

[0114] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0115] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0116] The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0117] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0118] The technical solution provided by the present application is introduced in detail above. Specific examples are used in this article to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea. At the same time, for general technicians in this field, according to the idea of ​​the present application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

Claims

1. A numerical simulation method for laser cavitation bubbles, characterized in that: include: In the process of root canal flushing using the jet generated by laser injection into water, the current apparent density of the fluid is updated using the current velocity vector of the fluid to obtain an updated current apparent density; The current mass flux is updated based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body; Inputting the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and updating the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector, so as to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function; Wherein, the updating of the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux includes: Using the law of conservation of energy and based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density, the input energy of the laser and the current mass flux, the current temperature of the fluid is updated to obtain the updated current temperature; The current mass flux is updated using the updated current temperature and the apparent thermal conductivity of the fluid to obtain an updated current mass flux; wherein the apparent thermal conductivity is a thermal conductivity determined according to the thermal conductivity of water and water vapor and the current gas-liquid phase function; The step of inputting the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and updating the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector comprises: Inputting the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to determine the boundary vortex vector of the fluid at the root canal wall based on the boundary velocity of the fluid at the root canal wall of the root canal, and determining the complete current vortex vector of the fluid according to the boundary vortex vector, and then updating the current vortex vector using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid and the surface tension vector; Determine a stream function vector based on a current displacement vector of the fluid and an updated current vortex vector, and determine a velocity potential function based on the current displacement vector, the current velocity vector and the updated current mass flux, so as to update a current velocity vector using the stream function vector and the velocity potential function; updating the current gas-liquid phase function using the current displacement vector, the updated current mass flux, and the updated current velocity vector; The coupling relationship includes: ； ； ； ； ； ； Wherein, the coupling relation adopts the Einstein summation convention, and Indicates three different directions. Indicates three different directions. Indicates three different directions. represents the boundary vortex vector of the fluid at the root canal wall, represents the boundary velocity of the fluid at the root canal wall, are displacement vectors, represents the curl operator, Both represent the complete vortex vector, All represent velocity vectors, t represents time, represents the apparent kinematic viscosity, represents the apparent density, p represents the fluid pressure, represents the gas-liquid phase function, represents the surface tension vector, denotes the stream function vector, represents the velocity potential function, represents the mass flux, is the density of water vapor, Represents the density of water.

2. The numerical simulation method of laser cavitation bubbles according to claim 1, characterized in that: The updating of the current apparent density of the fluid by using the current velocity vector of the fluid to obtain the updated current apparent density includes: Determine the apparent density at the next moment by using the current velocity vector and the current displacement vector of the fluid and based on the apparent density of the fluid at the current moment, so as to update the current apparent density to obtain an updated current apparent density; wherein the apparent density at the initial moment is a density determined according to the density of water and water vapor and the current gas-liquid phase function; And, the updated formula for the apparent density includes: ; t represents time, represents the apparent density, represents the displacement vector, represents the velocity vector; and the updated formula for the apparent density uses the Einstein summation convention, Indicates three different directions.

3. The numerical simulation method of laser cavitation bubbles according to claim 1, characterized in that: The temperature update formula includes: ； ； ； in, represents the apparent density, T represents the temperature, t represents the time, represents the displacement vector, represents the velocity vector, represents the apparent specific heat capacity, p represents the fluid pressure, represents the gas-liquid phase function, represents the apparent thermal conductivity, represents the mass flux, It represents the energy injected by laser into water per unit volume and per unit time. Indicated in The pulse function is not zero at is a distance vector, representing any position in space, Indicated in The input energy at , R is the gas constant of water vapor, is the specific heat capacity of water, represents the specific heat capacity of water vapor; And, the updated formula for mass flux includes: ; represents the latent heat of gas-liquid phase change; the updated formulas for temperature and mass flux both use the Einstein summation convention, Indicates three different directions.

4. The numerical simulation method of laser cavitation bubbles according to claim 1, characterized in that: Before the current vortex vector is updated by using the current velocity vector, the current gas-liquid phase function, the apparent kinematic viscosity of the fluid and the surface tension vector, the method further includes: Determining the apparent dynamic viscosity of the fluid according to the dynamic viscosity of water and water vapor and the current gas-liquid phase function, and determining the apparent kinematic viscosity of the fluid based on the ratio of the apparent dynamic viscosity to the updated current apparent density; The gas-liquid interface normal vector is determined according to the current displacement vector and the current gas-liquid phase function, and the curvature coefficient is determined according to the gas-liquid interface normal vector and the current displacement vector, so as to determine the surface tension vector based on the gas-liquid interface normal vector, the curvature coefficient, the current displacement vector and the current gas-liquid phase function.

5. A numerical simulation device for laser cavitation bubbles, characterized in that: The numerical simulation device of laser cavitation bubbles is used to implement the numerical simulation method of laser cavitation bubbles according to any one of claims 1 to 4, and the numerical simulation device of laser cavitation bubbles comprises: A first updating module is used to update the current apparent density of the fluid using the current velocity vector of the fluid during root canal flushing using the jet generated by laser injection into the water body to obtain an updated current apparent density; A second updating module is used to update the current mass flux based on the current gas-liquid phase function of the fluid, the current velocity vector, the updated current apparent density and the input energy of the laser to obtain the updated current mass flux; wherein the mass flux is the mass flux of the fluid vaporized at high temperature caused by the laser injection into the water body; A numerical simulation module is used to input the current velocity vector, the current gas-liquid phase function and the updated current mass flux into the coupling relationship between the velocity vector, the vortex vector and the gas-liquid phase function, so as to update the current vortex vector and the current velocity vector of the fluid based on the current gas-liquid phase function, and to update the current gas-liquid phase function using the updated current mass flux and the updated current velocity vector, so as to realize the numerical simulation of the laser cavitation bubble according to the updated current gas-liquid phase function.

6. An electronic device, characterized in that: include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the numerical simulation method of laser cavitation bubbles as claimed in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that: Used to store a computer program, which, when executed by a processor, implements the numerical simulation method of laser cavitation bubbles as described in any one of claims 1 to 4.

Images