Analysis method for round billet spray cooling water flow density and heat exchange coefficient based on nozzle layout

Abstract

The invention provides a method for analyzing the density and the heat exchange coefficient of round billet spray cooling water flow based on nozzle layout. Comprising the following steps: performing data fitting on nozzle water flow density distribution data after homogenization treatment; performing three-dimensional spherical grid division processing on the nozzle according to the spraying angle; grid characteristic parameters of each spraying grid are calculated; the spraying water amount of each spraying deviation angle is calculated according to the grid characteristic parameters; calculating the area of each spraying grid on the surface of the casting blank; acquiring the area of a spherical surface defined by projection points of connecting lines between the set points on the equal-water-flow-density spherical surface; based on the area of a spherical surface defined by the projection points, the spraying water amount of each spraying deviation angle and the area of each spraying grid on the surface of the casting blank, the casting blank cylindrical surface water flow density is calculated; and finally calculating the casting blank surface heat exchange coefficient. And a boundary condition basis is provided for a refined round billet three-dimensional temperature field mathematical model according to the analysis result of the water flow density and the heat exchange coefficient.

Description

Technical Field

[0001] The invention belongs to the technical field of continuous steel casting, and in particular relates to an analysis method for round billet spray cooling water flow density and heat transfer coefficient based on nozzle layout. Background Art

[0002] Continuous casting is the abbreviation of continuous steel casting. The process is that the molten steel continuously transfers and releases heat under continuous operation and gradually solidifies into a specific shape of ingot. Continuous steel casting has the advantages of fewer steps, shorter process, high metal recovery rate, low energy consumption and high degree of automation.

[0003] Round billet continuous casting machine is a near-net-shape continuous casting technology mainly used for the production of seamless steel pipe billets. By using directly cast round billets for piercing and rolling, steel mills can significantly reduce energy consumption and increase metal yield.

[0004] Compared with slabs or square billets, round billets do not have corners and corner cracks, but the complex heat exchange boundary conditions during the continuous casting of round billets will still affect the circumferential uniform cooling of the billet. Among the various heat exchange boundary conditions, the cooling heat exchange of the crystallizer and the radiation heat exchange of the secondary cooling zone are generally considered to be conditions that contribute to the circumferential uniform cooling of the billet; although the contact heat exchange of a single set of guide rollers belongs to the circumferential non-uniform heat exchange conditions, the overall heat exchange effect can be approximately regarded as uniform due to the alternating arrangement of the guide rollers in the direction of the billet drawing; the spray cooling of the nozzle is prone to uneven cooling due to the difference in the number of outer ring nozzles and the distance between the nozzle and the billet. If the billet is not cooled evenly, defects such as surface longitudinal cracks and ovality may occur. Therefore, studying the influence of nozzle layout on the cooling of round billets is of great significance for refining the heat exchange boundary conditions and improving the quality of billets. No effective solution has been proposed for the problems in related technologies. Summary of the invention

[0005] The purpose of the present invention is to provide an analysis method for the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout.

[0006] The present invention is achieved through the following technical solutions:

[0007] The present invention relates to an analysis method for round billet spray cooling water flow density and heat transfer coefficient based on nozzle layout, comprising the following steps:

[0008] Step S1, performing homogenization processing and data fitting on the nozzle water flow density distribution data; then performing three-dimensional spherical mesh processing on the nozzle according to the spraying angle to obtain a plurality of spraying grids;

[0009] Step S2, based on the data fitting result of the nozzle water flow density distribution data, the grid characteristic parameters of each spray grid are calculated; and then the spray water volume at each spray deviation angle is calculated according to the grid characteristic parameters;

[0010] Step S3, obtaining the coordinates of the boundary nodes in the cross section of the center of the circle at any position along the billet drawing direction, and calculating the area of ​​each spray grid on the billet surface based on the connection network structure between the nozzle, the boundary nodes and a plurality of set points on the round billet;

[0011] Step S4, obtaining the area of ​​the sphere formed by the projection points of the lines between the set points on the sphere of equal water flow density; calculating the water flow density of the casting billet cylinder based on the area of ​​the sphere formed by the projection points, the spraying water volume at each spraying deviation angle and the area of ​​each spraying grid on the casting billet surface;

[0012] Step S5, calculating the heat transfer coefficient of the billet surface based on the water flow density on the billet column surface and in combination with the billet surface temperature and the temperature of the spray water.

[0013] Preferably, in step S1, the homogenization and data fitting of the nozzle water flow density distribution data is a process of homogenizing the nozzle water flow density distribution data based on the nozzle grid position division principle, and performing data fitting on the nozzle water flow density distribution data after homogenization, specifically:

[0014] (1) Obtain nozzle water flow density distribution data through water flow density test;

[0015] (2) The grid position directly below the nozzle is set as the reference point, and the water flow density of the nozzles at other positions is adjusted to complete the uniform distribution of the water flow of the nozzles;

[0016] (3) Based on the normal distribution function, the data of the nozzle water flow density after uniform distribution processing is fitted to obtain the fitting function of the nozzle.

[0017] Preferably, in step S1, the process of performing three-dimensional spherical meshing processing on the nozzle according to the spraying angle to obtain a plurality of spraying meshes is specifically as follows: based on the spraying angle of the nozzle, three-dimensional spherical meshing is performed at a preset angle each time and terminated at a termination angle.

[0018] Preferably, in step S2, the process of calculating the grid characteristic parameters of each spray grid based on the data fitting result of the nozzle water flow density distribution data is specifically as follows:

[0019] (1) Obtain the spray length of each spray grid on a preset plane on one side of the spray;

[0020] (2) Calculate the water flow density of each spray grid on a predefined horizontal axis and the area of ​​the spray grid on the spray sphere of the nozzle according to the data fitting results of the nozzle water flow density distribution data and the spray height of the nozzle;

[0021] (3) Based on the water flow density of the spray grid on the predefined horizontal axis, the area of ​​the spray grid on the nozzle spray sphere, and the spray length of each spray grid on the preset plane, the comprehensive dimensionless water flow density of each spray grid is calculated.

[0022] Preferably, in step S2, the process of calculating the spray water volume at each spray deviation angle according to the grid characteristic parameters is specifically as follows:

[0023] (1) Calculate the water volume weight of each spray grid according to the comprehensive dimensionless water flow density of each spray grid;

[0024] (2) According to the water volume weight of each spray grid, the spray area, and the area of ​​each spray grid on the spray sphere of the nozzle, the spray water volume at each spray deviation angle is calculated.

[0025] Preferably, in step S3, the process of obtaining the coordinates of the boundary nodes in the cross section of the center of a circle at any position along the throwing direction is specifically as follows:

[0026] (1) construct a three-dimensional coordinate system with the center of the meniscus of the round billet as the origin, and establish the association law between the center and the boundary nodes at any position along the throwing direction;

[0027] (2) Obtain the angle between the line connecting the boundary node and the center of the circle and the line connecting the nozzle and the center of the circle, the geometric radius of the round billet and the coordinates of the center of the circle, and use the correlation law between the center of the circle and the boundary node at any position along the throwing direction to calculate the coordinates of the boundary node.

[0028] Preferably, in step S3, the process of calculating the area of ​​each spray grid on the surface of the billet based on the connection network structure between the nozzle, the boundary node and a plurality of set points on the round billet is specifically as follows:

[0029] (1) The boundary nodes rotate in two directions along the circumference of the round billet and extend in the forward and backward directions along the billet drawing direction to form an arc surface with a number of set points as boundaries;

[0030] (2) Obtain the intersection of the line between the set point and the center of the round billet and the sphere of equal water flow density, the boundary node, the length of the line between the set point and the nozzle, and the length of the line between each set point, and calculate the area of ​​each spray grid on the billet surface.

[0031] Preferably, in step S4, the process of obtaining the area of ​​the sphere enclosed by the projection points of the lines between the set points on the sphere of equal water flow density is specifically as follows: obtaining the length of the arc formed by the lines between the set points between the projection points on the sphere of equal water flow density, and calculating the area of ​​the sphere enclosed by the projection points of the arc formed by the several set points as boundaries on the sphere of equal water flow density.

[0032] Preferably, in step S4, the process of calculating the water flow density on the cylindrical surface of the ingot based on the area of ​​the sphere surrounded by the projection points, the spray water volume at each spray deviation angle and the area of ​​each spray grid on the surface of the ingot is specifically as follows:

[0033] (1) Calculate the water flow density of a single nozzle at the boundary node based on the area of ​​the sphere enclosed by the projection points, the spray water volume at each spray deviation angle, and the area of ​​each spray grid on the surface of the ingot;

[0034] (2) The water flow density on the cylindrical surface of the ingot is calculated based on the water flow density of a single nozzle at the boundary node.

[0035] Preferably, in step S5, the formula for calculating the heat transfer coefficient of the casting surface is:

[0036]

[0037] In formula (1),

[0038] H[z][r] is the spray heat transfer coefficient of the grid with the casting coordinate z and the circumferential coordinate r;

[0039] Vs[z][r] is the water flow density of the grid with the casting coordinate z and the circumferential coordinate r;

[0040] Ts[z][r] is the surface temperature of the billet at the grid with the billet drawing coordinate z and the circumferential coordinate r;

[0041] Tanh is the hyperbolic tangent function;

[0042] Tw is the temperature of the spray water.

[0043] The principle of the analysis method involved in the present invention is: data fitting is performed on the nozzle water flow density distribution data after homogenization treatment; the nozzle is divided into three-dimensional spherical grids according to the spray angle; the grid characteristic parameters of each spray grid are calculated; the spray water volume at each spray deviation angle is calculated according to the grid characteristic parameters; the area of ​​each spray grid on the surface of the ingot is calculated; the area of ​​the sphere surrounded by the projection points of the connecting lines between each set point on the sphere of equal water flow density is obtained; based on the area of ​​the sphere surrounded by the projection points, the spray water volume at each spray deviation angle and the area of ​​each spray grid on the surface of the ingot, the water flow density of the ingot cylindrical surface is calculated; and finally the heat transfer coefficient of the ingot surface is calculated.

[0044] The present invention has the following advantages:

[0045] Aiming at the secondary cooling process of continuous casting of round billets, the present invention establishes a mathematical model of water distribution on a spherical grid of a nozzle, and calculates the spray water volumes in different positions and areas under the nozzle spraying through the mathematical model of water distribution on the spherical grid of the nozzle and the test data of the original nozzle; establishes a mathematical model of water distribution on a cylindrical grid of a casting billet, and converts the water volume data of the nozzle into water flow density data on the cylindrical surface of the casting billet through the mathematical model of water distribution on the cylindrical surface of the casting billet, so as to provide a data basis for calculating the spray heat transfer coefficient; and calculates the spray heat transfer coefficient of each node on the cylindrical surface of the casting billet through the water flow density on the cylindrical surface of the casting billet, so as to provide a boundary condition basis for refining the mathematical model of the three-dimensional temperature field of the casting billet. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of an analysis method of round billet spray cooling water flow density and heat transfer coefficient based on nozzle layout involved in the present invention;

[0047] Figure 2 It is the water flow density distribution diagram of pure water nozzle;

[0048] Figure 3 It is the water flow density distribution diagram of the air-water nozzle;

[0049] Figure 4 This is a comparison chart of the original data and the fitting curve of the pure water nozzle;

[0050] Figure 5 It is a comparison chart of the original data and the fitting curve of the air-water nozzle;

[0051] Figure 6 It is a schematic diagram of the two-dimensional division of the spray grid;

[0052] Figure 7 It is a schematic diagram of the three-dimensional division of the spray grid;

[0053] Figure 8 This is a schematic diagram of the calculation results of the water weight of the sprinkler grid;

[0054] Fig. 9 It is a schematic diagram of the cross section of a round billet;

[0055] Fig.10 It is a schematic diagram of water flow density calculation;

[0056] Fig.11 It is the top view of water flow density calculation;

[0057] Fig.12 It is the side view of water flow density calculation;

[0058] Fig.13 This is the heat transfer coefficient diagram of the pure water nozzle casting surface;

[0059] Fig.14 This is the heat transfer coefficient diagram of the billet surface of the air-water nozzle. DETAILED DESCRIPTION

[0060] The present invention is described in detail below in conjunction with specific embodiments. It should be noted that the following embodiments are only further descriptions of the present invention, but the protection scope of the present invention is not limited to the following embodiments.

[0061] Example

[0062] This embodiment relates to an analysis method for the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout, see Figure 1 As shown, the following steps are included:

[0063] Step S1, performing homogenization processing and data fitting on the nozzle water flow density distribution data; then performing three-dimensional spherical mesh processing on the nozzle according to the spraying angle to obtain a plurality of spraying grids;

[0064] Step S2, based on the data fitting result of the nozzle water flow density distribution data, the grid characteristic parameters of each spray grid are calculated; and then the spray water volume at each spray deviation angle is calculated according to the grid characteristic parameters;

[0065] Step S3, obtaining the coordinates of the boundary nodes in the cross section of the center of the circle at any position along the billet drawing direction, and calculating the area of ​​each spray grid on the billet surface based on the connection network structure between the nozzle, the boundary nodes and a plurality of set points on the round billet;

[0066] Step S4, obtaining the area of ​​the sphere formed by the projection points of the lines between the set points on the sphere of equal water flow density; calculating the water flow density of the casting billet cylinder based on the area of ​​the sphere formed by the projection points, the spraying water volume at each spraying deviation angle and the area of ​​each spraying grid on the casting billet surface;

[0067] Step S5, calculating the heat transfer coefficient of the billet surface based on the water flow density on the billet column surface and in combination with the billet surface temperature and the temperature of the spray water.

[0068] The specific method of the analysis method involved in this embodiment is as follows:

[0069] 1. Mathematical model of heat transfer for round billet spray cooling

[0070] 1.1. Calculation of heat transfer coefficient on the surface of the ingot

[0071] The heat transfer characteristics of the air-water nozzle spraying atomized water droplets onto the high-temperature steel surface are analyzed, and the surface heat transfer coefficient obtained is a function of the surface temperature of the ingot and the water flow density:

[0072]

[0073] In formula (1):

[0074] H[z][r] represents the spray heat transfer coefficient of the grid with the casting coordinate z and the circumferential coordinate r, W / (㎡·℃);

[0075] Vs[z][r] represents the water flow density of the grid with the casting coordinate z and the circumferential coordinate r, Kg / (m 2 s);

[0076] Ts[z][r] represents the surface temperature of the billet at the grid with the billet drawing coordinate z and the circumferential coordinate r, °C;

[0077] Tanh() represents the hyperbolic tangent function;

[0078] Tw is the temperature of the spray water, °C;

[0079] It can be seen from formula (1) that by calculating the water flow density at the boundary, the corresponding heat transfer coefficient can be obtained.

[0080] 1.2 Calculation of nozzle water flow density

[0081] The models and parameters of pure water cone nozzles and air-water cone nozzles were obtained from a nozzle testing center, as shown in Table 1:

[0082] Table 1

[0083] parameter Pure water nozzle Air-water nozzle model 1 / 4PZ1577QZ5 HPZ1.8-65QZ2 Air pressure [MPa] 0 0.2 Water pressure [MPa] 0.3 0.2 <![CDATA[Gas flow rate [Nm 3 / h]]]> 0 7.30 Water flow rate W[L / min] 11.42 1.80 Spray height H[mm] 150 150 Spray angle [°] 77.8 66.5

[0084] See Figure 2 and Figure 3 As shown, the water flow density distribution was obtained from the water flow density tests of the pure water nozzle and the air-water nozzle.

[0085] The grid position directly below the nozzle is set to 0, and the other grid positions are increased in sequence. The water flow density distribution of the pure water nozzle and the air-water nozzle is homogenized to obtain the treated water flow density distribution, as shown in Table 2:

[0086] Table 2

[0087] Position(mm) Pure water nozzle Air-water nozzle Position(mm) Pure water nozzle Air-water nozzle 0 100 100 375 0 0 25 95.5 93.5 400 0 0 50 86 65.5 425 0 0 75 74.5 37.5 450 0 0 100 58 9.5 475 0.5 0.5 125 36.5 3.0 500 0 0 150 77.8 1.0 525 0.5 0.5 175 4 0 550 0.5 0.5 200 0.5 0 575 0 0 225 0.5 0.5 600 0 0 250 0 0 625 0 0 275 0 0 650 0 0 300 0.5 0.5 675 0 0 325 0.5 0.5 700 0 0 350 0 0 725 0 0

[0088] The above data are fitted according to the normal distribution function to obtain the fitting function of the pure water nozzle. The calculation formula is shown in formula (2):

[0089]

[0090] In formula (2):

[0091] fv(x) represents the water flow density at a vertical distance x from the center of the pure water nozzle, dimensionless;

[0092] x represents the vertical distance from the nozzle center, mm.

[0093] Comparison of the original data and fitting curve of the pure water nozzle, see Figure 4 shown.

[0094] The fitting function of the air-water nozzle is calculated as shown in formula (3):

[0095]

[0096] In formula (3):

[0097] fn(x) represents the water flow density at a vertical distance x from the center of the air-water nozzle, dimensionless;

[0098] x represents the vertical distance from the nozzle center, mm.

[0099] Comparison of the original data and fitting curve of the pure water nozzle, see Figure 5 shown.

[0100] like Figure 6 As shown, the conical nozzle is divided into three-dimensional spherical grids every 1° according to the spray angle, and the division is terminated when the angle is η; on the spray side, the spray length MN corresponding to each spray grid in the plane in the figure below can be obtained, and its calculation is shown in formula (4):

[0101] Lmn(ε)=H·(tan(ε+0.5)-tan(ε-0.5)) (4)

[0102] In formula (4):

[0103] ε represents the angle between the line connecting the spray center point of the εth spray grid and the nozzle and the center line of the nozzle, degrees;

[0104] H represents the distance between the nozzle and the test surface during the water flow density test, m;

[0105] Lmn(ε) represents the spray length MN, m, of the εth spray grid.

[0106] The calculation of the water flow density of each spray grid on the x-axis is shown in formula (5):

[0107]

[0108] In formula (5):

[0109] ε represents the angle between the line connecting the spray center point of the εth spray grid and the nozzle and the center line of the nozzle, degrees;

[0110] H represents the minimum distance between the nozzle and the billet, m;

[0111] fv() represents the function of finding the dimensionless water flow density of the pure water nozzle corresponding to the vertical distance from the nozzle center;

[0112] fn() represents the function of finding the dimensionless water flow density of the corresponding air-water nozzle from the vertical distance from the nozzle center;

[0113] W(ε) represents the dimensionless water flow density of the εth sprinkler grid.

[0114] The calculation of the area of ​​each spray grid on the spray sphere of the cone nozzle is shown in formula (6):

[0115]

[0116] In formula (6):

[0117] ε represents the angle between the line connecting the spray center point of the εth spray grid and the nozzle and the center line of the nozzle, degrees;

[0118] H represents the minimum distance between the nozzle and the billet, m;

[0119] A(ε) represents the spraying area of ​​the εth spray grid, m2.

[0120] The shape of the spray mesh after division, such as Figure 7 shown.

[0121] Therefore, the comprehensive dimensionless water flow density of each sprinkler grid is calculated as shown in formula (7):

[0122] Wfd(ε)=Lmn(ε)·W(ε)·A(ε) (7)

[0123] In formula (7):

[0124] ε represents the angle between the line connecting the spray center point of the εth spray grid and the nozzle and the center line of the nozzle, degrees;

[0125] Lmn(ε) represents the spray length MN of the εth spray grid, m;

[0126] W(ε) is the dimensionless water flow density of the εth sprinkler grid;

[0127] A(ε) represents the spraying area of ​​the εth spraying grid, m2;

[0128] Wfd(ε) represents the comprehensive dimensionless water flow density of the εth sprinkler grid.

[0129] The calculation of the water weight of each sprinkler grid is shown in formula (8):

[0130]

[0131] In formula (8):

[0132] ε represents the angle between the line connecting the spray center point of the εth spray grid and the nozzle and the center line of the nozzle, degrees;

[0133] Wfd(ε) refers to the integrated dimensionless water flow density of the εth sprinkler grid;

[0134] η represents the maximum spray angle of the nozzle, °;

[0135] Wfw(ε) refers to the water flow density weight of the εth sprinkler grid, dimensionless;

[0136] The calculated water weight of the sprinkler grid is shown in Figure 8 shown.

[0137] In the spray sphere formed by the total spray water volume W and the spray height H, for a spray area Sr and a spray deviation angle e, the spray water volume is SPw, and its calculation is shown in formula (9):

[0138]

[0139] In formula (9):

[0140] Sr represents the area of ​​a specific area, m2;

[0141] e represents the angle between the center point of the specific area and the line connecting the nozzle and the center line of the nozzle, °;

[0142] W represents the total water volume of the nozzle, L / min;

[0143] Wfw(e) represents the water flow density weight of the e-th sprinkler grid, dimensionless;

[0144] A(e) represents the area of ​​the e-th spray grid, m2;

[0145] SPw(Sr,e) represents the spray water volume in a specific area with an area of ​​Sr and a spray angle of e, L / min;

[0146] 1.3 Calculation of water flow density on the surface of the ingot

[0147] A three-dimensional coordinate system is established with the center of the meniscus of the round billet as the origin, ignoring the influence of the casting machine radius on the coordinate system. The horizontal direction of the origin is the X direction, the vertical direction is the Y direction, and the Z direction is the billet drawing direction.

[0148] like Fig. 9 As shown, the water spray volume of the nozzle is set to m, the number of nozzles in one circle of the billet is n, the geometric radius of the round billet is r, the minimum distance between the nozzle and the billet surface is R, and the maximum spray angle of the nozzle is γ.

[0149] The coordinates of the center of the circle at any position along the casting direction are set to (0, 0, Zm), the coordinates of the boundary node A in the cross section at the center of the circle are set to (Xa, Ya, Za), and the coordinates of the nozzle N where the node A is located are set to (Xn, Yn, Zn). Since the nozzle N is directly above the center of the circle M, its calculation is shown in formula (10):

[0150]

[0151] In formula (10):

[0152] Xn represents the x-axis coordinate of nozzle N, m;

[0153] Yn represents the y-axis coordinate of nozzle N, m;

[0154] Zn represents the z-axis coordinate of nozzle N, m;

[0155] r represents the radius of the round billet cross section, m;

[0156] R represents the minimum distance between the nozzle and the surface of the casting, m.

[0157] The spherical area of ​​equal water flow density formed by taking the coordinate of nozzle N as the center, R as the radius, and the nozzle spray angle γ as the radiation angle is Sn, and its calculation is shown in formula (11):

[0158] Sn=2πR 2 ·(1-cos(γ / 2)) (11)

[0159] In formula (11):

[0160] R represents the minimum distance between the nozzle and the surface of the casting, m;

[0161] γ represents the maximum spray angle of the nozzle, degrees.

[0162] The angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M is β, the maximum value of β is βm, each nozzle row has a total of n nozzles, and the range of β is (0, βs), as shown in formula (12):

[0163]

[0164] In formula (12):

[0165] n represents the number of nozzles in each nozzle row, dimensionless;

[0166] βs represents the research range of the nozzle's single-side spray angle, °.

[0167]

[0168] In formula (13):

[0169] r represents the radius of the round billet cross section, m;

[0170] R represents the minimum distance between the nozzle and the surface of the casting, m;

[0171] βm represents the maximum angle of the nozzle spraying to the billet from one side, degrees.

[0172] Since the node A and the center M are in the same cross section, therefore:

[0173]

[0174] In formula (14):

[0175] Xa represents the x-axis coordinate of node A, m;

[0176] Ya represents the y-axis coordinate of node A, m;

[0177] Za represents the z-axis coordinate of node A, m;

[0178] r represents the radius of the round billet cross section, m;

[0179] β represents the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M, °;

[0180] Z represents the z-axis coordinate of the center M, m.

[0181] A cylindrical grid is formed with node A as the center point. The grid is formed by rotating the line connecting the center of the circle and node A clockwise and counterclockwise along the circumferential direction by dθ / 2 degrees, and extending dl / 2 in the positive and negative directions along the billet drawing direction and projecting it on the billet surface. The grid is an arc surface with points A1, A2, A3 and A4 as boundaries. The area of ​​the arc surface is defined as Sa, as follows: Fig.10 As shown, then:

[0182] Sa=dθ·r·dl (15)

[0183] In formula (15):

[0184] dθ represents the circumferential grid step, °;

[0185] r represents the radius of the casting, m;

[0186] dl represents the step length in the throwing direction, m;

[0187] Sa represents the area of ​​the cylindrical grid, m2;

[0188] Setting the coordinates of A1, A2, A3 and A4 to (Xa1, Ya1, Za1), (Xa2, Ya2, Za2), (Xa3, Ya3, Za3), (Xa4, Ya4, Za4) respectively, we can get:

[0189]

[0190]

[0191] In formulas (16)-(19):

[0192] dθ represents the circumferential grid step, °;

[0193] β represents the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M, °;

[0194] r represents the radius of the casting, m;

[0195] dl represents the step length in the throwing direction, m;

[0196] Xa1, Ya1, Za1 represent the x-axis, y-axis, and z-axis coordinates of point A1, m;

[0197] Xa2, Ya2, Za2 represent the x-axis, y-axis, and z-axis coordinates of point A2, m;

[0198] Xa3, Ya3, Za3 represent the x-axis, y-axis, and z-axis coordinates of point A3, m;

[0199] Xa4, Ya4, Za4 represent the x-axis, y-axis, and z-axis coordinates of point A4, m;

[0200] Za represents the z-axis coordinate of node A, m.

[0201] The intersection points of the lines connecting points A, A1, A2, A3 and A4 and the center of the circle with the spherical surface Sn are set to B, B1, B2, B3 and B4 respectively, and the corresponding coordinates are (Xb, Yb, Zb), (Xb1, Yb1, Zb1), (Xb2, Yb2, Zb2), (Xb3, Yb3, Zb3), (Xb4, Yb4, Zb4), the length of the line connecting point A and nozzle N is Lan, the length of the line connecting point A1 and nozzle N is La1n, the length of the line connecting point A2 and nozzle N is La2n, the length of the line connecting point A3 and nozzle N is La3n, and the length of the line connecting point A4 and nozzle N is La4n. It can be calculated that:

[0202]

[0203] In formula (20):

[0204] Lan, La1n, La2n, La3n, La4n represent the length of the line connecting points A, A1, A2, A3, A4 and nozzle N, m;

[0205] Xa, Ya, Za represent the x-axis, y-axis, and z-axis coordinates of node A, m;

[0206] Xn, Yn, Zn represent the x-axis, y-axis, and z-axis coordinates of the nozzle N, m;

[0207] Xa1, Ya1, Za1 represent the x-axis, y-axis, and z-axis coordinates of point A1, m;

[0208] Xa2, Ya2, Za2 represent the x-axis, y-axis, and z-axis coordinates of point A2, m;

[0209] Xa3, Ya3, Za3 represent the x-axis, y-axis, and z-axis coordinates of point A3, m;

[0210] Xa4, Ya4, Za4 represent the x-axis, y-axis, and z-axis coordinates of point A4, m;

[0211] The length of the line connecting point A1 and point A2 is La1a2, the length of the line connecting point A1 and point A3 is La1a3, the length of the line connecting point A2 and point A4 is La2a4, the length of the line connecting point A3 and point A4 is La3a4, and the length of the line connecting point A1 and point A4 is La1a4. Calculate:

[0212]

[0213] In formula (21):

[0214] La1a2, La1a3, La2a4, La3a4, La1a4 represent the lengths of the lines connecting points A1 and A2, A1 and A3, A2 and A4, A3 and A4, A1 and A4, in m;

[0215] dθ represents the circumferential grid step, °;

[0216] dl represents the step length in the throwing direction, m;

[0217] r represents the radius of the casting, m.

[0218] The calculation formula of the area GS of each cylindrical grid on the surface of the ingot is as follows:

[0219] GS=La1a2·La1a3 (22)

[0220] In formula (22):

[0221] La1a2, La1a3 represent the length of the line between points A1 and A2, A1 and A3, m;

[0222] GS represents the area of ​​the cylindrical grid, m2.

[0223] The angle between lines La1n and La2n is α[La1n,La2n], the angle between lines La1n and La3n is α[La1n,La3n], the angle between lines La2n and La4n is α[La2n,La4n], the angle between lines La3n and La4n is α[La3n,La4n], the angle between lines La1n and La4n is α[La1n,La4n], the angle between lines Lmn and Lan is α[Lmn,Lan], then:

[0224]

[0225] In formula (23):

[0226] La1a2, La1a3, La1a4, La3a4, La2a4 represent the lengths of the lines connecting points A1 and A2, A1 and A3, A1 and A4, A3 and A4, A2 and A4, in m;

[0227] La1n, La2n, La3n, La4n, Lan represent the length of the line between points A1, A2, A3, A4, A and nozzle N, m;

[0228] Lmn represents the length of the line between the center M and the nozzle N, m;

[0229] α[La1n,La2n], α[La1n,La3n], α[La2n,La4n], α[La3n,La4n], α[La1n,La4n], α[Lmn,Lan] represent the angles between lines La1n and La2n, La1n and La3n, La2n and La4n, La3n and La4n, La1n and La4n, Lmn and Lan, in degrees;

[0230] r represents the radius of the casting, m;

[0231] R represents the minimum distance between the nozzle and the surface of the casting, m.

[0232] The projection of line La1a2 on the spray sphere Sn is an arc formed by connecting points B1 and B2, and its length is set to Ab1b2. The projection of line La1a3 on the sphere Sn is an arc formed by connecting points B1 and B3, and its length is set to Ab1b3. The projection of line La2a4 on the sphere Sn is an arc formed by connecting points B2 and B4, and its length is set to Ab2b4. The projection of line La3a4 on the sphere Sn is an arc formed by connecting points B3 and B4, and its length is set to Ab3b4. Then:

[0233]

[0234] In formula (24):

[0235] α[La1n,La2n], α[La1n,La3n], α[La2n,La4n], α[La3n,La4n], α[La1n,La4n] represent the angles between lines La1n and La2n, La1n and La3n, La2n and La4n, La3n and La4n, La1n and La4n, degrees;

[0236] R represents the minimum distance between the nozzle and the surface of the casting, m.

[0237] Ab1b2, Ab1b3, Ab2b4, Ab3b4, Ab1b4 represent the lengths of the projection arcs of points B1 and B2, B1 and B3, B2 and B4, B3 and B4, B1 and B4 on the spray sphere Sn, in m.

[0238] The projection of the node representative surface Sa on the spray sphere Sn is the sphere Sb surrounded by points B1, B2, B3 and B4. The sphere can be considered to be composed of the triangle E composed of arcs B1B2, B1B4, B2B4 and the triangle F composed of arcs B1B3, B1B4, B3B4. Therefore, the area Se of triangle E, the area Sf of triangle F and the area calculation formula of Sb are:

[0239]

[0240] In formulas (25)-(27):

[0241] Ab1b2, Ab1b3, Ab2b4, Ab3b4, Ab1b4 represent the lengths of the projection arcs of points B1 and B2, B1 and B3, B2 and B4, B3 and B4, B1 and B4 on the spray sphere Sn, in m.

[0242] SEa represents half of the sum of the three sides of triangle E, m;

[0243] SFa represents half of the sum of the three sides of triangle F, m;

[0244] Se represents the area of ​​triangle E, m2;

[0245] Sf represents the area of ​​triangle F, m2;

[0246] Sb represents the projection area of ​​the cylindrical grid Sa on the spray sphere, m2.

[0247] The calculation formula for the projection area St of Sb on the standard spray sphere of the nozzle is:

[0248]

[0249] In formula (28):

[0250] Sb represents the projection area of ​​the cylindrical grid Sa on the spray sphere, m2;

[0251] St represents the projection area of ​​Sb on the standard spray sphere of the nozzle, m2;

[0252] R represents the minimum distance between the nozzle and the surface of the casting, m.

[0253] H represents the distance between the nozzle and the test surface during the water flow density test, m;

[0254] Then the single nozzle water flow density Ws(β) at the node A is:

[0255]

[0256] In formula (29):

[0257] β represents the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M, °;

[0258] βm represents the maximum angle of the nozzle spraying to the billet from one side, °;

[0259] GS represents the area of ​​the cylindrical grid, m2;

[0260] St represents the projection area of ​​Sb on the standard spray sphere of the nozzle, m2;

[0261] α[Lmn,Lan] represents the angle between lines Lmn and Lan, degrees;

[0262] SPw(St,β=α[Lmn,Lan]) represents the spray water volume in a specific area with an area of ​​St and a spray angle of α[Lmn,Lan], L / min;

[0263] Ws(β) represents the water flow density of the cylindrical grid under a single nozzle when the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M is β, Kg / (m 2 ·s).

[0264] Because the water spraying areas of multiple nozzles on the ingot overlap, the water flow density Wm(β) of multiple nozzles at node A is:

[0265]

[0266] In formula (30):

[0267] β represents the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M, °;

[0268] βm represents the maximum angle of the nozzle spraying to the billet from one side, °;

[0269] βs represents the research range of the nozzle's single-side spray angle, °;

[0270] Ws(β) represents the water flow density of the cylindrical grid under a single nozzle when the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M is β, Kg / (m 2 s);

[0271] Wm(β) represents the water flow density of the cylindrical grid under the multi-nozzle when the angle between the line connecting the node A and the center M and the line connecting the nozzle N and the center M is β, Kg / (m 2 ·s).

[0272] The top view and side view of the water flow density calculation are as follows: Fig.11 and Fig.12 shown.

[0273] 2. Analysis of calculation results

[0274] The geometric parameters, nozzle parameters and physical parameters are shown in Table 3:

[0275] Table 3

[0276]

[0277]

[0278] After calculation, the distribution of heat transfer coefficients of pure water nozzles and air-water nozzles is obtained, see Fig.13 and Fig.14 shown.

[0279] In summary, the present invention aims at the secondary cooling process of continuous casting of round billets, establishes a mathematical model of the water distribution on the spherical surface of the nozzle grid, and calculates the spray water volume in different positions and different areas under the nozzle spraying through the mathematical model of the water distribution on the spherical surface of the nozzle and the test data of the original nozzle. A mathematical model of the water distribution on the cylindrical surface of the billet is established, and the water volume data of the nozzle is converted into the water flow density data of the cylindrical surface of the billet through the mathematical model of the water distribution on the cylindrical surface of the billet, providing a data basis for calculating the spray heat transfer coefficient. The spray heat transfer coefficient of each node on the cylindrical surface of the billet is calculated through the water flow density on the cylindrical surface of the billet, providing a boundary condition basis for refining the mathematical model of the three-dimensional temperature field of the round billet.

[0280] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which will not affect the essence of the present invention.

Claims

1. An analysis method for the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout, characterized in that: The following steps are involved: Step S1, performing homogenization processing and data fitting on the nozzle water flow density distribution data; then performing three-dimensional spherical mesh processing on the nozzle according to the spraying angle to obtain a plurality of spraying grids; Step S2, based on the data fitting result of the nozzle water flow density distribution data, the grid characteristic parameters of each spray grid are calculated; and then the spray water volume at each spray deviation angle is calculated according to the grid characteristic parameters; Step S3, obtaining the coordinates of the boundary nodes in the cross section of the center of the circle at any position along the billet drawing direction, and calculating the area of ​​each spray grid on the billet surface based on the connection network structure between the nozzle, the boundary nodes and a plurality of set points on the round billet; Step S4, obtaining the area of ​​the sphere formed by the projection points of the lines between the set points on the sphere of equal water flow density; calculating the water flow density of the casting billet cylinder based on the area of ​​the sphere formed by the projection points, the spraying water volume at each spraying deviation angle and the area of ​​each spraying grid on the casting billet surface; Step S5, calculating the heat transfer coefficient of the billet surface based on the water flow density on the billet column surface and in combination with the billet surface temperature and the temperature of the spray water.

2. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S1, the process of performing homogenization processing and data fitting on the nozzle water flow density distribution data is to perform homogenization processing on the nozzle water flow density distribution data based on the nozzle grid position division principle, and perform data fitting on the nozzle water flow density distribution data after homogenization processing, specifically: (1) Obtain nozzle water flow density distribution data through water flow density test; (2) The grid position directly below the nozzle is set as the reference point, and the water flow density of the nozzles at other positions is adjusted to complete the uniform distribution of the water flow of the nozzles; (3) Based on the normal distribution function, the data of the nozzle water flow density after uniform distribution processing is fitted to obtain the fitting function of the nozzle.

3. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S1, the process of performing three-dimensional spherical meshing processing on the nozzle according to the spraying angle to obtain a plurality of spraying meshes is specifically as follows: based on the spraying angle of the nozzle, three-dimensional spherical meshing is performed at a preset angle each time and terminated at a termination angle.

4. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S2, the process of calculating the grid characteristic parameters of each spray grid based on the data fitting result of the nozzle water flow density distribution data is specifically as follows: (1) Obtain the spray length of each spray grid on a preset plane on one side of the spray; (2) Calculate the water flow density of each spray grid on a predefined horizontal axis and the area of ​​the spray grid on the spray sphere of the nozzle according to the data fitting results of the nozzle water flow density distribution data and the spray height of the nozzle; (3) Based on the water flow density of the spray grid on the predefined horizontal axis, the area of ​​the spray grid on the nozzle spray sphere, and the spray length of each spray grid on the preset plane, the comprehensive dimensionless water flow density of each spray grid is calculated.

5. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S2, the process of calculating the spray water volume at each spray deviation angle according to the grid characteristic parameters is specifically as follows: (1) Calculate the water volume weight of each spray grid according to the comprehensive dimensionless water flow density of each spray grid; (2) According to the water volume weight of each spray grid, the spray area, and the area of ​​each spray grid on the spray sphere of the nozzle, the spray water volume at each spray deviation angle is calculated.

6. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S3, the process of obtaining the coordinates of the boundary nodes in the cross section of the center of a circle at any position along the throwing direction is specifically as follows: (1) construct a three-dimensional coordinate system with the center of the meniscus of the round billet as the origin, and establish the association law between the center and the boundary nodes at any position along the throwing direction; (2) Obtain the angle between the line connecting the boundary node and the center of the circle and the line connecting the nozzle and the center of the circle, the geometric radius of the round billet and the coordinates of the center of the circle, and use the correlation law between the center of the circle and the boundary node at any position along the throwing direction to calculate the coordinates of the boundary node.

7. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S3, the process of calculating the area of ​​each spray grid on the surface of the billet based on the connection network structure between the nozzle, the boundary node and a plurality of set points on the round billet is specifically as follows: (1) The boundary nodes rotate in two directions along the circumference of the round billet and extend in the forward and backward directions along the billet drawing direction to form an arc surface with a number of set points as boundaries; (2) Obtain the intersection of the line between the set point and the center of the round billet and the sphere of equal water flow density, the boundary node, the length of the line between the set point and the nozzle, and the length of the line between each set point, and calculate the area of ​​each spray grid on the billet surface.

8. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S4, the process of obtaining the area of ​​the sphere enclosed by the projection points of the lines between the set points on the sphere of equal water flow density is specifically as follows: obtaining the length of the arc formed by the lines between the set points between the projection points on the sphere of equal water flow density, and calculating the area of ​​the sphere enclosed by the projection points of the arc formed by the several set points as boundaries on the sphere of equal water flow density.

9. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S4, the process of calculating the water flow density on the cylindrical surface of the ingot based on the area of ​​the sphere surrounded by the projection points, the spray water volume at each spray deviation angle, and the area of ​​each spray grid on the surface of the ingot is specifically as follows: (1) Calculate the water flow density of a single nozzle at the boundary node based on the area of ​​the sphere enclosed by the projection points, the spray water volume at each spray deviation angle, and the area of ​​each spray grid on the surface of the ingot; (2) The water flow density on the cylindrical surface of the ingot is calculated based on the water flow density of a single nozzle at the boundary node.

10. The method for analyzing the water flow density and heat transfer coefficient of round billet spray cooling based on nozzle layout according to claim 1, characterized in that: In step S5, the formula for calculating the heat transfer coefficient of the casting surface is shown in formula (1): In formula (1), H[z][r] is the spray heat transfer coefficient of the grid with the casting coordinate z and the circumferential coordinate r; Vs[z][r] is the water flow density of the grid with the casting coordinate z and the circumferential coordinate r; Ts[z][r] is the surface temperature of the billet at the grid with the billet drawing coordinate z and the circumferential coordinate r; Tanh is the hyperbolic tangent function; Tw is the temperature of the spray water.

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