CN113569450B - Method for estimating and controlling suspension and residence of liquid drops - Google Patents
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Abstract
The invention discloses a method for predicting and controlling suspension and residence of liquid drops, which comprises the steps of coupling an ultrasonic nonlinear sound field with a two-phase flow field, discretizing a control equation by using a finite difference method and a lattice Boltzmann method, calculating the mutual influence rule of the sound field and liquid drop materials according to input ultrasonic sound source parameters, liquid drop parameters and volume, and obtaining the suspension position and form information of the liquid drop materials. Compared with the traditional simplified estimation method and experimental trial method, the invention can obtain more accurate suspension position and suspension form of the liquid material in the ultrasonic sound field at lower cost by utilizing the computer simulation method, and the method combines two-phase flow and nonlinear sound field calculation models, and can predict density distribution change and form change details of liquid drops in the sound field in the simulation process, wherein the details are difficult to observe through experimental means.
Description
Technical Field
The invention relates to a method for estimating and controlling liquid drop suspension and residence, and belongs to the field of numerical calculation.
Background
The material is subjected to sound radiation force generated by nonlinear sound wave vibration in a standing wave sound field formed by ultrasonic waves, so that gravity can be balanced, and artificial microgravity 'space environment' and container-free processing of the material can be realized on the ground. Due to the disturbance of the pulsating vibration caused by sound propagation to the interior of the liquid drop and the absence of the influence of natural convection caused by gravity, the material obtained by rapid solidification in the sound suspension environment can obtain uniform solidification structure more easily, and the performance of the material is greatly improved. Meanwhile, the microgravity environment realized by ultrasonic suspension is widely applied to the aspects of researching the phase change, the microstructure evolution and the thermophysical properties of the material in the metastable state. However, in the case of the existing ultrasonic levitation observation equipment, whether a specific liquid material can be stably levitated for a long time, whether the precise position of the material suspension stability and the specific form of the stabilized liquid can be predicted and controlled become problems to be solved urgently.
Because the interaction rule of the nonlinear sound field and the gas-liquid two-phase field is difficult to analyze theoretically, a numerical simulation technology taking a computer as a tool becomes an effective method capable of solving complex partial differential equations and unsteady physical phenomena. For nonlinear sound field problems, common numerical methods include a finite integration method, a finite element method, a boundary element method and the like, wherein the time domain finite difference method is widely applied due to the characteristics of simplicity, effectiveness, grid regulation, capability of calculating time domain arbitrary waveforms and the like.
A fluid flow model is required to be introduced for researching the dynamic behavior of a liquid drop material in the air, a classical fluid model comprises a microscopic model based on molecular dynamics, a mesoscopic model taking fluid particles as a research object and a macroscopic model starting from solving an N-S equation, wherein a lattice Boltzmann method in the mesoscopic method is based on a continuous Boltzmann equation, the equation is discretized in time, space and speed to obtain a lattice Boltzmann control equation, a complex collision operator can be linearized through a BGK, MRT and other relaxation models to obtain a numerical method which is easy to solve, efficient and stable, and the stability and accuracy of MRT are higher than those of BGK. On the basis of a fluid flow model, the acting force between homogeneous molecules and heterogeneous molecules is increased, a multiphase multi-component flow model can be obtained, common lattice Boltzmann two-phase flow models comprise a color gradient model, a free energy model, a Shan-Chen model and the like, wherein a chemical potential model is based on thermodynamics, naturally meets thermodynamic compatibility and Galileo invariance, describes the molecular thermal motion trend caused by density and free energy gradient, and better accords with the dynamics and thermodynamic laws of multiphase flow, so that the two-phase flow phenomenon can be effectively described.
Disclosure of Invention
The technical problem is as follows: the invention provides a solution based on the problem that the suspension position and the suspension form of a liquid material cannot be accurately estimated and controlled in an acoustic suspension experiment, and designs an estimation and control method with higher calculation efficiency and higher numerical stability by coupling nonlinear acoustic propagation and a two-phase flow field.
The technical scheme is as follows: to achieve the object of the present invention, the present invention provides a method for estimating and controlling the suspension and residence of liquid droplets, which is characterized by comprising the following steps:
(1) Dispersing a nonlinear wave equation describing finite amplitude by a finite difference method, and establishing a model describing ultrasonic sound wave transmission in different media;
(2) Dispersing a continuous Boltzmann equation describing the molecular motion of the fluid, introducing an MRT multi-relaxation model to linearize a collision operator, generating an external force term capable of describing intermolecular action of phases in a dispersed control equation by utilizing a chemical potential model and a Peng Robinson state equation, and establishing a numerical model describing multi-component and multi-phase;
(3) Inputting boundary conditions and initial conditions, and inputting sound source parameters and liquid drop parameters;
(4) Carrying out propagation and relaxation of the multiphase flow field and capturing a phase interface;
(5) Performing cross-medium propagation of a finite amplitude wave, calculating an acoustic radiation force;
(6) Repeating the steps (4) and (5) until the set time length is reached, stopping calculation, and performing data post-processing;
(7) Judging whether the suspension can be stably suspended, if so, turning to the step (8), and if not, returning to the step (3);
(8) The suspension position and suspension shape of the liquid drop are estimated and controlled.
The invention discloses a numerical method for estimating and controlling the suspension and residence of liquid drops, which comprises the steps of coupling an ultrasonic nonlinear sound field with a two-phase flow field, discretizing a control equation by using a finite difference method and a lattice Boltzmann method, writing the discretized control equation into a calculation program, calculating the mutual influence rule of the sound field and liquid drop materials according to input ultrasonic sound source parameters, liquid drop parameters and volume size, and obtaining the suspension position and form information of the liquid drop materials. Compared with the traditional simplified estimation method and experimental trial method, the invention can obtain more accurate suspension position and suspension form of the liquid material in the ultrasonic sound field at lower cost by utilizing the computer simulation method, and the method combines two-phase flow and nonlinear sound field calculation models, and can predict density distribution change and form change details of liquid drops in the sound field in the simulation process, wherein the details are difficult to observe through experimental means. In addition, experimenters can also carry out design and control simulation of a liquid drop suspension experiment through the method, the defects of high cost, high investment and long period of the conventional 'experience optimization' mode are overcome, and the 'scientific optimization' mode with low cost and high efficiency is realized.
Drawings
FIG. 1 is a flowchart of the process of estimating and controlling the suspension and residence of liquid droplets according to the present invention.
FIG. 2 shows the steps of the multi-physical field evolution of the method of the present invention.
FIG. 3 illustrates the method of the present invention after packaging.
FIG. 4 is a discrete diagram of the finite difference time domain method of the sound field of the present invention.
FIG. 5 is a schematic representation of the propagation and relaxation steps of the lattice Boltzmann method.
Fig. 6 is a boundary condition setting of the calculation region.
Detailed Description
A method for predicting and controlling suspension of liquid drops in a residence mode adopts a numerical model of coupling of an ultrasonic nonlinear sound field and a two-phase flow field, and calculates the predicted suspension position and form of the liquid drops by using the coupling of a model describing finite amplitude wave propagation and a model describing gas-liquid two-phase flow, as shown in figures 1-2, the method comprises the following steps:
(1) Dispersing a nonlinear wave equation describing finite amplitude by a finite difference method, and establishing a model describing ultrasonic sound wave transmission in different media;
(2) Dispersing a continuous Boltzmann equation describing fluid molecular motion, introducing an MRT multi-relaxation model to linearize a collision operator, generating an external force term capable of describing intermolecular action of phases in a dispersed control equation by utilizing a chemical potential model and a Peng Robinson state equation, and establishing a numerical model describing multi-component and multi-phase;
(3) Inputting boundary conditions and initial conditions, sound source parameters and liquid material physical parameters;
(4) Carrying out propagation and relaxation of the multiphase flow field and capturing a phase interface;
(5) Performing cross-medium propagation of the finite amplitude wave, and calculating acoustic radiation force;
(6) Repeating the steps (4) and (5) until the set time length is reached, stopping calculation, and performing data processing and analysis;
(7) Judging whether the suspension can be stably suspended, if so, turning to the step (8), and if not, returning to the step (3);
(8) The suspension position and suspension form of the liquid drop are estimated and controlled.
For a user of the program, parameters to be input include power and frequency of a sound source, density, viscosity, acoustic impedance and volume of liquid drops, experimental geometric conditions such as distance between the sound source and a reflection end and the like, sound field sound pressure and sound radiation force distribution data and two-phase field distribution data can be obtained through calculation, the positions and the shapes of the liquid drops are obtained, and the input parameters and the output data of the program are shown in fig. 3.
A model for describing the nonlinear propagation of the finite amplitude wave in a two-phase flow field consists of three basic equations, namely a propagation equation of the finite amplitude wave, a multiphase flow equation and a medium state equation.
In a second order approximation, a nonlinear finite amplitude acoustic wave equation with a dissipative term can be derived from the flow equation of the fluid:
wherein c is 0 Is the speed of sound, ρ 0 For the medium density at equilibrium, p is the pressure, t is the time,
it is shown that the derivation is calculated,
is Hamiltonian, beta is nonlinear coefficient, gamma is absorption coefficient, and l is medium particle kinetic energy and potential energy difference. The first term and the second term on the left side of the equation represent the propagation of sound waves in time and space, and the third term is an attenuation term and describes a dissipation phenomenon in the sound propagation process; the first term on the right of the equation is a nonlinear term describing nonlinear effects produced during finite amplitude wave propagation. The nonlinear acoustic wave equation is rewritten into the following form
Where v is an intermediate variable that participates in program calculations and does not represent particle velocity. The computational grid with alternate time and space configuration can save memory overhead and improve program computational efficiency, and the grid configuration is shown in figure 4, and the above formula is dispersed in two-dimensional space to obtain
Wherein
Wherein,
representing the pressure at time n, (i, j) coordinate grid points,
is an intermediate variable of similar speed, m is a dimensionless number, m = h/c 0 δ t ，h、δ t Respectively is a space step length and a time step length; z is acoustic impedance of the medium, which is an intrinsic parameter of the medium, and a and τ are coefficients. The time average of the nonlinear acoustic radiation pressure in one period is not zero, thus generating acoustic radiation force, and the acoustic radiation force applied to the fluid micro-cluster is equal to the space energy density difference of the sound field:
wherein, F s For acoustic radiation force, E for energy density in sound field space,<E>representing the time average of the energy. Analyzing the motion of fluid molecules from the angle of statistical mechanics to obtain a continuous Boltzmann equation, wherein collision terms in the continuous Boltzmann equation are complex nonlinear operatorsAnd is not beneficial to discretization, therefore, the MRT operator is introduced to linearize the collision operator omega (r, t) and discretize the continuous Boltzmann equation into a lattice Boltzmann equation, and then the fluid motion control equation is as follows:
wherein, f α (r, t) is a particle distribution function,
is a particle equilibrium distribution function, M is a transformation matrix, S is a relaxation matrix, F α In a two-dimensional plane, a D2Q9 format, i.e., a two-dimensional plane and nine discrete velocities, is often used for the total external force applied to the particles. In the lattice Boltzmann method, migration and collision of fluid micelles are key steps, and the implementation diagram is shown in fig. 5. The last term on the right side of the equation is the local force into which intermolecular forces can be introduced by introducing a chemical potential model, thus obtaining a model describing the two-phase field.
The chemical potential of fluid particles can be derived from the free energy density function:
where Φ is the free energy function, μ is the chemical potential, κ is the coefficient, ρ is the density, ψ is the bulk free energy density. The general form of the equation of state is expressed as:
p 0 ＝ρψ′(ρ)-ψ(ρ)
the intermolecular forces of the phases can be derived from chemical potential
Wherein F c (x) Is the intermolecular force that the particle at the x position is subjected to, ρ is the density, μ is the chemical potential, c 0 Is the medium speed of sound. The equation of state adopts Peng Robinson (PR) equation of state:
wherein R is the general gas constant, T is the temperature, a 0 ，b 0 For the coefficients, ρ is the density and α (T) represents a function of temperature. Because the pressure amplitude variation transmitted by the sound wave is high-order small quantity relative to the pressure of the medium background, the pressure of the limited amplitude wave and the medium pressure cannot be represented by one variable in a computer so as to avoid overlarge numerical errors, and the coupling mode of step evolution and interface capture becomes an effective means for avoiding errors. The phase interface position is obtained according to the calculation result of the two-phase flow field, the sound field performs cross-medium propagation according to the changed interface, the sound energy distribution is obtained, the sound radiation force is calculated, and the two-phase flow field introduces the sound radiation force into the relaxation process to realize the coupling of the two physical fields.
The computational regions and boundary conditions applied to the numerical model, including but not limited to the computational regions and boundary conditions shown in FIG. 6, wherein the sound source is part of the boundary conditions, producing simple harmonics determined by the sound source parameters; the reflecting end adopts a first type of boundary condition, and the first type of boundary condition is a total reflection boundary condition; and the rest boundaries are set as second-order approximate absorption boundary conditions to simulate the dissipation of sound waves radiated to the experimental environment space. The second order approximation absorption boundary condition, for example at x =0, is written as:
wherein v is y Representing the velocity component in the y-direction, Z being the acoustic impedance of the medium, p being the pressure, t being the time, c 0 Is the medium speed of sound.
The program implementation process comprises the following steps: as shown in fig. 2, the calculation of the two-phase flow field is divided into two steps of propagation and relaxation, a particle distribution function with discrete velocity is migrated to the next node according to the velocity direction, and is relaxed with all particle functions migrated to the node at the moment, so as to obtain the flow field distribution at a new moment, capture two-phase interfaces and use the two-phase interfaces as the interfaces for the propagation of the finite amplitude wave across the medium, so as to perform propagation evolution of the acoustic wave, when the acoustic wave crosses the medium, corresponding transmission and reflection are generated according to different physical parameters of the medium, and the acoustic radiation force is calculated by the acoustic energy gradient and used as an external force term to participate in the relaxation calculation of the flow field at the next moment. And after the calculated result enters a steady state or after a given time, obtaining the suspension position and the suspension form of the liquid drop in the sound field.
Claims (9)
1. A method for estimating and controlling the suspension and residence of liquid drops is characterized by comprising the following steps:
(1) Dispersing a nonlinear wave equation describing finite amplitude by a finite difference method, and establishing a model describing ultrasonic sound wave transmission in different media;
(2) Dispersing a continuous Boltzmann equation describing fluid molecular motion, introducing an MRT multi-relaxation model to linearize a collision operator, generating an external force term capable of describing intermolecular action of phases in a dispersed control equation by utilizing a chemical potential model and a Peng Robinson state equation, and establishing a numerical model describing multi-component and multi-phase;
(3) Inputting boundary conditions, initial conditions, sound source parameters and liquid drop parameters;
(4) Carrying out propagation and relaxation of the multiphase flow field and capturing a phase interface;
(5) Performing cross-medium propagation of a finite amplitude wave, calculating an acoustic radiation force;
(6) Repeating the steps (4) and (5) until the set time length is reached, stopping calculation, and performing data processing and analysis;
(7) Judging whether the suspension can be stably suspended, if so, turning to the step (8), and if not, returning to the step (3);
(8) The suspension position and suspension shape of the liquid drop are estimated and controlled.
2. A method of estimating and controlling droplet levitation and residence according to claim 1, wherein the second order approximate nonlinear propagation equation of finite amplitude wave is used as the sound field evolution control equation, which includes the evolution term, dissipation term and nonlinear term of sound wave in time and space, namely:
wherein c is 0 Is the speed of sound, ρ 0 For the medium density at equilibrium, p is the pressure, t is the time, gamma is the absorption coefficient, beta is the nonlinear coefficient, and l is the difference between kinetic energy and potential energy,
it is shown that the derivation is calculated,
is a hamiltonian.
3. The method for estimating and controlling the suspension and residence of liquid drops as claimed in claim 2, wherein the sound field evolution control equation is discretized by using finite difference time domain method, the difference method adopts time and space alternate grid configuration, and the difference format obtained after discretization is as follows:
wherein,
representing the pressure at time n, (i, j) at a grid point,
for intermediate variables of similar velocity, Z is the acoustic impedance of the medium, coefficient m = h/c 0 δ t H is the space step length, delta t A and tau are coefficients for the time step.
4. The method of claim 3, wherein the Peng Robinson equation of state is expressed as:
wherein R is the general gas constant, T is the temperature, a 0 ，b 0 For the coefficients, ρ is the density and α (T) represents a function of temperature.
5. The method for estimating and controlling the suspension and residence of a liquid drop according to claim 1, wherein the continuous Boltzmann equation is discretized by a lattice Boltzmann method to obtain a fluid motion control equation:
f α (r+e α δ t )-f α (r，t)＝Ω(r，t)+δ t F α (r，t)
f α representing the particle distribution function, r being the position vector, δ t Is a time step, e α Is a unit vector of discrete velocity direction, omega is a collision operator, F α Is the total force to which the particle is subjected.
6. The method of estimating and controlling droplet levitation and residence according to claim 5, wherein MRT multiple relaxation model is used to linearize the collision operator Ω (r, t) to obtain a more stable, accurate and efficient difference model, resulting in the following fluid motion control equation:
where M represents a transition matrix, S represents a relaxation matrix, f α Which represents the function of the distribution of the particles,
is a function of the particle equilibrium distribution.
7. A method of estimating and controlling droplet levitation and residence according to claim 1, wherein chemical potential models are used to describe the homogeneous or heterogeneous forces between phase molecules, the chemical potential of fluid particles being given by:
wherein phi is a free energy function, mu is a chemical potential, kappa is a coefficient, rho is a density, and psi is a bulk free energy density;
and the phase intermolecular acting force as an external force item participates in the relaxation of the fluid particle distribution function to obtain a lattice Boltzmann model which can describe a two-phase field, wherein the magnitude of the phase intermolecular acting force is calculated by the following formula:
wherein F c (x) Is the intermolecular force to which the particle at the x position is subjected, c 0 In the case of the speed of sound,
is a hamiltonian.
8. The method for estimating and controlling droplet suspension and residence according to claim 1, wherein the acoustic radiation force derived from the acoustic field evolution participates in the relaxation of the fluid particle distribution function as an external force term, and the magnitude of the acoustic radiation force is given by the acoustic field energy gradient:
wherein, F s For acoustic radiation force, E for energy density in sound field space,<E>the time average of the energy is represented,
is a hamiltonian.
9. The method of estimating and controlling droplet levitation and droplet retention as claimed in claim 1, wherein the sound source participates in the calculation as a boundary condition, generating a simple harmonic determined by the sound source parameters; the reflecting end adopts a first type of boundary condition, namely a total reflection boundary condition; and the rest boundaries are set as second-order approximate absorption boundary conditions to simulate the dissipation of sound waves radiated to the experimental environment space.
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| CN102567563A (en) * | 2011-10-18 | 2012-07-11 | 上海交通大学 | Accurately quantitative calculation method for near-field ultrasonic levitation force |
| CN108763688A (en) * | 2018-05-17 | 2018-11-06 | 西北工业大学 | A kind of numerical computation method of electrostatic suspension liquid alloy heat transfer |
| CN111931438A (en) * | 2020-08-11 | 2020-11-13 | 广西师范大学 | Method for simulating liquid drop wetting phenomenon by lattice Boltzmann model based on chemical potential |
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| CN102567563A (en) * | 2011-10-18 | 2012-07-11 | 上海交通大学 | Accurately quantitative calculation method for near-field ultrasonic levitation force |
| CN108763688A (en) * | 2018-05-17 | 2018-11-06 | 西北工业大学 | A kind of numerical computation method of electrostatic suspension liquid alloy heat transfer |
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