CN103258125A - Method for simulating ultrasonic wave cavitation bubble movement in liquid phase based on Rayleigh equation - Google Patents
Method for simulating ultrasonic wave cavitation bubble movement in liquid phase based on Rayleigh equation Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 29
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Abstract
The invention relates to a method for simulating ultrasonic wave cavitation bubble movement in a liquid phase based on a Rayleigh equation, and belongs to the field of phonochemistry and the field of computer simulation. According to the method for simulating the ultrasonic wave cavitation bubble movement in the liquid phase based on the Rayleigh equation, an energy conservation equation of bubble movement in liquid is taken as a prototype, a Rayleigh equation deducing method is utilized to simplify and deduce the energy conservation equation of the bubble movement under an ultrasonic wave field, solution and visualization research are conducted on a derivate equation, parameters of ultrasonic waves and solutions are adjusted to simulate an actual production condition, and a visualization module is utilized to show the relation between the process parameters and the caviation bubble movement in an intuitionistic mode. Due to the fact that the bubble movement has certain difficult observability, through simulation of the bubble movement in the ultrasonic wave field, the method for simulating the ultrasonic wave cavitation bubble movement in the liquid phase based on the Rayleigh equation can reveal the mechanism of an ultrasonic wave cavitation effect, reflects movement laws of cavitation bubbles in an intuitionistic mode, and provides a theoretical basis and parameter guidance for future production.
Description
Technical field
The present invention relates to a kind of method based on ultrasonic cavitation bubble motion in the Rayleigh equation simulation liquid phase, belong to phonochemistry and computer modeling technique field.
Background technology
At present, ultrasound wave all has numerous application in productive life, because ultrasound wave is a kind of mechanical wave, is carrying lot of energy in its communication process, when propagating through solution, will produce cavitation effect.Ultrasonic cavitation refers to that the micro-bubble in the liquid produces rapidly the effect that changes under action of ultrasonic waves, i.e. the process of vibrated-grow-bury in oblivion.Bubble is particularly buried in oblivion in the process in its cyclical variation, and the part can reach thousands of degree high temperature and thousands of atmospheric pressure near the bubble.And thisly bury in oblivion localized hyperthermia's high pressure effect of producing chemical reaction in the reinforced solution significantly owing to bubble, and as corroding metal, destroy biological tissue, accelerate chemical reaction velocity, produce optical radiation etc.
Though occurred much causing in liquid phase about ultrasound wave the report of cavitation effect both at home and abroad, but the overwhelming majority all be by adjust actual process parameter (as, solution temperature, concentration, pressure, ultrasonic power etc.) study the degree that ultrasound wave is strengthened chemical reaction, though actual production is had bigger directive significance, can not disclose the mechanism of ultrasonic cavitation.
Summary of the invention
The purpose of this invention is to provide a kind of method based on ultrasonic cavitation bubble motion in the Rayleigh equation simulation liquid phase, start with from the essence " bubble motion " of ultrasonic cavitation phenomenon, derive the motion of air bubbles equation, by correlation parameter (bubble radius such as research ultrasonic device and solution environmentals, the gas polytropic index, the surface tension of liquid parameter, the coefficient of viscosity, fluid density, the liquid internal static pressure, the bubble steam inside is pressed, ultrasonic frequency, ultrasonic intensity, the cavitation bubble equilibrium radius, solution temperature etc.) to the influence of bubble motion, utilize simulation means to analyze ultrasonic cavitation mechanism, and then produce theoretical direction is provided for the later stage.
The present invention realizes by following technical proposal: a kind of method based on ultrasonic cavitation bubble motion in the Rayleigh equation simulation liquid phase, and following each step of process:
(1) equation is established: liquid phase is assumed even ideal liquid, seeing bubble in the ultrasonic wave field as one is the oscillator of load with liquid, and keep spherical at the volley, suppose the loss of bubble motion noenergy, just should equal the kinetic energy that bubble increases to bubble institute work so with joint efforts, and utilize Rayleigh equation inference method to simplify and derive motion of air bubbles equation in the ultrasonic wave field;
Under above assumed condition, based on the method for Rayleigh equation inference, model is simplified, when bubble under bonding force P effect from radius R
0Change to radius R, then bonding force merit that bubble is done is:
Because noenergy loss just should equal the kinetic energy that bubble increases to bubble institute work so with withing joint efforts, constant density be in the leachate of ρ therefore bubble be written as because of the kinetic energy that workmanship with joint efforts increases:
Represent by integrated form, be written as:
When a branch of with P
ASin ω t is the ultrasound wave of vibrant characteristic when propagating in acid leaching solution, when bubble moves in leachate so, inevitably is subjected to the effect of a plurality of power, establishes the P that makes a concerted effort to be that is subjected to this moment; Suppose that at t constantly radius is the inside and outside P balance of making a concerted effort that the bubble of R is subjected in leachate, establishing the interior gaseous tension of bubble this moment is P
In, and bubble makes a concerted effort to be P outward
Out, then:
（5）
In the formula, P
v---the vapour pressure in the bubble, P
g---gaseous tension, P
ASin ω t---ultrasound wave acts on the pressure on the walls, ω=2 π f---hyperacoustic angular frequency, P
0---for acting on the hydrostatic pressure (being taken as atmospheric pressure at this) on the walls,
---act on the viscous force on the walls,
---acting on the surface tension on the walls, R---is the instantaneous radius of bubble,
---the movement rate of particle on the cavitation bubble wall, the P that makes a concerted effort that then acts on the bubble is expressed as:
Because gas is ideal gas in the hypothesis bubble, then gas pressure change meets the ideal gas equation of change, that is:
In the formula: R
0---bubble initial radium (m), k-polytropic index; Formula (6) is brought into formula (7), and the final expression formula that obtains the suffered P of making a concerted effort of bubble is:
（8）
In order to obtain the last equation of motion, bring formula (8) into energy conservation equation (3), again to the R differentiate on equation both sides, then:
(2) equation solution: different parameter conditions is set the Runge-Kutta algorithm on equation (9) the employing 4-5 rank of step (1) is found the solution, come the setting of ultrasonic equipment and solution environmental in the actual ultrasonic cavitation of the match system by changing parameter in the equation, be horizontal ordinate with the cavitation time again, R/R
0(bubble maximum radius/incipient bubble radius) draws out different parameters to the relation curve of cavitation influential effect for ordinate, draws extent of cavitation and the cycle of bubble by relation curve.
The parameter of described step (2) comprises bubble radius, gas polytropic index, surface tension of liquid parameter, the coefficient of viscosity, fluid density, liquid internal static pressure, bubble steam inside pressure, ultrasonic frequency, ultrasonic intensity, cavitation bubble equilibrium radius, solution temperature.
At present, in scientific research field, need expend a large amount of manpower financial capacities because experiment is produced, and have certain limitation; And the big ability that has exceeded people's deal with data of science computational data amount, thereby caused the experimental data of many preciousnesses can't obtain proper explanations and analysis.Problem at above-mentioned scientific research field existence, method based on ultrasonic cavitation bubble motion in the Rayleigh equation inference simulation liquid phase proposed by the invention, and calculate and simulate, change the abstracted informations such as bubble motion rule of complexity into visual information, having enriched the process of scientific analysis, is a kind of advanced person's scientific research method.
The advantage that the present invention possesses and effect:
The present invention starts with from the essence " bubble motion " of ultrasonic cavitation phenomenon, energy conservation equation with bubble motion in the liquid phase is prototype, derive the motion of air bubbles equation, by the influence of correlation parameters such as research ultrasonic device and solution environmental to bubble motion, utilize simulation means to analyze ultrasonic cavitation mechanism, and then produce theoretical direction is provided for the later stage.Because motion of air bubbles has certain difficult observation, the present invention is by simulating motion of air bubbles in the ultrasonic wave field, can disclose the mechanism of ultrasonic cavitation effect, this method simulates the relation of technological parameter and bubble cavitation effect, disclosed the mechanism of ultrasonic cavitation effect, react the characteristics of motion of cavitation bubble intuitively, provide theoretical foundation and parameter to instruct for producing future.
Description of drawings
Fig. 1 is bubble radius curve over time under the 20kHz condition for embodiment 1 ultrasonic frequency;
Fig. 2 is bubble radius curve over time under the 25kHz condition for embodiment 1 ultrasonic frequency;
Fig. 3 is bubble radius curve over time under the 30kHz condition for embodiment 1 ultrasonic frequency;
Fig. 4 is bubble radius curve over time under the 35kHz condition for embodiment 1 ultrasonic frequency;
Fig. 5 is 20w/cm for embodiment 2 sound intensitys
2Bubble radius curve over time under the condition;
Fig. 6 is 40w/cm for embodiment 2 sound intensitys
2Bubble radius curve over time under the condition;
Fig. 7 is 60w/cm for embodiment 2 sound intensitys
2Bubble radius curve over time under the condition;
Fig. 8 is 80w/cm for embodiment 2 sound intensitys
2Bubble radius curve over time under the condition;
Fig. 9 is 25 ℃ of following bubble radius curves over time for embodiment 3 leachate environment temperatures;
Figure 10 is 50 ℃ of following bubble radius curves over time for embodiment 3 leachate environment temperatures;
Figure 11 is 70 ℃ of following bubble radius curves over time for embodiment 3 leachate environment temperatures;
Figure 12 is 90 ℃ of following bubble radius curves over time for embodiment 3 leachate environment temperatures;
Figure 13 is 1 * 10 for embodiment 4 initial environment pressure
5Bubble radius curve over time under the Pa;
Figure 14 is 3 * 10 for embodiment 4 initial environment pressure
5Bubble radius curve over time under the Pa;
Figure 15 is 5 * 10 for embodiment 4 initial environment pressure
5Bubble radius curve over time under the Pa;
Figure 16 is 7 * 10 for embodiment 4 initial environment pressure
5Bubble radius curve over time under the Pa.
Embodiment
The present invention will be further described below by embodiment.
Simulate different ultrasonic frequencies to the bubble influence on cavitation:
Be simulated system with 70 ℃ 140g/L sulphuric leachates, calculating and adopting parameter is P
0=1.013 * 10
5Pa, P
v=31.176 * 10
3Pa, σ=6.4 * 10
-2N/m, k=1.33, u=1 * 10
-3Pas, R
0=5 * 10
-3, ρ=1063kg/m
-3(140g/L sulphuric leachate), p
a=1.5 * 10
-5Pa;
(1) equation is established: liquid phase is assumed even ideal liquid, seeing bubble in the ultrasonic wave field as one is the oscillator of load with liquid, and keep spherical at the volley, suppose the loss of bubble motion noenergy, just should equal the kinetic energy that bubble increases to bubble institute work so with joint efforts, and utilize Rayleigh equation inference method to simplify and derive motion of air bubbles equation in the ultrasonic wave field;
Under above assumed condition, based on the method for Rayleigh equation inference, model is simplified, when bubble under bonding force P effect from radius R
0Change to radius R, then bonding force merit that bubble is done is:
Because noenergy loss just should equal the kinetic energy that bubble increases to bubble institute work so with withing joint efforts, constant density be in the leachate of ρ therefore bubble be written as because of the kinetic energy that workmanship with joint efforts increases:
Represent by integrated form, be written as:
When a branch of with P
ASin ω t is the ultrasound wave of vibrant characteristic when propagating in acid leaching solution, when bubble moves in leachate so, inevitably is subjected to the effect of a plurality of power, establishes the P that makes a concerted effort to be that is subjected to this moment; Suppose that at t constantly radius is the inside and outside P balance of making a concerted effort that the bubble of R is subjected in leachate, establishing the interior gaseous tension of bubble this moment is P
In, and bubble makes a concerted effort to be P outward
Out, then:
In the formula, P
v---the vapour pressure in the bubble, P
g---gaseous tension, P
ASin ω t---ultrasound wave acts on the pressure on the walls, ω=2 π f---hyperacoustic angular frequency, P
0---for acting on the hydrostatic pressure (being taken as atmospheric pressure at this) on the walls,
---act on the viscous force on the walls,
---acting on the surface tension on the walls, R---is the instantaneous radius of bubble,
---the movement rate of particle on the cavitation bubble wall, the P that makes a concerted effort that then acts on the bubble is expressed as:
Because gas is ideal gas in the hypothesis bubble, then gas pressure change meets the ideal gas equation of change, that is:
In the formula: R
0---bubble initial radium (m), k-polytropic index; Formula (6) is brought into formula (7), and the final expression formula that obtains the suffered P of making a concerted effort of bubble is:
In order to obtain the last equation of motion, bring formula (8) into energy conservation equation (3), again to the R differentiate on equation both sides, then:
(2) equation solution: in the Matlab software platform, different parameter conditions is set to be found the solution the Runge-Kutta algorithm on equation (9) the employing 4-5 rank of step (1), come the setting of ultrasonic equipment and solution environmental in the actual ultrasonic cavitation of the match system by changing bubble radius, gas polytropic index, surface tension of liquid parameter, the coefficient of viscosity, fluid density, liquid internal static pressure, bubble steam inside pressure, ultrasonic frequency, ultrasonic intensity, cavitation bubble equilibrium radius, solution temperature parameter in the equation, wherein, the radius (R of R-bubble
0Then be its equilibrium value at the beginning); The polytropic index of k-gas (getting 1.33); σ, u and ρ-be respectively surface tension coefficient, the coefficient of viscosity and the density of 70 ℃ 140g/L sulphuric leachate; P
0The static pressure of-leachate; P
aThe pressure that-ultrasound wave acts on the bubble (gets 1.5 * 10
5Pa); P
v-70 ℃ of water saturation vapour pressures; When initial condition
, use sound intensity I=10w/cm
2, leaching that ultrasonic frequency f gets 20,25,30, the sinusoidal variations ultrasound wave effect frequency of 35kHz, the visualization model of recycling Matlab is horizontal ordinate with the cavitation time, R/R
0(bubble maximum radius/incipient bubble radius) draws out different parameters to the relation curve of cavitation influential effect for ordinate, and the extent of cavitation and the cycle that draw bubble by relation curve are seen Fig. 1.
Simulate different ultrasound wave acoustic pressures to the influence of bubble motion: method is identical with embodiment 1
Be simulated system with 70 ℃ 140g/L sulphuric leachates, calculating and adopting parameter is P
0=1.013 * 10
5Pa, P
v=31.176 * 10
3Pa, σ=6.4 * 10
-2N/m, k=1.33, u=1 * 10
-3Pas, R
0=5 * 10
-3, ρ=1063kg/m
-3(140g/L sulphuric leachate), f=20kHz, p
a=1.5 * 10
-5Pa.
Wherein, the radius (R of R-bubble
0Then be its equilibrium value at the beginning); The polytropic index of k-gas (generally getting 1.33); σ, u and ρ-be respectively surface tension coefficient, the coefficient of viscosity and the density of 70 ℃ 140g/L sulphuric leachate; P
0The static pressure of-leachate; P
a-ultrasound wave acts on the pressure P on the bubble
v-70 ℃ of water saturation vapour pressures; The f-ultrasonic frequency.
When initial condition
, strengthen leaching ultrasound wave acoustic pressure and get 20,40,60,80 w/cm
2Effect under, equation (9) is carried out cavitation bubble radius that numerical evaluation simulation obtains concerns over time and see Fig. 2.
Simulation different solutions temperature is to the influence of bubble motion: method is identical with embodiment 1
Be simulated system with the 140g/L sulphuric leachate, calculate and adopt parameter P0=1.013 * 10
5Pa, Pv=31.176 * 10
3Pa, R0=5 * 10
-3M, σ=6.4 * 10
-2N/m, k=1.33, u=1 * 10
-3Pas, ρ=1063kg/m
-3(140g/L sulphuric leachate), f=20kHz, Pa=6 * 10
-5Pa, sound intensity I=40w/cm
2
Wherein, the radius of R-bubble (R0 then is its equilibrium value at the beginning); The polytropic index of k-gas (generally getting 1.33); σ, u and ρ-be respectively surface tension coefficient, the coefficient of viscosity and the density of 70 ℃ 140g/L sulphuric leachate; The static pressure of P0-leachate; The Pa-ultrasound wave acts on pressure P v-70 ℃ of water saturation vapour pressure on the bubble; The f-ultrasonic frequency.
When initial condition
The initial temperature of setting leachate is respectively 25 ℃, 50 ℃, 70 ℃, 100 ℃ get under the situation, because the variation of the viscosity of 25～90 ℃ of interval water is little, and independent brief summary research viscosity have been arranged to influence on cavitation, so only consider variation such as the following table 1 of surface tension and saturated vapor pressure herein, equation (9) calculated the cavitation bubble radius that obtains of simulation see shown in Figure 3 with the variation of temperature relation.
The character of leachate under table 1 different temperatures
(in the * solution based on hydrone, so approximately think that the surface tension of water is leachate tension force under the different temperatures; So the leachate evaporation is based on the approximate relevant vapour pressure of getting pure water of evaporation of water saturated vapor pressure)
Simulation varying environment pressure is to the influence of bubble motion: method is identical with embodiment 1
Be simulated system with 70 ℃ 140g/L sulphuric leachates, calculating and adopting parameter is Pv=31.176 * 10
3Pa, R0=5 * 10
-3M, σ=6.4 * 10
-2N/m, k=1.33, u=1 * 10
-3Pas, ρ=1063kg/m
-3(140g/L sulphuric leachate), f=20kHz, Pa=6 * 10
-5Pa, sound intensity I=40w/cm
2
Wherein, the radius (R of R-bubble
0Then be its equilibrium value at the beginning); The polytropic index of k-gas (generally getting 1.33); σ, u and ρ-be respectively surface tension coefficient, the coefficient of viscosity and the density of 70 ℃ 140g/L sulphuric leachate; The static pressure of P0-leachate; The Pa-ultrasound wave acts on the bubble; Pv-70 ℃ of water saturation vapour pressure; The f-ultrasonic frequency.
When initial condition
, environmental pressure Pa is respectively 1 * 10
5, 3 * 10
5, 5 * 10
5, 7 * 10
5Under the Pa situation, to equation (9) carry out cavitation bubble radius that numerical evaluation simulation obtains concern over time see shown in Figure 4.
Claims (1)
1. method based on ultrasonic cavitation bubble motion in the Rayleigh equation simulation liquid phase is characterized in that through following each step:
(1) equation is established: liquid phase is assumed even ideal liquid, seeing bubble in the ultrasonic wave field as one is the oscillator of load with liquid, and keep spherical at the volley, suppose the loss of bubble motion noenergy, just should equal the kinetic energy that bubble increases to bubble institute work so with joint efforts, and utilize Rayleigh equation inference method to simplify and derive motion of air bubbles equation in the ultrasonic wave field;
Under above assumed condition, based on the method for Rayleigh equation inference, model is simplified, when bubble under bonding force P effect from radius R
0Change to radius R, then bonding force merit that bubble is done is:
Because noenergy loss just should equal the kinetic energy that bubble increases to bubble institute work so with withing joint efforts, constant density be in the leachate of ρ therefore bubble be written as because of the kinetic energy that workmanship with joint efforts increases:
Represent by integrated form, be written as:
When a branch of with P
ASin ω t is the ultrasound wave of vibrant characteristic when propagating in acid leaching solution, when bubble moves in leachate so, inevitably is subjected to the effect of a plurality of power, establishes the P that makes a concerted effort to be that is subjected to this moment; Suppose that at t constantly radius is the inside and outside P balance of making a concerted effort that the bubble of R is subjected in leachate, establishing the interior gaseous tension of bubble this moment is P
In, and bubble makes a concerted effort to be P outward
Out, then:
（5）
In the formula, P
v---the vapour pressure in the bubble, P
g---gaseous tension, P
ASin ω t---ultrasound wave acts on the pressure on the walls, ω=2 π f---hyperacoustic angular frequency, P
0---for acting on the hydrostatic pressure (being taken as atmospheric pressure at this) on the walls,
---act on the viscous force on the walls,
---acting on the surface tension on the walls, R---is the instantaneous radius of bubble,
---the movement rate of particle on the cavitation bubble wall, the P that makes a concerted effort that then acts on the bubble is expressed as:
Because gas is ideal gas in the hypothesis bubble, then gas pressure change meets the ideal gas equation of change, that is:
In the formula: R
0---bubble initial radium (m), k-polytropic index; Formula (6) is brought into formula (7), and the final expression formula that obtains the suffered P of making a concerted effort of bubble is:
In order to obtain the last equation of motion, bring formula (8) into energy conservation equation (3), again to the R differentiate on equation both sides, then:
(2) equation solution: different parameter conditions is set the Runge-Kutta algorithm on equation (9) the employing 4-5 rank of step (1) is found the solution, come the setting of ultrasonic equipment and solution environmental in the actual ultrasonic cavitation of the match system by changing parameter in the equation, be horizontal ordinate with the cavitation time again, R/R
0(bubble maximum radius/incipient bubble radius) draws out different parameters to the relation curve of cavitation influential effect for ordinate, draws extent of cavitation and the cycle of bubble by relation curve.
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Cited By (3)
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| CN105975700A (en) * | 2016-05-10 | 2016-09-28 | 北京理工大学 | Numerical method simulating ultrasonic cavity dynamics behavior |
| CN108446519A (en) * | 2018-04-10 | 2018-08-24 | 哈尔滨理工大学 | Bubble transient motion model building method is purified under ultrasound and eddy flow field in melt |
| CN108763623A (en) * | 2018-04-10 | 2018-11-06 | 哈尔滨理工大学 | Bubble rapid transfer mass model building method is purified under ultrasound and eddy flow field in melt |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105975700A (en) * | 2016-05-10 | 2016-09-28 | 北京理工大学 | Numerical method simulating ultrasonic cavity dynamics behavior |
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| CN108446519A (en) * | 2018-04-10 | 2018-08-24 | 哈尔滨理工大学 | Bubble transient motion model building method is purified under ultrasound and eddy flow field in melt |
| CN108763623A (en) * | 2018-04-10 | 2018-11-06 | 哈尔滨理工大学 | Bubble rapid transfer mass model building method is purified under ultrasound and eddy flow field in melt |
| CN108763623B (en) * | 2018-04-10 | 2021-09-07 | 哈尔滨理工大学 | Method for constructing transient mass transfer model of purified bubbles in melt under ultrasonic and rotational flow fields |
| CN108446519B (en) * | 2018-04-10 | 2022-02-11 | 哈尔滨理工大学 | Method for constructing transient motion model of purified bubbles in melt under ultrasonic and rotational flow fields |
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