CN110426333B - Method for detecting particle content of suspension by using cylinder scattering sound pressure - Google Patents
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Abstract
The invention discloses a method for detecting the particle content of a suspension by using cylinder scattering sound pressure, which comprises the following steps: s01, establishing a cylinder model in the suspension containing the particles, introducing an Mcclements model, and obtaining an incident wave number expression under the model; s02, deducing a scattering sound pressure expression under the cylinder model in the silt particle-containing suspension; s03, obtaining theoretical scattering sound pressure distribution corresponding to different particle contents theoretically through data processing software simulation; s04, actually measuring the scattering sound pressure around the cylinder through instrument equipment, and exciting ultrasonic waves to the measured cylinder to obtain the actual scattering sound pressure distribution condition; and S05, comparing the actual scattering sound pressure distribution with the theoretical scattering sound pressure distribution, and obtaining the content of particles around the cylinder according to the scattering sound pressure distribution. The method for detecting the content of the suspension particles by using the cylinder scattering sound pressure has the advantages of simple operation and time saving.
Description
Technical Field
The invention relates to a method for detecting the particle content of a suspension by using cylinder scattering sound pressure, belonging to the technical field of ultrasonic nondestructive detection.
Background
With the development of the acoustic field, the sound wave scattering is very wide in practical application, such as exploration engineering, water acoustics, medical instrument and material detection, and the like. At present, the research on reflecting the characteristics of a target object by researching the scattering of the target object to sound waves in water is more, but the research on the scattering characteristics of the target object in suspension is less, and in practical situations, the water is often doped with silt particles, so that the problem is more complicated.
The traditional particle measurement methods include a sieving method, a microscopy method, an electric induction method, a sedimentation method and the like. But the screening method has long measuring time and is relatively rough; the microscope method has low measuring speed and high cost; the electric induction method requires that the particles to be detected are all suspended in the electrolyte solution, and has limitations.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects of the prior art and provides a method for detecting the content of suspension particles by using cylinder scattering sound pressure, which is simple to operate and saves time.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for detecting the particle content of a suspension by using cylinder scattering sound pressure comprises the following steps:
s01, establishing a cylinder model in the suspension containing the particles, introducing an Mcclements model, and obtaining an incident wave number expression under the model;
s02, deriving a scattering sound pressure expression under the cylinder model in the silt particle suspension according to the relation between the scattering sound pressure and the potential function of the cylinder, the radial particle velocity relation between the incident wave and the scattering wave on the surface of the cylinder and the wave number relation;
s03, obtaining theoretical scattering sound pressure distribution corresponding to different particle contents theoretically through data processing software simulation;
s04, actually measuring the scattering sound pressure around the cylinder through instrument equipment, and exciting ultrasonic waves to the measured cylinder to obtain the actual scattering sound pressure distribution condition;
and S05, comparing the actual scattering sound pressure distribution with the theoretical scattering sound pressure distribution, and obtaining the content of particles around the cylinder according to the scattering sound pressure distribution.
In S01, the expression of the ECAH model is as follows:
wherein k islIs the complex wavenumber of the acoustic wave under the ECAH model,
is the volume content of the particles, k is the complex wave number of the continuous phase of the fluid, AnAn n-th order ultrasonic scattering coefficient matrix, b particle size and i imaginary unit, and finally solving a linear equation of 6 orders to obtain A by combining the boundary conditions of the particle surface based on the wave equationn；
The Mcclements model assumes that the first two terms in the coefficient matrix dominate the propagation of the wave, and the first two terms have coefficients A0And A1The expressions in the case of long-wave incidence are respectively formula (2) and formula (3):
A0＝i(kb)3[(ρk'2/ρ'k2)-1]/3-k2bcTρτH(β/ρCb-β'/ρ'Cb')2 (2)
A1＝-i(kb)3/3·(ρ-ρ')/{2(ρ-ρ')/[1+3(1+i)δv/2b+3iδv 2/2b2]+3ρ} (3)
wherein H ═ {1/(1-iz) - τ/τ '. tan (z')/[ tan (z ') -z']}-1，z＝(1+i).b/δt，
Beta is the coefficient of thermal expansion, T is the absolute temperature, tau is the coefficient of thermal conductivity, CbSpecific heat capacity at constant pressure, viscosity, and deltavIs the viscous skin depth, δtFor thermal skin depth, ω is angular frequency, ρ is density, c is acoustic velocity, and each parameter is superscripted' ″ to represent a discrete particle phase parameter and not superscripted to represent a fluid continuous phase parameter.
S02, a plane wave p incident on the cylinder is transmittedi(r, θ, t) is decomposed into the superposition of cylindrical waves of each order to obtain the formula (4)
Wherein r is the distance from the scattering point to be measured to the center of the cylinder, p0Is the sound pressure amplitude of incident wave, t is a time factor,
J0(klr) is a zero order Bessel function of the first kind, Jn(klr) is a first class n-order Bessel function, omega is angular frequency, and theta is a scattered wave angle;
since the scattered wave is a wave in the positive direction r, the scattered wave can be expressed as a formula (5) by each order of cylindrical waves:
wherein the content of the first and second substances,
for the second type of hank function,
a is the radius of the cylinder,
is the derivative of a first class of nth order bessel function,
is the derivative of a second class of hank functions;
depending on the boundary conditions of the cylinder(s),
the far-field scattering sound pressure can be obtained as
In S03, the finite element simulation software Matlab software simulates the scattering sound pressure distribution under different particle contents theoretically. .
The particle volume contents set during the simulation were 0.6, 0.8 and 1.0.
In S04, the apparatus includes an ultrasonic signal generator and a sound pressure measuring instrument, the ultrasonic signal generator excites ultrasonic waves from one side of the cylinder, and the sound pressure measuring instrument acquires signals from the periphery of the cylinder to obtain actually measured scattered sound pressure distribution.
The invention has the beneficial effects that: the invention provides a method for detecting the particle content of suspension by using cylinder scattering sound pressure, which combines an Mcclements model with a cylinder model, deduces the scattering sound pressure according to the relation between the scattering sound pressure and a potential function, the relation between the incident wave on the surface of the cylinder and the radial particle velocity of the scattering wave and the relation between the wave number.
Drawings
FIG. 1 is a diagram of a mathematical model of the present invention;
fig. 2 shows the distribution of scattering sound pressure around the cylinder theoretically obtained according to the present invention with the particle volume contents of 0.6, 0.8 and 1.0, respectively.
Detailed Description
The present invention is further described with reference to the accompanying drawings, and the following examples are only for clearly illustrating the technical solutions of the present invention, and should not be taken as limiting the scope of the present invention.
In recent decades, as researchers have increasingly studied scattering properties of cylinders in particle suspensions and isotropic media, the scattering properties of target objects are studied by introducing relevant particle models, so as to reflect the characteristics of the target objects. The invention discloses a method for detecting the content of suspension particles by using cylinder scattering sound pressure, which combines an Mcclements model with a cylinder model, and the method is characterized in that a mathematical model diagram of the method is shown in figure 1, incident waves are incident along the z direction, a rectangular coordinate system is converted into a cylindrical coordinate system for calculation for simple calculation, a is the radius of a cylinder, r is the distance from a point to be measured in scattering to the center of the cylinder, and theta is a scattering angle.
The method specifically comprises the following steps:
step one, establishing an ECAH model containing particle suspension, introducing an Mccelements model, and obtaining an incident wave number expression under the model. The ECAH model is mainly used for researching the fluctuation condition in suspension containing spherical particles, when a plane wave is incident on the particles, 6 waves can be excited, and the complex wave number k under the model islFrom the relationship between these 6 amplitudes compared to the incident amplitude, the expression is as follows:
wherein k islIs the complex wavenumber of the acoustic wave under the ECAH model,
is the volume content of the particles, k is the complex wave number of the continuous phase of the fluid, AnAn n-th order ultrasonic scattering coefficient matrix, b particle size and i imaginary unit, and finally solving a linear equation of 6 orders to obtain A by combining the boundary conditions of the particle surface based on the wave equationn、
The first two terms in the coefficient matrix play a leading role in wave propagation, and the ECAH model is simplified based on the leading role, so that the Mccelements model is obtained. First two coefficients A0And A1The expressions in the case of long-wave incidence are respectively formula (2) and formula (3):
A0＝i(kb)3[(ρk'2/ρ'k2)-1]/3-k2bcTρτH(β/ρCb-β'/ρ'Cb')2 (2)
A1＝-i(kb)3/3·(ρ-ρ')/{2(ρ-ρ')/[1+3(1+i)δv/2b+3iδv 2/2b2]+3ρ} (3)
wherein H ═ {1/(1-iz) - τ/τ '. tan (z')/[ tan (z ') -z']}-1，z＝(1+i).b/δt，
Beta is the coefficient of thermal expansion, T is the absolute temperature, tau is the coefficient of thermal conductivity, CbSpecific heat capacity at constant pressure, viscosity, and deltavIs the viscous skin depth, δtFor thermal skin depth, ω is angular frequency, ρ is density, c is acoustic velocity, and each parameter is superscripted' ″ to represent a discrete particle phase parameter and not superscripted to represent a fluid continuous phase parameter.
And step two, deriving a scattering sound pressure expression under the cylinder model in the silt particle suspension according to the relation between the scattering sound pressure and the potential function of the Mcclements model, the relation between the incident wave on the surface of the cylinder and the radial particle velocity of the scattering wave and the relation between the wave numbers. Directing a plane wave p incident on a cylinderi(r, θ, t) is decomposed into the superposition of cylindrical waves of each order to obtain the formula (4)
Wherein r is the distance from the scattering point to be measured to the center of the cylinder, p0Is the sound pressure amplitude of incident wave, t is a time factor,
J0(klr) is a zero order Bessel function of the first kind, Jn(klr) a first class of nth order Bessel functions, wherein omega is angular frequency and theta is a scattered wave angle;
since the scattered wave is a wave in the positive direction r, the scattered wave can be expressed as a formula (5) by using a cylindrical wave of each order
Wherein the content of the first and second substances,
for the second type of hank function,
a is the cylinder radius, Jn(klr) is a first class of nth order bessel function,
is the derivative of a first class of nth order bessel function,
is the derivative of the second type of hank function.
Depending on the boundary conditions of the cylinder(s),
wherein a is the radius of the cylinder, and the obtained far-field scattered sound pressure is
And thirdly, obtaining theoretical scattering sound pressure distribution corresponding to different particle contents theoretically through simulation of data processing software. The distribution of the scattering sound pressure around the cylinder obtained by the theory of the volume content of the particles of 0.6, 0.8 and 1.0 is shown in fig. 2.
And fourthly, actually measuring the scattering sound pressure around the cylinder through instrument equipment, and exciting ultrasonic waves to the measured cylinder to obtain the actual scattering sound pressure distribution condition. The instrument equipment comprises an ultrasonic signal generator and a sound pressure measuring instrument, wherein the ultrasonic signal generator excites ultrasonic waves from one side of a cylinder, and the sound pressure measuring instrument acquires signals from the periphery of the cylinder to obtain actually-measured scattered sound pressure.
And step five, comparing the actual scattering sound pressure distribution condition with the theoretical scattering sound pressure distribution, and obtaining the content of particles around the cylinder according to the scattering sound pressure distribution.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (5)
1. A method for detecting the particle content of a suspension by using cylinder scattering sound pressure is characterized in that: the method comprises the following steps:
s01, establishing a cylinder model in the particle-containing suspension, introducing an Mccelements model to obtain an incident wave number expression under the model, wherein the Mccelements model is obtained by simplifying an ECAH model, and the expression of the ECAH model is as follows:
wherein k islIs the complex wavenumber of the acoustic wave under the ECAH model,
is the volume content of the particles, k is the complex wave number of the continuous phase of the fluid, AnAn nth order ultrasonic scattering coefficient matrix, b particle size, i imaginary unit, and a 6 th order linear equation are obtained by combining the boundary conditions of the particle surface based on the wave equationn；
The Mccclements model assumes in a coefficient matrixThe first two terms have a dominant effect on the propagation of the wave, and the first two terms have coefficients A0And A1The expressions in the case of long-wave incidence are respectively formula (2) and formula (3):
A0＝i(kb)3[(ρk'2/ρ'k2)-1]/3-k2bcTρτH(β/ρCb-β'/ρ'Cb')2 (2)
A1＝-i(kb)3/3·(ρ-ρ')/{2(ρ-ρ')/[1+3(1+i)δv/2b+3iδv 2/2b2]+3ρ} (3)
wherein H ═ {1/(1-iz) - τ/τ '. tan (z')/[ tan (z ') -z']}-1，z＝(1+i)·b/δt，
Beta is the coefficient of thermal expansion, T is the absolute temperature, tau is the coefficient of thermal conductivity, CbSpecific heat capacity at constant pressure, viscosity, and deltavIs the viscous skin depth, δtThe thermal skin depth, omega is angular frequency, rho is density, c is sound velocity, each parameter is added with a prime sign' ″ to represent a discrete particle phase parameter, and the parameter is not added with a prime sign to represent a fluid continuous phase parameter;
s02, deriving a scattering sound pressure expression under the cylinder model in the silt particle suspension according to the relation between the scattering sound pressure and the potential function of the cylinder, the radial particle velocity relation between the incident wave and the scattering wave on the surface of the cylinder and the wave number relation;
s03, obtaining theoretical scattering sound pressure distribution corresponding to different particle contents theoretically through data processing software simulation;
s04, actually measuring the scattering sound pressure around the cylinder through instrument equipment, and exciting ultrasonic waves to the measured cylinder to obtain the actual scattering sound pressure distribution condition;
and S05, comparing the actual scattering sound pressure distribution with the theoretical scattering sound pressure distribution, and obtaining the content of particles around the cylinder according to the scattering sound pressure distribution.
2. The method for detecting the particle content of the suspension by using the cylinder scattering sound pressure as claimed in claim 1, wherein: s02, a plane wave p incident on the cylinder is transmittedi(r, θ, t) is decomposed into the superposition of cylindrical waves of each order to obtain the formula (4)
Wherein r is the distance from the scattering point to be measured to the center of the cylinder, p0Is the sound pressure amplitude of incident wave, t is a time factor,
J0(klr) is a zero order Bessel function of the first kind, Jn(klr) is a first class n-order Bessel function, omega is angular frequency, and theta is a scattered wave angle;
since the scattered wave is a wave in the positive direction r, the scattered wave can be expressed as a formula (5) by each order of cylindrical waves:
wherein the content of the first and second substances,
for the second type of hank function,
a is the radius of the cylinder,
is the derivative of a first class of nth order bessel function,
is the derivative of a second class of hank functions;
depending on the boundary conditions of the cylinder(s),
the far-field scattering sound pressure can be obtained as
3. The method for detecting the particle content of the suspension by using the cylinder scattering sound pressure as claimed in claim 1, wherein: in S03, the finite element simulation software Matlab software simulates the scattering sound pressure distribution under different particle contents theoretically.
4. The method for detecting the particle content of the suspension by using the cylinder scattering sound pressure as claimed in claim 3, wherein: the particle volume contents set during the simulation were 0.6, 0.8 and 1.0.
5. The method for detecting the particle content of the suspension by using the cylinder scattering sound pressure as claimed in claim 1, wherein: and S04, the instrument equipment comprises an ultrasonic signal generator and a sound pressure measuring instrument, the ultrasonic signal generator excites ultrasonic waves from one side of the cylinder, and the sound pressure measuring instrument acquires signals from the periphery of the cylinder to be measured to obtain the distribution of actually measured scattered sound pressure.
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