Method for measuring average particle size of particulate matter

Abstract

The application discloses a kind of measurement methods of particulate matter average particle size, belong to particle size measurement technical field, including selecting vertical placement's cylindrical flat bottom silo, its bottom has adjustable diameter's round hole, silo diameter is greater than the 2.5 times of round hole diameter;After particulate matter is mixed, load into silo, and the particle accumulation height is greater than the 1.2 times of silo diameter;The maximum value D of round hole diameter is set max As calibration diameter D0, and measure corresponding particle flow Q0 as calibration flow;Adjust round hole diameter to different set value D, for each D value, measure the mass of particles Q flowed in unit time, and record data;The measured Q value is normalized, calculate q=Q / Q0, and construct q-D relationship diagram;Using software fitting q-D relationship diagram, the average particle size of particles can be calculated.The method has the advantages of good stability, low cost, simple operation, etc.

Description

Technical Field

[0001] This invention belongs to the field of particle size measurement technology, specifically, it relates to a method for measuring the average particle size of particulate matter. Background Technology

[0002] In daily production and life, we often encounter various particulate materials, such as soybeans, glass beads, sand, and coal dust. They are often numerous and very small in size, making the measurement of their average particle size a challenge.

[0003] To address this issue, existing technologies such as AI image recognition, ultrasonic and laser diffuse reflectance measurement have already found some applications in average particle size measurement. However, these solutions also have some drawbacks, such as the instruments being too expensive, the barrier to entry being too high, and the fact that measurements can only be taken in a laboratory setting. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing instruments for measuring the average particle size of particulate matter are too expensive and have too high a barrier to entry. Instead, it proposes a method for measuring the average particle size of particulate matter that has the advantages of good stability, low cost, and simple operation.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for measuring the average particle size of particulate matter, comprising the following steps:

[0006] Step S1: Select a vertically placed cylindrical flat-bottomed silo with an adjustable diameter hole at the bottom, and ensure that the silo diameter is 2.5 times larger than the diameter of the hole;

[0007] Step S2: After mixing the particulate matter thoroughly, load it into the silo, with the particle stacking height greater than 1.2 times the silo diameter;

[0008] Step S3: Set the maximum value D of the circular hole diameter. max The calibration diameter D0 is used as the calibration diameter, and the corresponding particle flow rate Q0 is measured as the calibration flow rate.

[0009] Step S4: Adjust the diameter of the circular hole to different set values ​​D. For each D value, measure the mass Q of particles flowing out per unit time and record the data.

[0010] Step S5: Normalize the measured Q value, calculate q = Q / Q0, and construct the qD relationship graph;

[0011] Step S6: Use software to fit the qD relationship graph to obtain the fitting parameters c and k. Based on the k value obtained from the fitting, calculate the average particle size.

[0012] Furthermore, the method for measuring the average particle size of particulate matter, for spherical particles passing through a circular hole at the bottom of the silo, satisfies: Q = C0ρg 1 / 2 (D-kd) 5 / 2 Where Q is the mass of particles flowing out per unit time, ρ is the density of the particle pack, g is the gravitational acceleration, D is the diameter of the orifice, d is the particle size, and C0 and k are dimensionless parameters.

[0013] Furthermore, the method for measuring the average particle size of particulate matter is applicable to non-spherical particles and mixed particles of different sizes:

[0014]

[0015] Where Q is the mass of particles flowing out per unit time, ρ is the density of the particle pack, g is the acceleration due to gravity, and D is the diameter of the orifice. p is the equivalent diameter of the i-th particle, defined as the diameter of a sphere with the same volume. i It is the total proportion of the i-th type of particle, obviously C0 is the weighted average particle size of the mixture, and C0 and k are dimensionless parameters.

[0016] right Normalization is performed to obtain The relationship, the fitted formula is:

[0017]

[0018] Where c is the fitting parameter, It is the normalized granular flow rate. Q0 is the particle flow rate measurement value corresponding to the calibration diameter D0.

[0019] Furthermore, the method for measuring the average particle size of particulate matter measures a particle size range of 0.5 mm to 0.22 mm. min D min It is the minimum value of D.

[0020] Through the above design scheme, the present invention can bring the following beneficial effects: The present invention proposes a method for measuring the average particle size of particulate matter. This method only requires loading a sufficient amount of well-mixed particles into a silo and measuring the particle flow rate corresponding to several sets of bottom circular holes with different diameters to complete the measurement of the average particle size. Attached Figure Description

[0021] The accompanying drawings are provided to further illustrate the invention and form part of this application. The illustrative embodiments and descriptions of the invention are used to understand the invention and do not constitute an undue limitation thereof. In the drawings:

[0022] Figure 1 This is a flowchart of the method for measuring the average particle size of particulate matter proposed in this invention.

[0023] Figure 2 For experimental results Figure 1 ;

[0024] Figure 3 For experimental results Figure 2 . Detailed Implementation

[0025] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, this invention is not limited to the following embodiments, and specific implementation methods can be determined according to the technical solutions of this invention and actual circumstances. To avoid obscuring the essence of this invention, well-known methods and processes are not described in detail.

[0026] To address the shortcomings of existing instruments for measuring the average particle size of particulate matter, such as being too expensive, having a high barrier to entry, and being limited to laboratory settings, this invention proposes a method for measuring the average particle size of particulate matter. This method offers advantages such as good stability, low cost, and ease of operation. By using this method, one only needs to load a sufficient amount of well-mixed particles into a silo and measure the particle flow rate corresponding to several sets of circular holes of different diameters at the bottom of the silo to complete the measurement of the average particle size.

[0027] The principle is explained in detail below:

[0028] For a vertically placed, cylindrical, flat-bottomed silo with a circular opening at the bottom, according to the Beverloo formula, the flow rate of spherical particles loaded within it through the circular opening at the bottom of the silo satisfies:

[0029] Q=C0ρg 1 / 2 (D-kd) 5 / 2

[0030] Where Q is the mass of particles flowing out per unit time, ρ is the density of the particle pack, g is the gravitational acceleration, D is the diameter of the circular hole, d is the particle size, C0 and k are the fitting parameters obtained by the fitting software, which are dimensionless parameters. The fitting software used in this invention is Origin, but it is not limited to this, as long as the method steps proposed in this invention can be executed.

[0031] Due to the Janssen effect, stress saturation occurs within the particle pack, meaning that when the particle pack height is sufficiently high, the pressure at the bottom of the pack becomes independent of its height. In this invention, the particle pack height is greater than 1.2 times the silo diameter D, and the silo diameter is greater than 2.5 times the orifice diameter D, thus ensuring that the particle flow rate Q remains stable.

[0032] For non-spherical particles and mixed particles of different diameters, there is a generalized Beverloo formula.

[0033]

[0034] Where Q is the mass of particles flowing out per unit time, ρ is the density of the particle pack, g is the acceleration due to gravity, and D is the diameter of the orifice. p is the equivalent diameter of the i-th particle, defined as the diameter of a sphere with the same volume. i It is the total proportion of the i-th type of particle, obviously This is the weighted average particle size of the mixture, where C0 and k are dimensionless parameters.

[0035] In practice, it has been found that the Beverloo formula exhibits significant bias in predicting particle flow rate Q when D is relatively small. Mankoc et al. proposed a correction to this problem.

[0036]

[0037] The lower limit of the applicable range of the revised formula can reach... The bias was eliminated. Therefore, it is possible to fit the relationship between the mass Q of particles flowing out per unit time and the diameter D of the orifice. To avoid the fitting formula becoming overparameterized and unable to converge, this invention normalizes the original formula, obtaining... The relationship, the fitted formula is:

[0038]

[0039] Where c is the fitting parameter, It is the normalized granular flow rate. Q0 is the measured particle flow rate corresponding to a selected orifice diameter D0, also known as the calibration flow rate. In actual operation, the maximum value of D can be selected, i.e., D0. max It is least affected by the parameter c.

[0040] Using this method, the present invention only requires loading a sufficient amount of uniformly mixed particles into the silo, measuring several sets of different values ​​of D corresponding to Q, obtaining the qD data graph after normalization with calibrated flow rate, and then using software to fit the values ​​of c and k, and calculating... This allows for the determination of the average particle size. Measurement.

[0041] Recommended particle size range for measurement: 0.5mm-0.22D min D min This is the minimum value of D. If the particle size is below this range, it will be significantly affected by air resistance and intermolecular forces. If it is above this range, intermittent flow or even blockage will occur.

[0042] This invention utilizes the Beverloo formula to determine the flow rate of particles through a vertical cylindrical flat-bottomed silo with a circular hole at the bottom. The equivalent diameter (average particle size) is obtained by measuring the relationship between the mass Q of particles flowing out per unit time and the diameter D of the circular hole. For non-spherical particles and mixed particles of different diameters, there is a generalized Beverloo formula. However, in practice, it has been found that the Beverloo formula exhibits significant prediction errors when D is small, therefore a modified formula is proposed. Ultimately, by simply loading a sufficient quantity of homogenized particles into a silo, measuring Q corresponding to several different D values, normalizing the data with a calibrated flow rate to obtain the qD data graph, and then fitting the values ​​of c and k using software, the average particle size can be calculated. Where c is the fitting parameter. The recommended particle size range for measurement is 0.5 mm to 0.22 D. min D min This is the minimum value of D. Below this range, it will be affected by air resistance, while above this range, intermittent flow or even blockage will occur.

[0043] like Figure 1 As shown, the present invention provides a method for measuring the average particle size of particulate matter, comprising:

[0044] Step S1: Select a vertically placed cylindrical flat-bottomed silo with an adjustable diameter hole at the bottom, and ensure that the silo diameter is 2.5 times larger than the diameter of the hole;

[0045] Step S2: After mixing the particulate matter thoroughly, load it into the silo, with the particle stacking height greater than 1.2 times the silo diameter;

[0046] Step S3: Set the maximum value D of the circular hole diameter. max The calibration diameter D0 is used as the calibration diameter, and the corresponding particle flow rate Q0 is measured as the calibration flow rate.

[0047] Step S4: Adjust the diameter of the circular hole to different set values ​​D. For each D value, measure the mass Q of particles flowing out per unit time and record the data.

[0048] Step S5: Normalize the measured Q value, calculate q = Q / Q0, and construct the qD relationship graph;

[0049] Step S6: Use software to fit the qD relationship graph to obtain the fitting parameters c and k. Based on the k value obtained from the fitting, calculate the average particle size.

[0050] from Figure 2 and Figure 3It can be seen that the particle size fitting value obtained by the method of the present invention is close to the actual particle size value.

[0051] In summary, the method proposed in this invention only requires loading a sufficient amount of well-mixed particles into the silo and measuring the particle flow rate corresponding to several sets of bottom circular holes with different diameters to complete the measurement of the average particle diameter.

Claims

1. A method for measuring the average particle size of particulate matter, characterized in that, Includes the following steps: Step S1: Select a vertically placed cylindrical flat-bottomed silo with an adjustable diameter hole at the bottom, and ensure that the silo diameter is 2.5 times larger than the diameter of the hole; Step S2: After mixing the particulate matter thoroughly, load it into the silo, with the particle stacking height greater than 1.2 times the silo diameter; Step S3: Set the maximum value D of the circular hole diameter. max The calibration diameter D0 is used as the calibration diameter, and the corresponding particle flow rate Q0 is measured as the calibration flow rate. Step S4: Adjust the diameter of the circular hole to different set values ​​D. For each D value, measure the mass Q of particles flowing out per unit time and record the data. Step S5: Normalize the measured Q value, calculate q = Q / Q0, and construct the qD relationship graph; Step S6: Use software to fit the qD relationship graph to obtain the fitting parameters c and k. Based on the k value obtained from the fitting, calculate the average particle size.

2. The method for measuring the average particle size of particulate matter according to claim 1, characterized in that: The flow rate of spherical particles through a circular orifice at the bottom of the silo satisfies: Q = C0ρg 1 / 2 (D-kd) 5 / 2 Where Q is the mass of particles flowing out per unit time, ρ is the density of the particle pack, g is the gravitational acceleration, D is the diameter of the orifice, d is the particle size, and C0 and k are dimensionless parameters.

3. The method for measuring the average particle size of particulate matter according to claim 1, characterized in that: For non-spherical particles and mixed particles of different sizes: Where Q is the mass of particles flowing out per unit time, ρ is the density of the particle pack, g is the acceleration due to gravity, and D is the diameter of the orifice. p is the equivalent diameter of the i-th particle, defined as the diameter of a sphere with the same volume. i It is the total proportion of the i-th type of particle, obviously C0 is the weighted average particle size of the mixture, and C0 and k are dimensionless parameters. right Normalization is performed to obtain The relationship, the fitted formula is: Where c is the fitting parameter, It is the normalized granular flow rate. Q0 is the particle flow rate measurement value corresponding to the calibration diameter D0.

4. The method for measuring the average particle size of particulate matter according to claim 1, characterized in that: The measured particle size range was 0.5 mm to 0.22 D. min D min It is the minimum value of D.

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