CN111159926B - Liquid surface vibration isolation evaluation method based on Navier-Stokes equation and ALE - Google Patents

Liquid surface vibration isolation evaluation method based on Navier-Stokes equation and ALE Download PDF

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CN111159926B
CN111159926B CN201911159841.6A CN201911159841A CN111159926B CN 111159926 B CN111159926 B CN 111159926B CN 201911159841 A CN201911159841 A CN 201911159841A CN 111159926 B CN111159926 B CN 111159926B
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liquid level
liquid
vibration
ale
navier
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CN111159926A (en
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陈磊
王云涛
王冲
陈佳
郑东晖
胡晨辉
杨光
吴志飞
孔璐
张正宇
崔鑫莹
马致遥
黄晨
马海颖
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Nanjing University of Science and Technology
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    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/02—Analysing fluids
    • G01N29/036—Analysing fluids by measuring frequency or resonance of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
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Abstract

The invention discloses a liquid surface vibration isolation evaluation method based on a Navier-Stokes equation and an ALE. The method comprises the following steps: firstly, acquiring the density and dynamic viscosity of liquid and the geometric dimension of an acrylic square disc containing different damping when the liquid level is absolutely checked, and placing a vibration measuring instrument beside the liquid in an actual experiment so as to obtain the vibration frequency of the environment around the liquid level; then, the actual vibration frequency is combined with the gravity acceleration to obtain the acceleration of the cross section liquid level in the x direction and the y direction through decomposition; then establishing parameters and variables in COMSOL Multiphysics software, drawing the geometrical shape of an acrylic square disc containing damping, and establishing an incompressible Navier-Stokes equation and an ALE deformation grid; and finally, dividing a triangular finite element analysis unit, and performing transient research to obtain a simulation result of the vibration isolation effect of the free liquid level. The invention improves the detection efficiency and accuracy of the absolute detection of the liquid level.

Description

Liquid surface vibration isolation evaluation method based on Navier-Stokes equation and ALE
Technical Field
The invention belongs to the technical field of light interference measurement, and particularly relates to a liquid surface vibration isolation evaluation method based on a Navier-Stokes equation and an ALE.
Background
In the interference detection, the detection precision of the surface shape error is mainly influenced by the quality of a reference surface. In order to obtain absolute surface shape error distribution information of a measured surface, two existing solutions are provided, wherein the first solution is to provide a reference surface with higher surface shape precision, which is limited by the existing surface shape processing level; the second method is to calibrate the reference surface error and separate the influence of the reference surface error to improve the detection precision, namely absolute detection. In the plane absolute inspection, the error calibration of the reference surface can be realized by using a liquid level natural reference method.
The liquid level is taken as a standard plane, and the curvature radius of the liquid level is theoretically consistent with that of the earth due to the influence of gravity. If y is the radius of the liquid level and R is the radius of the earth, the deviation of the liquid level from the standard plane is h-y 2 /(2R). For computer-based level interference verification, h is a known fixed system error that can be eliminated during testing. The actual error due to the uneven change of the gravity of the earth is far smaller than that of other factors. Since the sag of the liquid surface having different diameters is different from each other and the sag is only λ/340 for a liquid surface having a diameter of 300mm, the liquid surface can be used as an absolute reference of the plane. In 2016, the advanced technology center of Raja Ramanna, SanJib Chatterjee et al, discussed a polarization dephasing Fizeau interferometer with a liquid surface as a reference plane, where the liquid surface reference plane was chosen from paraffin oil and placed on a high quality vibration isolation platform with proper liquid surface closure. In 2019, the whole ocean and the like propose a method for consolidating through an interference methodA method for measuring absolute flatness of a thin X-ray substrate is provided. The power term of the surface evenness of the projection surface of the interferometer is obtained by adopting dimethyl silicone oil as a reference surface. The liquid surface is used as a reference surface for absolute detection, so that the absolute calibration of the plane can be directly finished without complex operation, and the absolute calibration is relatively easy to realize; the liquid level calibration method has the disadvantages that the reference liquid level is very easily influenced by external environments, such as temperature, vibration, airflow and other external disturbances, the liquid level is very easily disturbed, the surface shape of the liquid level is damaged, and a high-precision calibration result is difficult to obtain in the actual use process. The liquid level stability evaluation of the liquid level natural reference method is mostly quantitative analysis from multiple measurement results, and the liquid level itself cannot be directly quantified all the time.
Disclosure of Invention
The invention aims to provide a quantifiable liquid surface vibration isolation assessment method based on a Navier-Stokes equation and an ALE, which has high efficiency and high accuracy.
The technical solution for realizing the purpose of the invention is as follows: a liquid level vibration isolation assessment method based on a Navier-Stokes equation and an ALE comprises the following steps:
step 1, establishing a Cartesian space coordinate system by taking a vertical observation surface as an outward z-axis and an observation surface as an x-y plane, inquiring to obtain density rho and dynamic viscosity eta of liquid used for absolute inspection of a liquid level, and placing a vibration measuring instrument beside the liquid in an actual experiment so as to obtain vibration frequency f of the environment around the liquid level;
step 2, combining the actual vibration frequency f with the gravity acceleration g, and decomposing to obtain the acceleration g of the cross-section liquid in the x and y directions x 、g y ；
Step 3, establishing parameters and variables in COMSOL Multiphysics software, and drawing the geometrical shape of the acrylic square disc containing the damping;
step 4, establishing an incompressible Navier-Stokes equation and an ALE deformation grid;
step 5, dividing a triangular finite element analysis unit, and performing transient analysis to obtain a simulation result of the free liquid level vibration isolation effect;
and 6, generating a one-dimensional liquid upper surface line graph and a two-dimensional liquid surface graph in a simulation result, quantifying the vibration isolation effect of the acrylic square plate with different damping, and exporting an animation to visually display the change process of the free liquid level.
Further, in step 1, taking the outward vertical observation plane as the z axis and the x-y plane in the observation plane, establishing a cartesian space coordinate system, inquiring to obtain the density ρ and the dynamic viscosity η of the liquid used for absolute detection of the liquid level, and placing a vibration measuring instrument beside the liquid in an actual experiment to obtain the vibration frequency f of the environment around the liquid level, specifically as follows:
setting the required vibration frequency f as a statistical average value, and taking the statistical average value obtained by multiple measurements as the final vibration frequency f:
Figure BDA0002285763810000021
in the formula (f) i The vibration frequency measured for the ith time;
the obtained statistical average vibration frequency f has periodic phase change; vibration phase to be varied with time
Figure BDA0002285763810000022
Expressed as:
Figure BDA0002285763810000023
in the formula (I), the compound is shown in the specification,
Figure BDA0002285763810000024
the phase of the periodic oscillation is denoted by t, and the oscillation time is denoted by t.
Further, the actual vibration frequency f is combined with the gravity acceleration g in the step 2, and the acceleration g of the cross-section liquid in the x direction and the y direction is obtained through decomposition x 、g y The method comprises the following steps:
the liquid in the acrylic square plate swings due to external vibration, and the swing is divided into gravity vectors in the x direction and the y direction to be represented, and the gravity vectors are transverseAcceleration g of cross-sectional liquid in two directions of x and y x 、g y Respectively as follows:
Figure BDA0002285763810000031
in the formula, g x 、g y Acceleration of the cross-section liquid in the x direction and the y direction respectively, g is gravity acceleration, and g is 9.81m/s 2 ，
Figure BDA0002285763810000032
Is the phase of the vibration as a function of time.
Further, the establishment of the incompressible Navier-Stokes equation and the ALE deformation grid in step 4 is as follows:
step 4.1, setting the bottom and the periphery of the acrylic square plate as sliding walls, setting the free liquid level as an open boundary, and performing numerical simulation on the fluid in a geometric model of the acrylic square plate with the damping by using a finite element method under the condition of a fixed constraint boundary of the free liquid level and the acrylic square plate, namely solving the shaking of the free liquid level in the acrylic square plate with the damping by using an incompressible Navier-Stokes equation to obtain a fluid flowing speed field and pressure field distribution; the incompressible Navier-Stokes equation as a macroscopic continuous model is based on continuous assumptions, and the fluid follows the laws of mass conservation, momentum conservation and energy conservation, and solves the velocity field u ═ u, w and the pressure p:
Figure BDA0002285763810000033
in the formula, rho is the density of the fluid, u is the velocity of the fluid, p is the pressure, I is a unit matrix, eta is the dynamic viscosity of the fluid, and F represents the volume force influencing the fluid;
step 4.2, solving the problem of irregular calculation of the Navier-Stokes equation by adopting an ALE technology, namely solving the domain boundary by adopting a moving grid, coupling the moving grid to a normal line of the surface of the fluid, and following the object which simulates the motion by adopting the ALE technology;
the grid equation boundary conditions for the free surface are:
Figure BDA0002285763810000034
in the formula (x) t ,y t ) T The speed of movement of the grid is represented,
Figure BDA0002285763810000035
a normal vector representing the boundary is shown,
Figure BDA0002285763810000036
representing the velocity vector of the fluid.
Compared with the prior art, the invention has the following remarkable advantages: (1) the COMSOL simulation is utilized, so that manpower, material resources and time are saved, and the detection efficiency is improved; (2) by utilizing digital simulation, the speed of a single point of the free surface along with time, the change curve of the whole surface along with time and the pressure distribution of free fluid at different depths can be accurately calculated, and the specific situation of the liquid in the acrylic square plate in the liquid level absolute test when the liquid vibrates along with the influence of the surrounding environment can be really reduced; (3) the parameters are quantized from the liquid level, accurate data for ensuring the stability of the liquid level are obtained, and an effective solution is provided for liquid level vibration isolation during absolute inspection of the liquid level through optical interference.
Drawings
Fig. 1 is a schematic diagram of a liquid level absolute checking device based on a point light source ectopic space synchronous phase shifting type Fizeau interferometer.
FIG. 2 is a schematic view of the geometry of the acrylic square plate with damping according to the present invention.
FIG. 3 is a diagram illustrating the result of triangular finite element partitioning according to the present invention.
FIG. 4 is a diagram of a liquid upper surface line of a one-dimensional liquid upper surface and a two-dimensional liquid surface diagram in the present invention, wherein (a) is a diagram of a one-dimensional liquid upper surface line and (b) is a diagram of a two-dimensional liquid surface.
FIG. 5 is a diagram showing the results of the effects of different damping positions on the liquid level vibration isolation in the present invention, wherein (a) is a diagram showing the results of the damping being placed to the left, (b) is a diagram showing the results of the damping being placed in the middle, and (c) is a diagram showing the results of the damping being placed to the right.
FIG. 6 is a graph showing the results of the vibration isolation of the liquid surface by the liquid surface height in the present invention, wherein (a) is a graph showing the results of the vibration isolation of the liquid surface by the liquid surface height of 25mm, (b) is a graph showing the results of the vibration isolation of the liquid surface by the liquid surface height of 20mm, (c) is a graph showing the results of the vibration isolation of the liquid surface by the liquid surface height of 15mm, (d) is a graph showing the results of the vibration isolation of the liquid surface by the liquid surface height of 10mm, and (e) is a graph showing the results of the vibration isolation of the liquid surface by the liquid surface height of 5 mm.
Fig. 7 is a schematic diagram showing the results of the effects of different damping amounts on the liquid level vibration isolation in the present invention, wherein (a) is a schematic diagram showing the results of the effects of 1 damping amount on the liquid level vibration isolation, (b) is a schematic diagram showing the results of the effects of 2 damping amounts on the liquid level vibration isolation, (c) is a schematic diagram showing the results of the effects of 3 damping amounts on the liquid level vibration isolation, and (d) is a schematic diagram showing the results of the effects of 4 damping amounts on the liquid level vibration isolation.
Detailed Description
The invention relates to a liquid surface vibration isolation evaluation method based on a Navier-Stokes equation and an ALE (equivalent algorithm), which comprises the following steps of:
step 1, establishing a Cartesian space coordinate system by taking a vertical observation surface as an outward z-axis and an observation surface as an x-y plane, inquiring to obtain density rho and dynamic viscosity eta of liquid used for absolute inspection of a liquid level, and placing a vibration measuring instrument beside the liquid in an actual experiment so as to obtain vibration frequency f of the environment around the liquid level;
step 2, combining the actual vibration frequency f with the gravity acceleration g, and decomposing to obtain the acceleration g of the cross-section liquid in the x and y directions x 、g y ；
Step 3, establishing parameters and variables in COMSOL Multiphysics software, and drawing the geometrical shape of the acrylic square disc containing the damping;
step 4, establishing an incompressible Navier-Stokes equation and an ALE deformation grid;
step 5, dividing a triangular finite element analysis unit, and performing transient analysis to obtain a simulation result of the free liquid level vibration isolation effect;
and 6, generating a one-dimensional liquid upper surface line graph and a two-dimensional liquid surface graph in a simulation result, quantifying the vibration isolation effect of the acrylic square plate with different damping, and exporting an animation to visually display the change process of the free liquid level.
Further, in step 1, taking the outward vertical observation plane as the z axis and the x-y plane in the observation plane, establishing a cartesian space coordinate system, inquiring to obtain the density ρ and the dynamic viscosity η of the liquid used for absolute detection of the liquid level, and placing a vibration measuring instrument beside the liquid in an actual experiment to obtain the vibration frequency f of the environment around the liquid level, specifically as follows:
setting the required vibration frequency f as a statistical average value, and taking the statistical average value obtained by multiple measurements as the final vibration frequency f:
Figure BDA0002285763810000051
in the formula (f) i The vibration frequency measured for the ith time;
the obtained statistical average vibration frequency f has periodic phase change; vibration phase to be varied with time
Figure BDA0002285763810000052
Expressed as:
Figure BDA0002285763810000053
in the formula (I), the compound is shown in the specification,
Figure BDA0002285763810000054
the phase of the periodic oscillation is denoted by t, and the oscillation time is denoted by t.
Further, the actual vibration frequency f is combined with the gravity acceleration g in the step 2, and the acceleration g of the cross-section liquid in the x direction and the y direction is obtained through decomposition x 、g y The method comprises the following steps:
the liquid in the acrylic square plate swings due to external vibration, and the swing is divided intoThe acceleration g of the cross-section liquid in the x and y directions is expressed by solving the gravity vector in the x and y directions x 、g y Respectively as follows:
Figure BDA0002285763810000061
in the formula, g x 、g y Acceleration of the cross-section liquid in the x direction and the y direction respectively, g is gravity acceleration, and g is 9.81m/s 2 ，
Figure BDA0002285763810000062
Is the phase of the vibration as a function of time.
Further, the establishment of the incompressible Navier-Stokes equation and the ALE deformation grid in step 4 is as follows:
step 4.1, setting the bottom and the periphery of the acrylic square plate as sliding walls, setting the free liquid level as an open boundary, and performing numerical simulation on the fluid in a geometric model of the acrylic square plate with the damping by using a finite element method under the condition of a fixed constraint boundary of the free liquid level and the acrylic square plate, namely solving the shaking of the free liquid level in the acrylic square plate with the damping by using an incompressible Navier-Stokes equation to obtain a fluid flowing speed field and pressure field distribution; the incompressible Navier-Stokes equation as a macroscopic continuous model is based on continuous assumptions, and the fluid follows the laws of mass conservation, momentum conservation and energy conservation, and solves the velocity field u ═ u, w and the pressure p:
Figure BDA0002285763810000063
in the formula, rho is the density of the fluid, u is the velocity of the fluid, p is the pressure, I is a unit matrix, eta is the dynamic viscosity of the fluid, and F represents the volume force influencing the fluid;
step 4.2, solving the problem of irregular calculation of the Navier-Stokes equation by adopting an ALE technology, namely solving a domain boundary by adopting a moving grid, coupling the moving grid to a normal line of the surface of the fluid, and following an object which simulates motion by adopting the ALE technology;
the grid equation boundary conditions for the free surface are:
Figure BDA0002285763810000064
in the formula (x) t ,y t ) T The speed of movement of the grid is represented,
Figure BDA0002285763810000065
a normal vector representing the boundary is shown,
Figure BDA0002285763810000066
representing the velocity vector of the fluid.
The present invention will be described in further detail with reference to the accompanying drawings.
With reference to fig. 1, the free liquid level vibration isolation evaluation method based on the Navier-Stokes equation and the ALE technology comprises the following steps:
step 1, combine figure 1, based on the absolute verifying attachment of liquid level of pointolite dystopy space synchronization phase shifting formula fizeau interferometer, including pointolite 1, first collimation objective 2, chess board grating 3, first convergent lens 4, aperture diaphragm 5, beam splitting subassembly 6, beam splitting board 7, CCD8, formation of image objective 9, lens array 10, beam splitting formation of image subassembly 11, second collimating mirror 12, reference mirror 13, the ya keli square dish 14 that holds liquid, free liquid level rock simulation result 15.
The method comprises the following steps of establishing a Cartesian space coordinate system by taking a vertical observation surface as an outward z axis and an observation surface as an x-y plane, inquiring to obtain density rho and dynamic viscosity eta of liquid used for absolute inspection of the liquid level, and placing a vibration measuring instrument beside the liquid in an actual experiment so as to obtain the vibration frequency f of the environment around the liquid level, wherein the specific steps are as follows:
setting the required vibration frequency f as a statistical average value, and taking the statistical average value obtained by multiple measurements as the final vibration frequency
Figure BDA0002285763810000071
In the formula f i The vibration frequency measured for the ith time;
the obtained statistical average vibration frequency f has periodic phase change; vibration phase to be varied with time
Figure BDA0002285763810000072
Expressed as:
Figure BDA0002285763810000073
in the formula
Figure BDA0002285763810000074
The phase of the periodic oscillation is denoted by t, and the oscillation time is denoted by t.
Step 2, combining the actual vibration frequency f with the gravity acceleration g, and decomposing to obtain the acceleration g of the cross-section liquid in the x and y directions x 、g y The method comprises the following steps:
the liquid in the acrylic square plate swings due to external vibration, the swing can be expressed by gravity vectors decomposed into x and y directions, and the acceleration g of the cross-section liquid in the x and y directions x 、g y Respectively as follows:
Figure BDA0002285763810000075
in the formula, g x 、g y Acceleration of the cross-section liquid in the x direction and the y direction respectively, g is gravity acceleration, 9.81m/s 2 。
And 3, establishing parameters and variables in COMSOL Multiphysics software by combining the graph shown in FIG. 2, and drawing the geometrical shape of the acrylic square disk containing the damping.
Step 4, establishing an incompressible Navier-Stokes equation and an Arbitrary Lagrangian-Eulerian (ALE) deformation grid technology, specifically as follows:
step 4.1, setting the bottom and the periphery of the acrylic square plate as sliding walls, setting the free liquid level as an open boundary, and performing numerical simulation on the fluid in a geometric model of the acrylic square plate with the damping by using a finite element method under the condition of a fixed constraint boundary of the free liquid level and the acrylic square plate, namely solving the shaking of the free liquid level in the acrylic square plate with the damping by using an incompressible Navier-Stokes equation to obtain a fluid flowing speed field and pressure field distribution; the incompressible Navier-Stokes equation as a macroscopic continuous model is based on continuous assumptions, and the fluid follows the laws of mass conservation, momentum conservation and energy conservation, and solves the velocity field u ═ u, w and the pressure p:
Figure BDA0002285763810000081
in the formula, rho is the density of the fluid, u is the velocity of the fluid, p is the pressure, I is a unit matrix, eta is the dynamic viscosity of the fluid, and F represents the volume force influencing the fluid;
step 4.2, solving the problem of irregular calculation of the Navier-Stokes equation by adopting an ALE technology, namely solving a domain boundary by adopting a moving grid, coupling the moving grid to a normal line of the surface of the fluid, and following an object which simulates motion by adopting the ALE technology;
the grid equation boundary conditions for the free surface are:
Figure BDA0002285763810000082
in the formula (x) t ,y t ) T The speed of movement of the grid is represented,
Figure BDA0002285763810000083
a normal vector representing the boundary is shown,
Figure BDA0002285763810000084
representing the velocity vector of the fluid.
And 5, dividing the triangular finite element analysis units by combining the graph 3, and performing transient research to obtain a simulation result of the liquid level vibration isolation effect.
And 6, generating a one-dimensional liquid upper surface line graph and a two-dimensional liquid surface graph in the research result by combining the graphs in the figures 4(a) to 4(b), quantifying the vibration isolation effect of the acrylic square disc with different damping, and deriving an animation to visually display the change process of the free liquid level.
Examples
Aiming at the influence of different damping positions on liquid level vibration isolation, two dampers with the width of 40mm and the height of 5mm are respectively placed in the acrylic square plate with the width of 360mm and the height of 20mm at the left side, the right side and the middle position, and simulation analysis is carried out as shown in fig. 5(a) to 5 (c). Through comparative analysis, it can be concluded that table 1:
TABLE 1
Position of damping To the left Intermediate (II) To the right
Liquid level shaking range (mm) 1.4 1.1 1.4
Curve of liquid level sloshing High at the left side The left and right are the same High at the right side
It can be seen that the vibration isolation effect is best when the damping is in the middle; the damping deflected to one side is equivalent to forming a wall at the middle position, so that a sloshing liquid level curve deflected to one side is formed.
Aiming at the influence of the liquid level height on the liquid level vibration isolation, liquids with the heights of 25mm, 20mm, 15mm, 10mm and 5mm are respectively put into acrylic square plates with the widths of 360mm and the heights of 20mm, and no damping is generated, and simulation analysis is carried out as shown in fig. 6(a) to 6 (e). Initial curve fluctuation is removed, only curve fluctuation in stable vibration is studied, and a conclusion can be drawn through comparative analysis, as shown in table 2:
TABLE 2
Liquid level height (mm) 25 20 15 10 5
Liquid level shaking range (mm) 18 10 7 5 3
It can be seen that the lower the liquid level is, the smaller the shaking condition of the liquid level is, and the stronger the capability of isolating external vibration is; compared with the liquid level shaking with damping, the liquid level shaking range is obviously enlarged when no damping exists; damping plays an important role in liquid level vibration isolation.
Aiming at the influence of different damping quantities on liquid level vibration isolation, 1, 2, 3 and 4 dampers with the width of 40mm and the height of 5mm are symmetrically placed in an acrylic square plate with the width of 360mm and the height of 20mm respectively, and simulation analysis is carried out as shown in figures 7(a) to 7 (d). Through comparative analysis, it can be concluded that, as shown in table 3:
TABLE 3
Amount of damping 1 2 3 4
Liquid level shaking range (mm) 1.2 1.2 1.1 1.0
It can be seen that the damping is uniformly distributed, the more the damping is, the better the vibration isolation effect is, but the effect difference is not large, which indicates that the damping quantity is not a key factor of the liquid vibration isolation.
In conclusion, the measurement result of the invention can be used for completing an experiment by controlling variables, the COMSOL simulation can be used for saving manpower, material resources and time, accurately calculating the speed of a single point of a free surface along with time, the change curve of the whole surface along with time and the pressure distribution of free fluid at different depths, and really reducing the specific situation when the liquid in the acrylic square plate vibrates along with the influence of the surrounding environment in the absolute detection of the liquid level. The invention realizes low cost and can quantize related data, and provides a solution for liquid level vibration isolation of absolute liquid level inspection.

Claims (3)

1. A liquid level vibration isolation assessment method based on a Navier-Stokes equation and an ALE is characterized by comprising the following steps:
step 1, establishing a Cartesian space coordinate system by taking a vertical observation surface as an outward z-axis and an observation surface as an x-y plane, inquiring to obtain density rho and dynamic viscosity eta of liquid used for absolute inspection of a liquid level, and placing a vibration measuring instrument beside the liquid in an actual experiment so as to obtain vibration frequency f of the environment around the liquid level;
step 2, combining the actual vibration frequency f with the gravity acceleration g, and decomposing to obtain the acceleration g of the cross-section liquid in the x and y directions x 、g y ；
Step 3, establishing parameters and variables in COMSOLULTIPhysics software, and drawing the geometrical shape of the acrylic square plate with the damping;
step 4, establishing an incompressible Navier-Stokes equation and an ALE deformation grid;
step 5, dividing a triangular finite element analysis unit, and performing transient analysis to obtain a simulation result of the free liquid level vibration isolation effect;
step 6, generating a one-dimensional liquid upper surface line graph and a two-dimensional liquid surface graph in a simulation result, quantifying the vibration isolation effect of acrylic square plates with different damping, and exporting an animation to visually display the change process of the free liquid level;
establishing the incompressible Navier-Stokes equation and the ALE deformation grid in the step 4 specifically comprises the following steps:
step 4.1, setting the bottom and the periphery of the acrylic square plate as sliding walls, setting the free liquid level as an open boundary, and performing numerical simulation on the fluid in a geometric model of the acrylic square plate with the damping by using a finite element method under the condition of a fixed constraint boundary of the free liquid level and the acrylic square plate, namely solving the shaking of the free liquid level in the acrylic square plate with the damping by using an incompressible Navier-Stokes equation to obtain a fluid flowing speed field and pressure field distribution; the incompressible Navier-Stokes equation as a macroscopic continuous model is based on continuous assumptions, and the fluid follows the laws of mass conservation, momentum conservation and energy conservation, and solves the velocity field u ═ u, w and the pressure p:
Figure FDA0003690900320000011
in the formula, rho is the density of the fluid, u is the velocity of the fluid, p is the pressure, I is a unit matrix, eta is the dynamic viscosity of the fluid, and F represents the volume force influencing the fluid;
step 4.2, solving the problem of irregular calculation of the Navier-Stokes equation by adopting an ALE technology, namely solving a domain boundary by adopting a moving grid, coupling the moving grid to a normal line of the surface of the fluid, and following an object which simulates motion by adopting the ALE technology;
the grid equation boundary conditions for the free surface are:
Figure FDA0003690900320000021
in the formula (x) t ,y t ) T The speed of movement of the grid is represented,
Figure FDA0003690900320000022
a normal vector representing the boundary is shown,
Figure FDA0003690900320000023
representing the velocity vector of the fluid.
2. The liquid level vibration isolation assessment method based on the Navier-Stokes equation and the ALE according to claim 1, wherein in the step 1, a Cartesian space coordinate system is established with a vertical observation plane as an outward z-axis and an observation plane as an x-y plane, the density p and the dynamic viscosity η of the liquid used for absolute inspection of the liquid level are obtained through query, and a vibration measuring instrument is placed beside the liquid in an actual experiment, so that the vibration frequency f of the environment around the liquid level is obtained, specifically as follows:
setting the required vibration frequency f as a statistical average value, and taking the statistical average value obtained by multiple measurements as the final vibration frequency f:
Figure FDA0003690900320000024
in the formula (f) i The vibration frequency measured for the ith time;
the obtained statistical average vibration frequency f has periodic phase change; vibration phase to be varied with time
Figure FDA0003690900320000028
Expressed as:
Figure FDA0003690900320000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003690900320000026
the phase of the periodic oscillation is denoted by t, and the oscillation time is denoted by t.
3. The liquid level vibration isolation assessment method based on Navier-Stokes equation and ALE according to claim 1, wherein the acceleration g of the cross-section liquid in the x and y directions is obtained by decomposing the actual vibration frequency f in combination with the gravity acceleration g in the step 2 x 、g y The method comprises the following steps:
the liquid in the acrylic square plate swings due to external vibration, the swing is decomposed into gravity vectors in the x direction and the y direction to represent, and the acceleration g of the cross-section liquid in the x direction and the y direction x 、g y Respectively as follows:
Figure FDA0003690900320000027
in the formula, g x 、g y Acceleration of the cross-section liquid in the x direction and the y direction respectively, g is gravity acceleration, and g is 9.81m/s 2 ，
Figure FDA0003690900320000031
Is the phase of the vibration as a function of time.
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