CN102944507B - A kind of measurement mechanism of lightweight abnormity particle drag coefficient and measuring method - Google Patents

Abstract

The invention discloses a measuring device and a measuring method for the drag coefficient of light irregular particles, including a transparent fluidized cavity, an air compressor, an air flow meter, a first image acquisition unit, a second image acquisition unit, and a sheet-shaped laser Light source and processing unit; the air supply port of the air compressor is connected to the air inlet at the bottom of the transparent fluidized cavity through a pipeline, and a valve and the air flow meter are arranged on the pipeline, and the transparent fluidized cavity The upper part is provided with a feeding port; the first image acquisition unit, the second image acquisition unit and the sheet-shaped laser light source are located outside the transparent fluidized cavity, and the central axis of the transparent fluidized cavity is located at the center of the sheet-shaped laser light source In the plane of the optical path, the connection line between the first image acquisition unit and the second image acquisition unit is perpendicular to the optical path plane of the sheet-shaped laser light source; the image output terminals of the first image acquisition unit and the second image acquisition unit and the image of the processing unit connected to the input.

Description

Measuring device and method for drag coefficient of light irregular particles

technical field

The invention relates to a measuring device and a measuring method for the drag coefficient of light special-shaped particles, and belongs to the technical field of fluidized bed and multiphase flow measurement.

Background technique

Gas-solid two-phase flow is a common phenomenon in petrochemical, metallurgy, cement and other multi-process industries. The study of the interaction mechanism between particles and fluids is helpful for rational design, scale-up and energy efficiency optimization of gas-solid two-phase flow. Industrial systems or process equipment. The drag coefficient characterizes the interaction strength between particles and fluid, and is one of the core parameters to reveal the interaction mechanism between particles and fluid. Its numerical value is not only affected by the Reynolds number of the airflow field, but also related to the characteristics of the particle itself, such as material, shape, size, surface roughness and other factors.

Due to the importance of the drag coefficient in gas-solid/liquid flow, scholars at home and abroad have carried out a lot of experiments, theoretical and numerical simulation work on it, and have obtained results for spherical or regular shapes (such as discs, Elliptical, rod-shaped, etc.) particle drag coefficient theoretical model or empirical formula and other achievements, and the development of the application of sedimentation method to measure the drag coefficient of regular shape particles, and there are corresponding commercial testing equipment. The measurement principle is to calculate the drag coefficient of particles in the static flow field by measuring the final settling velocity of the particles in the liquid when they move at a constant speed, and according to the force model of the particles moving at a uniform speed in the liquid.

However, for the measurement of the drag number of light (density smaller than water), irregular (irregular shape), and rough surface particles, conventional sedimentation method equipment using water or oil as the medium is not suitable. The main problems are:

(1) The density of the particles suitable for the sedimentation method needs to be greater than the density of the liquid, but for biomass particles such as millet, straw and other crops, most of them have a fibrous structure and are light in texture, so the use of gravity sedimentation equipment needs to choose a low density and viscous liquid. Fluid medium with high hysteresis coefficient. This is time-consuming and labor-intensive, and requires further analysis to determine the flow characteristic parameters of the fluid medium. In addition, when using a liquid medium, the fluid will infiltrate the surface of the particle so that it penetrates into the particle, which will also change the physical properties of the particle itself, thereby affecting the accuracy of the drag force measurement;

(2) When the particles fall in the gas, due to the behavior of acceleration and rotation, the particles are not only affected by the drag force, gravity, buoyancy and additional mass force, but also affected by the Bassett force produced by the acceleration or deceleration of the particles. (Basset) force, Magnus force caused by the rotational motion of particles, etc. Compared with the air medium, the viscosity coefficient of the liquid is larger, and the rotation behavior of light and special-shaped particles in the air is difficult to reproduce in the liquid medium, so the drag coefficient of the light and special-shaped particles in the air medium is measured than in the liquid. The measured value in the medium is closer to the real working condition of the gas-solid two-phase flow in the industrial system or equipment, and the measured value is more accurate and reliable;

(3) Since the drag coefficient of particles is related to the Reynolds number of the flow field, compared with the liquid flow field, the high Reynolds number flow field is easier to realize through the flow valve.

In addition, for the measurement of the drag coefficient of light irregular particles, scholars at home and abroad have also proposed the method of using a single high-definition high-speed camera, but this method is limited by the viewing angle of a single camera, and cannot accurately measure the drag coefficient of the irregular particles in the flow field. The angular velocity and the windward cross-section during the three-dimensional rotation process, the measurement method needs to be further studied and perfected.

Contents of the invention

The purpose of the present invention is to provide a device suitable for measuring the drag coefficient of light special-shaped particles and a measurement method using the device, so as to solve the problem that the gravity sedimentation method and single high-speed camera technology are not suitable for measuring the drag coefficient of this type of particle question.

In order to achieve the above objectives, the technical solution of the present invention is as follows: a device for measuring the drag coefficient of light irregular particles, characterized in that it includes a transparent fluidized cavity, an air compressor, an air flow meter, a first image acquisition unit, A second image acquisition unit, a sheet-shaped laser light source and a processing unit;

The air supply port of the air compressor is connected to the air inlet at the bottom of the transparent fluidized cavity through a pipeline, the pipeline is provided with a valve and the air flow meter, and the upper part of the transparent fluidized cavity is provided with a feeding port ; The first image acquisition unit, the second image acquisition unit and the sheet-shaped laser light source are located outside the transparent fluidized cavity, and the central axis of the transparent fluidized cavity is located in the optical path plane of the sheet-shaped laser light source. The connection line between the first image acquisition unit and the second image acquisition unit is perpendicular to the light path plane of the sheet-shaped laser light source;

The image output ends of the first image acquisition unit and the second image acquisition unit are connected to the image input end of the processing unit.

More preferably, the first image acquisition unit and the second image acquisition unit are both digital cameras with a resolution of not less than 640×480 pixels and a sampling rate of not less than 25 frames per second.

In a more preferred solution, the thickness of the sheet-shaped laser light source is adjustable.

In a more preferred solution, the transparent fluidized cavity is square.

More preferably, the processing unit is a computer equipped with an image acquisition card.

Adopt the measuring method of the measuring device of the drag coefficient of the lightweight special-shaped particle of the present invention, comprise the steps:

1) Adjust the opening of the valve on the pipeline connected to the air compressor to keep the airflow field in the transparent fluidization chamber at a stable gas velocity;

2) Turn on the sheet-shaped laser light source, turn on two image acquisition units with different sampling frequencies at the same time, put the measured particles into the transparent fluidization cavity through the feeding port, and send the video data acquired by the image acquisition unit to the processing unit;

3) The processor unit obtains the distance ΔS _ii′ of the particles in the two frames of images corresponding to the two digital cameras by comparing the pictures obtained by the two digital cameras, i=1,2,…,n; then the particles pass through ΔS _{ii ′} has an average velocity of: $u_i=\frac{{\mathrm{\ΔS}}_{i-i^{\′}}}{\mathrm{\Δt}}---(1-1);$

Among them, Δt is the time for the particle to pass through the distance of ΔS ii _′ , and ΔS _ii′ is the difference between the distance values of the corresponding pictures of the two cameras relative to the same reference line; i is the serial number of the picture;

According to the formula (1-1), the acceleration of the particles falling at this distance Si is:

Among them, S _i is the distance between the i-th picture and the i-1-th picture; t _i is the time for the particle to pass through the distance of S _i ;

From the formula (1-1) (1-2), (i=1,2,...,n);

Among them, u _p is the average velocity of the particle, a _p is the average acceleration of the particle;

Set the angle θ _i between the long axis direction of the particles in each frame of video and the horizontal direction; by comparing the pictures obtained by two digital cameras, the angle between the long axis direction and the horizontal axis of the particles in the two frames of images corresponding to the two digital cameras is obtained. Angle difference Δθ _ii′ ;

but $w_i=\frac{{\mathrm{\Δ\θ}}_{i-i^{\′}}}{\mathrm{\Δt}}---(1-3);$

The average angular velocity of the particles is obtained from the formula (1-3):

4) According to the particle force model: $\stackrel{\&Right\; Arrow;}{f_g}+\stackrel{\&Right\; Arrow;}{f_{\mathrm{D.}}}+\stackrel{\&Right\; Arrow;}{f_b}+\stackrel{\&Right\; Arrow;}{f_m}+\stackrel{\&Right\; Arrow;}{f_B}+\stackrel{\&Right\; Arrow;}{f_m}=m_p\stackrel{\&Right\; Arrow;}{a_p}---\left(1\right)$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; proj</span>}}<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; \&pi;\&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\frac{\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; d\&tau;</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

A _proj = A ₀ cosθ (8)

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

in, is the particle acceleration, They are the gravity, drag force, buoyancy force, additional mass force, Basset force and Magnus force of the particle;

Among them, r _p is the equivalent diameter of the particle; m _p is the mass of a single particle; V _p is the volume of a single particle; is the relative velocity between the particle and the fluid, that is, is the velocity of the fluid, is the velocity of a single particle, for ρ _p is the density of the particles; ρ _f is the density of the fluid; μ _f is the shear viscosity coefficient of the fluid; A _proj is the projected area of the particles facing the moving direction _; The average value of the angle between the long axis of the particles in the measurement area and the horizontal direction;

From formulas (1) to (9), the drag coefficient of a single particle can be calculated as:

In a more preferred solution, the two image acquisition units are synchronously triggered by the processing unit, and their frame rates are set at intervals of 3 to 5 frames, so as to obtain image sequences with time intervals of milliseconds.

Wherein, formulas 1 to 9 are all known technologies and will not be described in detail.

Compared with prior art, the beneficial effect of the present invention:

(1) Non-contact measurement, the measurement process does not interfere with the interaction between the particles in the fluidization chamber and the airflow field;

(2) Using dual-camera difference-frequency shooting technology, it is possible to capture detailed shapes (translation, rotation and acceleration) of particles running in the airflow field, and to obtain images of millisecond-level time intervals of particles falling in the fluidization chamber sequence;

(3) This device can measure the acceleration and angular velocity of the particles during the running process, so it can indirectly measure the Basset (Basset) force and Mag that affect the measurement accuracy of the drag coefficient due to the acceleration and rotation of the particles. Magnus force;

(4) Compared with the technique of measuring particle drag coefficient by gravity sedimentation method, since the fluid medium is air, the test conditions simulated by the device of the present invention are closer to the working conditions of the actual gas-solid two-phase flow system, so the measurement results are more accurate ;

(5) Compared with the liquid medium, the gas flow field medium is used, and the test is more convenient, and it is easy to determine the corresponding particle drag coefficient under the condition of high Reynolds number.

Description of drawings

Fig. 1 is a system schematic diagram of a specific embodiment of the device for measuring the drag coefficient of lightweight special-shaped particles of the present invention;

Among them, fluidization chamber 1, particle 2, industrial camera 3, sheet-shaped laser source 4, computer 7, control valve 8, air flow meter 9, and air compressor 10.

Fig. 2 Schematic diagram of the measurement principle of the average velocity and average acceleration of the special-shaped particles;

Fig. 3 Schematic diagram of measurement principle of rotational angular velocity of special-shaped particles.

detailed description

Specific embodiments of the present invention will be described in detail below with reference to FIGS. 1 , 2 and 3 .

A device for measuring the drag coefficient of light irregular particles, characterized in that it includes a transparent fluidized cavity, an air compressor, an air flow meter, a first image acquisition unit, a second image acquisition unit, a sheet-shaped laser light source and processing unit;

The air supply port of the air compressor is connected to the air inlet at the bottom of the transparent fluidized cavity through a pipeline, the pipeline is provided with a valve and the air flow meter, and the upper part of the transparent fluidized cavity is provided with a feeding port ; The first image acquisition unit, the second image acquisition unit and the sheet-shaped laser light source are located outside the transparent fluidized cavity, and the central axis of the transparent fluidized cavity is located in the optical path plane of the sheet-shaped laser light source. The connection line between the first image acquisition unit and the second image acquisition unit is perpendicular to the light path plane of the sheet-shaped laser light source;

The image output ends of the first image acquisition unit and the second image acquisition unit are connected to the image input end of the processing unit.

More preferably, the first image acquisition unit and the second image acquisition unit are both digital cameras with a resolution of not less than 640×480 pixels and a sampling rate of not less than 25 frames per second.

In a more preferred solution, the thickness of the sheet-shaped laser light source is adjustable.

In a more preferred solution, the transparent fluidized cavity is square.

More preferably, the processing unit is a computer equipped with an image acquisition card.

Adopt the measuring method of the measuring device of the drag coefficient of the lightweight special-shaped particle of the present invention, comprise the steps:

1) Adjust the opening of the valve on the pipeline connected to the air compressor to keep the airflow field in the transparent fluidization chamber at a stable gas velocity;

2) Turn on the sheet-shaped laser light source, turn on two image acquisition units with different sampling frequencies at the same time, put the measured particles into the transparent fluidization cavity through the feeding port, and send the video data acquired by the image acquisition unit to the processing unit;

3) The processor unit obtains the distance ΔS _ii′ of the particles in the two frames of images corresponding to the two digital cameras by comparing the pictures obtained by the two digital cameras, i=1,2,…,n; then the particles pass through ΔS _{ii ′} has an average velocity of: $u_i=\frac{{\mathrm{\&Delta;S}}_{i-i^{\&prime;}}}{\mathrm{\&Delta;t}}---(1-1);$

Among them, Δt is the time for the particle to pass through the distance of ΔS ii _′ , and ΔS _ii′ is the difference between the distance values of the corresponding pictures of the two cameras relative to the same reference line; i is the serial number of the picture, and i=1 means the first picture;

According to the formula (1-1), the acceleration of the particle falling at the distance of S _i is:

Among them, S _i is the distance between the i-th picture and the i-1-th picture; t _i is the time for the particle to pass through the distance of S _i ;

From the formula (1-1) (1-2), (i=1,2,...,n);

Among them, u _p is the average velocity of the particle, a _p is the average acceleration of the particle;

Set the angle θ _i between the long axis direction of the particles in each frame of video and the horizontal direction; by comparing the pictures obtained by two digital cameras, the angle between the long axis direction and the horizontal axis of the particles in the two frames of images corresponding to the two digital cameras is obtained. Angle difference Δθ _ii′ ;

but $w_i=\frac{{\mathrm{\&Delta;\&theta;}}_{i-i^{\&prime;}}}{\mathrm{\&Delta;t}}---(1-3);$

The average angular velocity of the particles is obtained from the formula (1-3):

4) According to the particle force model: $\stackrel{\&Right\; Arrow;}{f_g}+\stackrel{\&Right\; Arrow;}{f_{\mathrm{D.}}}+\stackrel{\&Right\; Arrow;}{f_b}+\stackrel{\&Right\; Arrow;}{f_m}+\stackrel{\&Right\; Arrow;}{f_B}+\stackrel{\&Right\; Arrow;}{f_m}=m_p\stackrel{\&Right\; Arrow;}{a_p}---\left(1\right)$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; proj</span>}}<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; \&pi;\&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\frac{\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; d\&tau;</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}\mathrm{<span\; class="notranslate">\; d\&tau;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&pi;r</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

A _proj = A ₀ cosθ (8)

${\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

in, is the particle acceleration, They are the gravity, drag force, buoyancy force, additional mass force, Basset force and Magnus force of the particle;

Among them, r _p is the equivalent diameter of the particle; m _p is the mass of a single particle; V _p is the volume of a single particle; is the relative velocity between the particle and the fluid, that is, is the velocity of the fluid, is the velocity of a single particle, for ρ _p is the density of the particles; ρ _f is the density of the fluid; μ _f is the shear viscosity coefficient of the fluid; A _proj is the projected area of the particles facing the moving direction _; The average value of the angle between the long axis of the particles in the measurement area and the horizontal direction;

From formulas (1) to (9), the drag coefficient of a single particle can be calculated as:

In a more preferred solution, the two image acquisition units are synchronously triggered by the processing unit, and their frame rates are set at intervals of 3 to 5 frames, so as to obtain image sequences with time intervals of milliseconds.

The present invention is aimed at the problems existing in the measurement methods of the drag coefficient of particles, and proposes to use two digital cameras with different frame rates and apply the difference frequency shooting technology to simultaneously record the process of light and special-shaped particles running in the airflow field. Video image sequences with millisecond time intervals can be obtained. Through the method of image processing, the moving position and rotation angle of the particles in the airflow field are measured, and the translational velocity, translational acceleration and rotational angular velocity of the particles are calculated. Then, according to the force formula of the particles in the airflow field, the drag coefficient of the particles is calculated.

The object of the present invention is achieved in this way: in the gas-solid two-phase flow, the drag force of the particles in the fluid is the most basic form of interaction between the particles and the fluid. When the velocity of the particles is different from the velocity of the fluid, the interaction will occur. The side with high speed will be resisted by the side with low speed; the side with low speed will be dragged by the side with high speed. Resistance and drag are equal in magnitude and opposite in direction. Usually the fluid velocity is greater than the particle velocity, so that the particle experiences a drag force from the fluid. The drag coefficient of a particle is the ratio of the drag force of the fluid acting on the particle to the product of the projected area of the particle in its direction of motion and the product of the fluid dynamic pressure. The factors that affect the particle drag coefficient are: particle Reynolds number, shape factor, windward area , surface roughness and wall effects and other factors. The measurement parameters corresponding to the influencing factors include: particle translational velocity, particle translational acceleration, angle between the long axis direction of the particle and the horizontal direction, particle angular velocity, and windward area. The use of gas medium is closer to the realization of working conditions in gas-solid two-phase flow systems or equipment than liquid media such as oil and water.

In order to realize the object of the present invention: build measuring devices including video acquisition, video processing and auxiliary parts: wherein the video acquisition part is made up of two digital cameras, a computer and a sheet-shaped laser light source, by the difference frequency shooting technology of two cameras, Record the running state of the particles; the computer video processing part is a computer equipped with an image acquisition card, which uses digital image processing technology to process the obtained video, and analyzes the position, long axis diameter and horizontal direction of the particles on each frame of the video image The included angle and the time interval between frames are calculated to calculate the particle’s translational velocity, translational acceleration, rotational angular velocity, and the average windward cross-sectional area of the particle in the rotation period. The force formula calculates the drag coefficient of the measured particles; the auxiliary part of the measurement includes a transparent square fluidization chamber, an air flow valve, a flow meter and an air compressor. During the measurement, by changing the opening of the valve, the amount of air supplied by the air compressor can be adjusted, thereby adjusting the speed of the airflow field in the fluidization cavity, and the total air flow is measured by the air flow meter.

The specific implementation steps are:

1. Adjust the container to the vertical state, select the area to be measured, the vertical height L of the measurement area is greater than 0.5m (the height of the container is 1.2m), the initial position of the particle drop during measurement should avoid the influence of the wall and the entrance, set two The frame rates of the digital cameras are 30fps and 27fps respectively. Adjust the height of the two digital cameras and the position of the laser so that the digital camera and the laser are aligned with the measurement area. The measurement area is overlapped by the shooting range of the camera and the optical path plane of the sheet-shaped laser light source Partly, the central axis of the transparent fluidization cavity is located in the plane of the measurement area, and the upper end of the measurement area is 5cm away from the upper end of the opening of the fluidization cavity. At the same time, two digital cameras are placed at the same level and relatively in the middle of the measurement area.

2. Use a data transmission line to connect the image output ends of the two digital cameras with the input ends of the image acquisition card, power on the computer and the digital camera in turn, and use the video acquisition software matched with the image acquisition card to drop a single particle freely from the feeding position to make the particle The largest cross-section faces the falling direction of the particles, observe the effect of the captured image, adjust the position of the digital camera and the laser, make the laser irradiate the measurement area, and make the particles fall in the middle of the picture.

3. After the working conditions to be measured are ready, start to shoot the video of the flow field, click to start the measurement, the two digital cameras work synchronously, then put the particles at the feeding position, record the particle movement video and save it. The single shooting time depends on the single frame image resolution, image acquisition speed, and computer memory size, and it is guaranteed that the video size of a single shot does not exceed the available size of the computer memory.

The above descriptions are only preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments, but all equivalent modifications or changes made by those of ordinary skill in the art according to the disclosure of the present invention should be included within the scope of protection described in the claims.

Claims (6)

1. The measuring method of the drag coefficient of the light special-shaped particles is characterized in that a measuring device of the drag coefficient of the light special-shaped particles is adopted, and the device comprises a transparent fluidization cavity, an air compressor, an air flow meter, a first image acquisition unit, a second image acquisition unit, a sheet-shaped laser light source and a processing unit;

the air inlet of the air compressor is connected with the air inlet at the bottom of the transparent fluidization cavity through a pipeline, a valve and the air flow meter are arranged on the pipeline, and a charging opening is arranged at the upper part of the transparent fluidization cavity; the first image acquisition unit, the second image acquisition unit and the sheet-shaped laser light source are positioned outside the transparent fluidization cavity, the central axis of the transparent fluidization cavity is positioned in the light path plane of the sheet-shaped laser light source, and the connecting line of the first image acquisition unit and the second image acquisition unit is vertical to the light path plane of the sheet-shaped laser light source;

the image output ends of the first image acquisition unit and the second image acquisition unit are connected with the image input end of the processing unit, and the sampling frequencies of the two image acquisition units are different;

the specific measurement method comprises the following steps:

1) adjusting the opening of a valve on a pipeline connected with an air compressor to ensure that the airflow field in the transparent fluidized cavity keeps stable air speed;

2) opening a sheet-shaped laser light source, simultaneously opening two image acquisition units with different sampling frequencies, putting the measured particles into the transparent fluidized cavity through a feeding port, and sending video data acquired by the image acquisition units to a processing unit;

3) the processor unit obtains the distance delta S of the particles in the two frames of images corresponding to the two digital cameras by comparing the images obtained by the two digital cameras_i-i'I ═ 1,2, …, n; the particles pass through Δ S_i-i'The average speed of (d) is: <math> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;S</mi> <mrow> <mi>i</mi> <mo>-</mo> <msup> <mi>i</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <mrow> <mi>&Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

wherein, Delta t is the passing Delta S of the particles_i-i'Time of this distance, Δ S_i-i'For two cameras corresponding to a picture relative to a same referenceThe difference in the distance values of the lines; i is a picture number;

the particle number S is obtained from the formula (1-1)_iAcceleration of this distance drop:

wherein S is_iIs the distance between the ith picture and the (i-1) th picture; t is t_iIs the passage of particles through S_iThe time of this distance;

obtained by the formulas (1-1) and (1-2), <math> <mrow> <msub> <mi>u</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>u</mi> <mi>i</mi> </msub> </mrow> <mi>n</mi> </mfrac> <mo>,</mo> <msub> <mi>a</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mi>n</mi> </mfrac> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

wherein u is_pIs the average velocity of the particles, a_pIs the average acceleration of the particles;

setting the included angle theta between the long axis direction of the particles in each frame of video and the horizontal direction_i(ii) a Obtaining the difference between the long axis direction of the particles in the two frames of images corresponding to the two digital cameras and the included angle of the horizontal axis by comparing the images obtained by the two digital camerasΔθ_i-i'；

Then <math> <mrow> <msub> <mi>w</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;&theta;</mi> <mrow> <mi>i</mi> <mo>-</mo> <msup> <mi>i</mi> <mo>&prime;</mo> </msup> </mrow> </msub> </mrow> <mrow> <mi>&Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

The average angular velocity of the particles is obtained from the formula (1-3):

4) according to the particle stress model: <math> <mrow> <mover> <msub> <mi>F</mi> <mi>g</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>+</mo> <mover> <msub> <mi>F</mi> <mi>D</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>+</mo> <mover> <msub> <mi>F</mi> <mi>b</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>+</mo> <mover> <msub> <mi>F</mi> <mi>m</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>+</mo> <mover> <msub> <mi>F</mi> <mi>B</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>+</mo> <mover> <msub> <mi>F</mi> <mi>M</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>m</mi> <mi>p</mi> </msub> <mover> <msub> <mi>a</mi> <mi>p</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mover> <mi>F</mi> <mo>&RightArrow;</mo> </mover> <mi>g</mi> </msub> <mo>=</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <msubsup> <mi>&pi;r</mi> <mi>p</mi> <mn>3</mn> </msubsup> <msub> <mi>&rho;</mi> <mi>p</mi> </msub> <mover> <mi>g</mi> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>m</mi> <mi>p</mi> </msub> <mover> <mi>g</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mover> <msub> <mi>F</mi> <mi>D</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>C</mi> <mi>D</mi> </msub> <msub> <mi>&rho;</mi> <mi>f</mi> </msub> <msub> <mi>A</mi> <mrow> <mi>p</mi> <mi>r</mi> <mi>o</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> <mover> <msub> <mi>u</mi> <mi>r</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> <mover> <msub> <mi>u</mi> <mi>r</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mover> <mi>F</mi> <mo>&RightArrow;</mo> </mover> <mi>a</mi> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <msubsup> <mi>&pi;r</mi> <mi>p</mi> <mn>3</mn> </msubsup> <msub> <mi>&rho;</mi> <mi>p</mi> </msub> <mover> <mi>g</mi> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>V</mi> <mi>p</mi> </msub> <msub> <mi>&rho;</mi> <mi>f</mi> </msub> <mover> <mi>g</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mover> <msub> <mi>F</mi> <mi>m</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <msubsup> <mi>&pi;r</mi> <mi>p</mi> <mn>3</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>&rho;</mi> <mi>f</mi> </msub> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <msubsup> <mi>&pi;r</mi> <mi>p</mi> <mn>3</mn> </msubsup> <msub> <mi>&rho;</mi> <mi>f</mi> </msub> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>V</mi> <mi>p</mi> </msub> <msub> <mi>&rho;</mi> <mi>f</mi> </msub> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mover> <msub> <mi>F</mi> <mi>B</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>6</mn> <msubsup> <mi>r</mi> <mi>p</mi> <mn>2</mn> </msubsup> <msqrt> <mrow> <msub> <mi>&pi;&rho;</mi> <mi>f</mi> </msub> <msub> <mi>&mu;</mi> <mi>f</mi> </msub> </mrow> </msqrt> <msubsup> <mstyle> <mo>&Integral;</mo> </mstyle> <msub> <mi>t</mi> <mn>0</mn> </msub> <mi>t</mi> </msubsup> <mfrac> <mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>&tau;</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mi>t</mi> <mo>-</mo> <mi>&tau;</mi> </mrow> </msqrt> </mfrac> <mi>d</mi> <mi>&tau;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mover> <msub> <mi>F</mi> <mi>M</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msubsup> <mi>&pi;r</mi> <mi>p</mi> <mn>3</mn> </msubsup> <msub> <mi>&rho;</mi> <mi>f</mi> </msub> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>&times;</mo> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

A_proj＝A₀cosθ (8)

<math> <mrow> <msub> <mi>&omega;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mi>&theta;</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,is the acceleration of the particles and is the acceleration of the particles,gravity, drag force, buoyancy, additional mass force, Basset force and Magnus force of the particles respectively;

wherein r is_pIs the equivalent diameter of the particle; m is_pMass of individual particles; v_pIs the volume of a single particle;as the relative velocity of the particles and the fluid, i.e. Is the velocity of the fluid and is,is the velocity of the individual particles and is,is composed ofThe mold of (4); rho_pIs the density of the particles; rho_fIs the density of the fluid; mu.s_fIs the fluid shear viscosity coefficient; a. the_projThe projected area of the particles facing the moving direction; a. the₀Is the maximum cross-sectional area of the particle; theta is the average value of the included angle between the long axis of the particles in the measurement area and the horizontal direction;

the drag coefficient of the individual particles is calculated from equations (1) to (9):

2. the method of claim 1, wherein the first and second image capturing units are digital cameras, and have a resolution of no less than 640 x 480 pixels and a sampling rate of no less than 25 frames per second.

3. The method as claimed in claim 1, wherein the thickness of the sheet-shaped laser light source is adjustable.

4. The method of claim 1, wherein the transparent fluidization chamber is square.

5. The method as claimed in claim 1, wherein the processing unit is a computer equipped with an image acquisition card.

6. The method for measuring the drag coefficient of light special-shaped particles as claimed in claim 1, wherein the two image acquisition units are triggered synchronously by the processing unit, and the frame rate interval is 3-5 frames.