Calculation method of aggregation and growth of aluminum oxide inclusions in molten steel

Abstract

The application discloses a calculation method of aggregation and growth of aluminum oxide inclusions in molten steel and relates to the technical field of steel smelting. i ; S3, calculating the number density reduction amount D i of the i-th group of inclusions, so as to solve the PBE equation. In the calculation method of aggregation and growth of inclusions in molten steel, the inclusions are divided into several groups according to the size range in practice, and only equations with the same number of groups of inclusions are solved during solving, so that the calculation cost is greatly saved.

Description

Technical Field

[0001] This invention belongs to the field of iron and steel smelting technology, specifically a calculation method for the polymerization and growth of alumina inclusions in molten steel. Background Technology

[0002] In the production of clean steel, in order to ensure that the surface quality and performance of the finished product meet the user requirements, it is necessary to control the aluminum oxide inclusions in the steel, mainly including the quantity, size and distribution of aluminum oxide inclusions.

[0003] Regarding the calculation of the aggregation and growth of alumina inclusions in steel, due to the complexity of the collision mechanism between inclusions, it is difficult to obtain an analytical solution for the governing equation of inclusion size distribution, namely the Population Balance Equation (PBE). Two commonly used methods are:

[0004] 1) Exact solution. This method involves a large amount of computation and has a high solution cost, so it is mostly used to verify the accuracy of other numerical solutions.

[0005] 2) Particle size grouping method. This method is widely used to calculate the polymerization and growth process of inclusions in molten steel and to predict the size distribution of inclusions in molten steel. The drawback of this method is that it cannot ensure that the number of inclusions before and after polymerization is consistent with the actual situation. In addition, the collision of inclusions with the same particle size in the same group is calculated repeatedly. Summary of the Invention

[0006] The purpose of this invention is to provide a calculation method for the polymerization and growth of alumina inclusions in molten steel, so as to solve at least one aspect of the problems and defects mentioned in the background art.

[0007] The specific calculation method for the polymerization and growth of alumina inclusions in molten steel includes the following steps:

[0008] Includes the following steps:

[0009] S1. Divide the aluminum oxide inclusions in the molten steel into several groups according to their size range;

[0010] S2. Calculate the number density increment C of the i-th group of inclusions. i ;

[0011]

[0012] In the formula,

[0013] N j N k The number density of inclusions in groups j and k is (numbers / m³). 3 ;

[0014] Q j,k Let m be the collision frequency between the j-th group of inclusions and the k-th group of inclusions. 3 / s;

[0015] δ j，k For the Kronecker function,

[0016] S3. Calculate the decrease in the number density D of the i-th group of inclusions. i ;

[0017] The i-th group of inclusions will decrease in number density when it collides with any other group of inclusions, as expressed by:

[0018]

[0019] The final expression for the PBE equation of the number density of each group of inclusions in step S1 is:

[0020]

[0021] According to one technical solution of the calculation method of the present invention, at least the following beneficial effects are achieved:

[0022] The calculation method for inclusion aggregation and growth in molten steel provided by this invention divides inclusions into several groups according to their actual size range. During the solution process, only an equal number of equations need to be solved for each inclusion size group, significantly reducing computational costs. Furthermore, through this grouping, inclusions after collisions are reasonably assigned to corresponding groups based on quantity and mass conservation, solving the problem of inclusion quantity deviating from reality before and after aggregation in conventional calculations. It also corrects the problem of repeated calculations when inclusions in the same group collide, significantly improving the accuracy of the calculation results.

[0023] Let x j and x k Let x be the characteristic volume of the j-th and k-th inclusions, then x must exist. j and x k Satisfy x i-1 <(x) j +x k ) < x i+1 If x i-1 <x j +x k ≤x i ,but The polymerized particles x j +x k They will be assigned to the (i-1)th and ith groups respectively, and denoted as a and b, to ensure that the quantity and volume of inclusions are kept constant before and after aggregation.

[0024] a and b satisfy the relation Seeking

[0025] If x i <x j +x k <x i+1 ,but The polymerized particles x j +x k The inclusions are assigned to groups i and (i+1) respectively, denoted as a and b. To ensure the conservation of the quantity and volume of inclusions before and after aggregation, a and b satisfy the following relationship: Seeking

[0026] According to some embodiments of the present invention, the interval division in step S1 is performed according to a geometric sequence.

[0027] According to some embodiments of the present invention, the common ratio of the geometric sequence is greater than 1.

[0028] According to some embodiments of the present invention, the common ratio of the geometric sequence is greater than 2.

[0029] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 100.

[0030] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 80.

[0031] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 50.

[0032] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 40.

[0033] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 30.

[0034] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 20.

[0035] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2 to 10.

[0036] According to some embodiments of the present invention, the common ratio of the geometric sequence is 2.

[0037] According to some embodiments of the present invention, the molten steel is RH-refined molten steel.

[0038] According to some embodiments of the present invention, the initial quantity density of the inclusions is calculated using the following formula:

[0039]

[0040] In the formula, w O This refers to the mass concentration of dissolved oxygen.

[0041] d is the diameter of the inclusion, in meters (m).

[0042] According to some embodiments of the present invention, the initial diameter of the inclusion is 1 μm to 100 μm.

[0043] According to some embodiments of the present invention, the initial diameter of the inclusion is 1 μm to 50 μm.

[0044] According to some embodiments of the present invention, the initial diameter of the inclusion is 1 μm to 20 μm.

[0045] According to some embodiments of the present invention, the initial diameter of the inclusion is 2 μm to 50 μm.

[0046] According to some embodiments of the present invention, the initial quantity density calculation of the inclusions is based on the assumption that the inclusions are spherical. Attached Figure Description

[0047] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0048] Figure 1 This is a flowchart of the calculation method in an embodiment of the present invention.

[0049] Figure 2 The result is the calculation result in Embodiment 1 of the present invention.

[0050] Figure 3 The results are from Comparative Example 1 of this invention. Detailed Implementation

[0051] The following will describe the concept and technical effects of the present invention clearly and completely with reference to embodiments, so as to fully understand the purpose, features and effects of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the scope of protection of the present invention.

[0052] In the description of this invention, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0053] Unless otherwise specified in the examples, the procedures should be performed under standard conditions or conditions recommended by the manufacturer. Reagents or instruments whose manufacturers are not specified are all commercially available products.

[0054] The calculation method for the aggregation and growth of inclusions in molten steel according to embodiments of the present invention includes the following steps:

[0055] S1. Based on the dissolved oxygen concentration in the steel after RH refining, the initial distribution of the number and size of inclusions is obtained.

[0056] S2. Based on the size range of inclusions in molten steel, the size of inclusions in molten steel is divided into several groups according to certain rules.

[0057] To save computational effort, a geometric sequence is chosen for partitioning, with the common ratio arbitrarily given as a value greater than 1, taking into account the balance between computational effort and accuracy.

[0058] S3. Based on the conservation of quantity and mass, classify the aggregated and grown inclusions into the corresponding inclusion groups.

[0059] S4. List the PBE equations corresponding to the mixed groups in step S2.

[0060] S5. Solve the PBE equations for all inclusions to determine the number and size distribution of inclusions.

[0061] Example 1

[0062] This embodiment describes a calculation method for the aggregation and growth of inclusions in molten steel, consisting of the following steps:

[0063] S1. In this embodiment, the dissolved oxygen concentration after the RH refining of molten steel is 400 ppm;

[0064] Assumptions: (1) The inclusions are spherical; (2) Initially, only inclusions with a diameter of 2 μm exist in the molten steel.

[0065] Based on the above assumptions, the number density of inclusions with a diameter of 2 μm at the initial time is calculated as follows:

[0066]

[0067] In the formula, N1(0) is the number density of the first group of inclusions at time 0, in units / m³. 3 .

[0068] S2. In this embodiment, inclusions with diameters ranging from 2.0 μm to 20.0 μm are considered. The volume ratio between adjacent inclusions is set to 2, dividing them into 11 groups. The characteristic diameters of the inclusion particles in each group, from smallest to largest, are: 2.0 μm, 2.52 μm, 3.18 μm, 4.0 μm, 5.04 μm, 6.36 μm, 8.0 μm, 10.08 μm, 12.70 μm, 16.0 μm, and 20.16 μm. The corresponding characteristic volumes for each group are x1 = 1, x2 = 2, x3 = 4, x4 = 8, x5 = 16, x6 = 32, x7 = 64, x8 = 128, x9 = 256, x... 10 =512 and x 11 =1024.

[0069] S3. Taking group 3 as an example, calculate its quantity density increment. From step S1, we know that the characteristic volume of group 3 is x3 = 4, the characteristic volume of group 2 is x2 = 2, and the characteristic volume of group 4 is x4 = 8. Therefore, there exist 2 < x1 + x2 < 8, 2 < x1 + x3 < 8, 2 < x2 + x2 < 8, and 2 < x2 + x3 < 8. Taking the inclusions in groups 1 and 2 as examples, since 2 < x1 + x2 ≤ 4, then... The polymerized particles x1+x2 will be assigned to groups 2 and 3, respectively, and denoted as a and b. To ensure the conservation of the quantity and volume of inclusions before and after polymerization, a and b satisfy the following relationship: Then a = b = 0.5, which results in the following increase in the number density of the third group of inclusions: Similarly, the number density increase of the inclusions in group 3 brought about by the aggregation of groups 1 and 3 is: The number density increase of the inclusions in the third group caused by the aggregation of the second and third groups is: In this application, inclusions within the same group collide and aggregate. Because the value of N is much greater than 1, its magnitude is usually in the range of 10. 12 above, so This solves the problem of redundant calculations for inclusion collision aggregation between groups in conventional algorithms. The aggregation of inclusions in groups 2 and 3 brings about an increase in the number density of inclusions in group 3 as follows: In summary, the increase in the number density of inclusions in group 3 is...

[0070] S4. Taking the third group as an example, calculate the reduction in the number density of inclusions in the third group.

[0071] The collision between the third group of inclusions and any other group of inclusions will lead to a decrease in their number density.

[0072] S5. Based on steps S3 and S4, the PBE equations corresponding to the number density of each group of inclusions in step S1 can be listed as follows:

[0073]

[0074] S6. Solve the system of equations in S5 to obtain the number density distribution of all grouped inclusions. The calculation results are shown below. Figure 2 .

[0075] Comparative Example

[0076] S1: Same as S1 in the above embodiment.

[0077] S2: Considering inclusions with diameters ranging from 2.0 μm to 20.0 μm, the volume ratio between adjacent inclusions is set to 2, dividing them into 11 groups. The characteristic diameters of the inclusion particles in each group, from smallest to largest, are: 2.0 μm, 2.52 μm, 3.18 μm, 4.0 μm, 5.04 μm, 6.36 μm, 8.0 μm, 10.08 μm, 12.70 μm, 16.0 μm, and 20.16 μm. The corresponding characteristic volumes for each group are x1 = 1, x2 = 2, x3 = 4, x4 = 8, x5 = 16, x6 = 32, x7 = 64, x8 = 128, x9 = 256, x 10 =512 and x 11 =1024. Among them, the first group represents inclusions with a volume between (0.5, 1.5], the second group represents inclusions with a volume between (1.5, 3], the third group represents inclusions with a volume between (3, 6], and so on.

[0078] S3: Taking group 3 as an example, calculate its number density increment. From S1, we know that group 3 represents inclusions with volumes between (3, 6). Therefore, there exist 3 < x² + x² ≤ 6, 3 < x¹ + x³ ≤ 6, and 3 < x² + x³ ≤ 6. Taking the polymerization of inclusions in groups 1 and 3 as an example, to ensure the mass conservation of inclusions before and after polymerization, the number of inclusions after polymerization is... The increase in the number density of inclusions in group 3 is Similarly, the increase in the number density of the third group of inclusions due to the aggregation of the second and third group of inclusions can be obtained as follows: The increase in the number density of inclusions in group 3 due to the aggregation of inclusions in groups 2 and 3 is as follows: This shows that the comparative algorithm can only guarantee the conservation of inclusion mass before and after polymerization, but not the conservation of quantity. Furthermore, the comparative algorithm contains errors in calculating collisions between inclusions within the same group; the collision frequency between inclusions within the same group is calculated repeatedly. In the comparative algorithm, C...22 =Q 2,2 N2 2 Its correct expression should be:

[0079] S4. Taking the third group as an example, calculate the reduction in the number density of inclusions in the third group.

[0080] The collision between the third group of inclusions and any other group of inclusions will lead to a decrease in their number density.

[0081] In the formula, In the comparative calculation of D3, the collision frequency of inclusions between groups was also calculated repeatedly.

[0082] S5. Based on the calculation methods in S1 to S4, the PBE equations corresponding to the number density of inclusions in each group in comparative example S1 can be listed as follows:

[0083]

[0084] S5. Solve the system of equations in S4 to obtain the quantity and size distribution of all grouped inclusions. The calculation results are shown in [the table]. Figure 3 .

[0085] The above is a comparative method for calculating the polymerization and growth of alumina inclusions in molten steel. Obviously, this comparative method cannot ensure the conservation of the number of inclusion particles before and after polymerization, and the collision frequency of inclusion particles within the same group is repeatedly calculated, resulting in omissions in the formula itself. Compared to this invention, its calculation method has significant flaws and lower calculation accuracy.

[0086] In summary, the calculation method for inclusion aggregation and growth in molten steel provided in this application divides inclusions into several groups according to their actual size range using a geometric progression. During the solution process, only an equal number of equations need to be solved for each inclusion size group, significantly reducing computational costs. Furthermore, through this grouping, inclusions after collisions are reasonably assigned to corresponding groups based on quantity and mass conservation, resolving the problem of inclusion quantity deviating from reality before and after aggregation in conventional calculations. Simultaneously, it corrects the problem of repeated calculations when inclusions in the same group collide, significantly improving the accuracy of the calculation results.

[0087] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A calculation method for the polymerization and growth of alumina inclusions in molten steel, characterized in that, Includes the following steps: S1. Divide the aluminum oxide inclusions in the molten steel into several groups according to their size range; S2. Calculate the number density increment of the i-th group of inclusions. ; ； In the formula, ; For the first j , k Number density of inclusions, individuals / m 3 ; For the first j Group of inclusions and the first k Collision frequency between groups of inclusions, m 3 / s; For the Kronecker function, ; , ； S3. Calculate the decrease in the number density of the i-th group of inclusions. ; The i-th group of inclusions will decrease in number density when it collides with any other group of inclusions, as expressed by: ； The final expression for the PBE equation of the number density of inclusions in each group is: ； Solve the PBE equation to obtain the quantity and size distribution of all grouped inclusions.

2. The calculation method for the polymerization and growth of alumina inclusions in molten steel according to claim 1, characterized in that, In step S1, the intervals are divided according to a geometric sequence.

3. The calculation method for the polymerization and growth of alumina inclusions in molten steel according to claim 2, characterized in that, The common ratio of the geometric sequence is greater than 1.

4. The calculation method for the polymerization and growth of alumina inclusions in molten steel according to claim 2, characterized in that, The common ratio of the geometric sequence is greater than 2.

5. The calculation method for the polymerization and growth of alumina inclusions in molten steel according to claim 1, characterized in that, The molten steel is RH-refined molten steel.

6. The calculation method for the polymerization and growth of alumina inclusions in molten steel according to claim 1, characterized in that, The initial number density of the inclusions is calculated using the following formula: In the formula, This refers to the mass concentration of dissolved oxygen. d is the diameter of the inclusion, in meters (m).

Images