Method for estimating flow rate distribution of sprayed material, method for estimating temperature distribution of object, method for designing spray nozzle, and method for creating learned model

Abstract

Provided are a method for estimating a flow rate distribution of an injected material, a method for estimating a temperature distribution of an object, a method for designing a spray nozzle, and a method for creating a learned model, which are capable of accurately estimating a flow rate distribution of an injected material injected from a spray nozzle on an injection surface while using a particle method having a track record as a numerical simulation method even for a gas-liquid multiphase fluid.SOLUTION: An inflow particle arrangement interval d ' obtained from a filling rate α of the liquid phase and an initial inter-particle distance d is defined as a particle interval in the particle inflow region, a function of a probability that particles are generated in the particle inflow region is defined as a particle generation rate function P, and coordinates of the injected material in the particle inflow region are represented by the inflow particle arrangement interval d ' and the particle generation rate function P, the particle generation rate function P is calculated in advance by using a flow rate distribution on a test ejection surface measured in advance by using a test spray nozzle having the same shape as the spray nozzle.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for estimating the flow rate distribution of a spray object, a method for estimating the temperature distribution of an object, a method for designing a spray nozzle, and a method for creating a trained model. [Background technology]

[0002] Spray nozzles are widely used for cooling, coating, cleaning, etc. Spray nozzles are broadly divided into one-fluid nozzles that spray only liquid, and two-fluid nozzles that spray both liquid and gas.

[0003] When performing uniform cooling or coating, attention must be paid to the behavior of the sprayed liquid. When the amount of liquid sprayed is small, it is sufficient to focus only on the spray surface directly below the spray nozzle, but when the amount of liquid sprayed is large, the behavior of the liquid after it hits the spray surface is also important. Fluid simulation is one method for understanding the behavior of the liquid after it hits the spray surface, but numerical simulation is difficult because the liquid sprayed from the spray nozzle is very small compared to the analysis area and the entire area is a free interface.

[0004] For such phenomena dominated by the free interface, analysis using the particle method is effective. For example, Non-Patent Document 1 models particles being sprayed in random directions within the spray nozzle's injection range. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Yamazaki, Hakuko et al., "Analysis of Spray Water Behavior in Secondary Cooling of Continuous Casting Using Particle Method," Iron and Steel Institute of Japan, Tetsu-to-Haganen, Vol. 99, 2013 Summary of the Invention [Problem to be solved by the invention]

[0006] However, the method in Non-Patent Document 1 has difficulty adequately reproducing the behavior of the liquid after impact with the injection surface when there is a large deviation in the flow rate distribution within the injection area. The fluid injected from a spray nozzle is generally called a "gas-liquid multiphase fluid," and exhibits much more complex behavior than a purely liquid fluid. Therefore, even if a proven particle method is used, it is extremely difficult to estimate the flow rate distribution on the injection surface.

[0007] The present invention has been made in consideration of the above, and aims to provide a method for estimating the flow rate distribution of a spray object, a method for estimating the temperature distribution of an object, a method for designing a spray nozzle, and a method for creating a trained model, which can accurately estimate the flow rate distribution on the injection surface of a spray object injected from a spray nozzle, even for gas-liquid multiphase fluids, while still using a particle method that has a proven track record as a numerical simulation method. [Means for solving the problem]

[0008] (1) A method for estimating a flow rate distribution of a sprayed object according to the present invention is a method in which a computer estimates a flow rate distribution of a sprayed object on a spray surface by using a particle method, the method comprising the steps of: When executing the particle method, The injection material is made into particles, a particle spacing in the particle inflow region is defined as an inflow particle arrangement spacing d' obtained from a liquid phase filling rate α in a particle inflow region set in an intermediate region of the spray path of the spray nozzle and an initial inter-particle distance d, which is an inter-particle distance of the sprayed material immediately after spraying, A function of the probability that the particles are generated in the particle inflow region is defined as a particle generation rate function P, The coordinates of the ejection object within the particle inflow region are expressed by the inflow particle arrangement interval d' and the particle generation rate function P, The particle generation rate function P is calculated in advance using a flow rate distribution on a test injection surface that is measured in advance using a test spray nozzle having the same shape as the spray nozzle.

[0009] (2) The method for estimating flow rate distribution of a jet object according to the present invention is the method for estimating flow rate distribution of a jet object described in (1) above, When a printing device equipped with the spray nozzle is used, the flow rate distribution of the sprayed material on the spray surface of the printing target is estimated.

[0010] (3) The method for estimating the temperature distribution of an object according to the present invention, when using a heating device or a cooling device equipped with the spray nozzle, estimates the flow rate distribution of the sprayed material on the spray surface by the method for estimating the flow rate distribution of the sprayed material described in (1) above, and estimates the temperature distribution of the object to be heated or cooled based on the estimation result.

[0011] (4) The spray nozzle design method according to the present invention estimates the flow rate distribution of the spray material on the spray surface using the method for estimating the flow rate distribution of the spray material described in (1) above, and determines the arrangement and number of spray nozzles based on the estimation results.

[0012] (5) The method for estimating the temperature distribution of an object according to the present invention uses the method for estimating the flow rate distribution of an injected object described in (1) above to estimate multiple flow velocities in the normal direction and multiple flow velocities in the tangential direction relative to the injection surface of the cooling liquid injected from a spray nozzle, and learns a model using the multiple normal flow velocities and the multiple tangential flow velocities as input values ​​and the amount of heat dissipated as an output value. [Effects of the Invention]

[0013] According to the method for estimating the flow rate distribution of a sprayed material according to the present invention, it is possible to accurately estimate the flow rate distribution on the spray surface of a sprayed material sprayed from a spray nozzle, even for a gas-liquid multiphase fluid, while still using the particle method, which has a proven track record as a numerical simulation method. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a diagram for explaining the spray surface of a spray nozzle and a particle inflow region in a method for estimating the flow rate distribution of a spray object according to an embodiment. [Figure 2]FIG. 2 is a diagram for explaining a particle inflow region and a particle flow velocity direction in a conventional method for estimating the flow rate distribution of a jet of injection material. [Figure 3] FIG. 3 is a diagram for explaining a particle inflow region and a particle flow velocity direction in the method for estimating the flow rate distribution of a jet object according to the embodiment. [Figure 4] FIG. 4 is a block diagram showing a schematic configuration of a jet flow rate distribution estimation device according to an embodiment. [Figure 5] FIG. 5 is a diagram for explaining an orthogonal coordinate space around the spray nozzle (on the particle inflow region) in the method for estimating the flow rate distribution of the injection object according to the embodiment. [Figure 6] FIG. 6 is a diagram for explaining the initial inter-particle distance d in the particle inflow region and the inflow particle arrangement interval d′ in the method for estimating the flow rate distribution of a jet object according to the embodiment. [Figure 7] FIG. 7 is a flowchart showing an example of the flow of pre-calculation processing of the arrangement interval d' of inflowing particles, which is performed only once before the start of analysis by the particle method, in the method for estimating the flow rate distribution of a jet object according to the embodiment. [Figure 8] FIG. 8 is a diagram showing an example of a flow rate distribution on a test ejection surface measured in advance using a test spray nozzle having the same shape as the spray nozzle in the method for estimating the flow rate distribution of an ejection object according to the embodiment. [Figure 9] FIG. 9 is a flowchart showing an example of the flow of particle inflow processing performed at each step during analysis by the particle method in the method for estimating the flow rate distribution of a jet object according to the embodiment. [Figure 10] FIG. 10 is a diagram illustrating an example of a bounding box created using the x-axis radius of an elliptical particle inflow region and the y-axis radius of a particle inflow region in the method for estimating the flow rate distribution of a jet object according to an embodiment. [Figure 11] FIG. 11 is a diagram showing an example of a result of analyzing the flow rate distribution by the particle method in the method for estimating the flow rate distribution of a jet object according to the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0015] A method for estimating the flow rate distribution of a jetted object, a method for estimating the temperature distribution of an object, a method for designing a spray nozzle, and a method for creating a trained model according to embodiments of the present invention will be described with reference to the drawings. Note that the components in the following embodiments include those that are easily replaceable by a person skilled in the art, or those that are substantially identical. Furthermore, in the following description, descriptions of identical or overlapping parts will be omitted or simplified as appropriate. Furthermore, in each of the drawings referred to below, identical or overlapping parts are assigned the same reference numerals.

[0016] (Conventional method using particle method) Numerical analysis is one method for quantitatively evaluating the flow of a spray (e.g., cooling water) ejected from a spray nozzle. However, in order to accurately track the interface shape of the sprayed material using conventional fluid simulation methods, an extremely fine mesh is required, which is difficult from the perspective of computational load.

[0017] Unlike conventional numerical analysis methods that use grids, the particle method is a simulation method that uses movable particles as calculation points. Due to its characteristics, it is suitable for analyzing large interface deformation problems, such as the behavior of sprayed objects in spray cooling. However, particle methods are not good at analyzing multiphase fluids with large density differences, so it is generally difficult to analyze gas-liquid multiphase fluids that involve complex interactions between the liquid and gas phases, such as the flow inside a two-fluid nozzle. In other words, because the particle method is a method for numerically simulating the behavior of a "liquid phase fluid," if even a small amount of a "gas phase" with a significantly different density is mixed in, the simulation will not work well.

[0018] Furthermore, faithfully analyzing the process by which a liquid breaks down into droplets in an actual jet is not realistic because it would increase the calculation load. Therefore, in order to analyze a spray nozzle within a realistic calculation time, a model is created in which the fluid flows into the analysis domain in a granular state. Since it is difficult to analyze all of the actual spray droplets, a certain number of droplets are considered to be one particle in the particle method. Furthermore, in order to make the modeled particles move in the same way as spray nozzle jets, an inflow velocity is given in a direction within the spray nozzle's spray angle.

[0019] (Outline of flow rate distribution estimation method according to the present invention) In conventional estimation methods using particle methods, for example, a single point at the outlet of a spray nozzle is set as the particle inflow position in the particle method, as shown in Figure 2. In this case, if particles are brought closer together than the inter-particle distance, the density in the analysis increases, which could cause the analysis to become unstable. Therefore, the maximum injection amount that can be injected is the product of the injection velocity and the cross-sectional area of ​​a single particle, that is, the product of the injection velocity and the square of the inter-particle distance. In other words, with conventional estimation methods using particle methods, the problem arises that when the injection amount is large, the particles cannot all fit in.

[0020] On the other hand, in the present invention, as shown in FIG. 1, an elliptical region is set a little beyond the spray nozzle outlet, i.e., in the intermediate region of the spray nozzle's injection path, and this region is set as the particle inflow position in the particle method. This ensures sufficient space in the region where the particles are placed, thereby avoiding the above problem. In the present invention, this elliptical particle inflow position is defined as the "particle inflow region." Note that in this embodiment, the injection surface of the spray nozzle to be analyzed is set to an elliptical shape, and therefore the particle inflow region in FIG. 1 is also set to an elliptical shape accordingly. Here, the injection surface of the spray nozzle is set to an elliptical shape in order to, for example, cool the object to be cooled (e.g., a cast slab) as uniformly as possible.

[0021] In this embodiment, the term "intermediate region in the spray nozzle's injection path" refers to the intermediate region in the injection path of the material injected from the injection orifice of the spray nozzle until it reaches the injection surface. More specifically, the intermediate region is located on the injection path of the material after it leaves the injection orifice and before it collides with the injection surface, and is a region in which the flow of the material has completed its initial acceleration from the injection orifice, a spray pattern has been formed, and the flow of the material has not yet been affected by interaction with the injection surface. The intermediate region in the spray nozzle's injection path functions as a reference position for defining a representative cross section of the flow of the material, and a particle inflow region is set at this position. The intermediate region in the spray nozzle's injection path is appropriately determined depending on the distance from the injection orifice, the shape characteristics of the injection pattern, and the injection conditions, and is used to set the initial conditions in the particle method.

[0022] Furthermore, in conventional estimation methods using particle methods, it is assumed that particles are sprayed in random directions from a single point at the outlet of the spray nozzle, so the distribution of particle presence, i.e., the flow rate distribution on the spray surface, is uniform, as shown in Figure 2. In contrast, in the present invention, as will be described later, the particle presence distribution is calculated using a particle generation rate function P, reflecting the flow rate distribution on a test spray surface obtained in advance through experiments. This makes it possible to reproduce the bias in the flow rate distribution on the spray surface on the surface of a specific object.

[0023] Furthermore, in the conventional estimation method using the particle method, the flow velocity direction of particles in the particle method was set to a random direction within the injection range, as shown in Figure 2. This setting resulted in a uniform distribution of particles on the injection surface, i.e., the flow rate distribution. In contrast, in the present invention, the particle inflow region is set to an elliptical shape, the same as the injection surface, and it is assumed that the injected material reaches the injection surface while maintaining the flow rate distribution in the particle inflow region. Therefore, the flow velocity direction of particles in the particle method is calculated according to the coordinates of the particle inflow region (x-axis coordinate, y-axis coordinate (see Figure 5)). This makes it possible to reproduce the bias in the flow rate distribution on the injection surface on the surface of a specific object.

[0024] In this embodiment, the particle inflow region is described as being elliptical, but the shape of the particle inflow region can be changed to match the shape of the spray nozzle injection surface to be analyzed. That is, if the injection surface of the spray nozzle to be analyzed is circular, the particle inflow region of the present invention will also be circular, and if the injection surface of the spray nozzle to be analyzed is rectangular, the particle inflow region can also be set to the same rectangular shape.

[0025] (Flow rate distribution estimation device) The ejected object flow rate distribution estimation device according to the embodiment is realized by a general-purpose information processing device such as a personal computer or a workstation, or a server located on a cloud, etc. The flow rate distribution estimation device 1 includes an input unit 11, a calculation unit 12, and an output unit 13, as shown in FIG.

[0026] The input unit 11 is an input means for the calculation unit 12, and is realized by an input device such as a keyboard, a mouse pointer, a numeric keypad, etc. The input unit 11 inputs information necessary for various processes in the calculation unit 12.

[0027] The calculation unit 12 is realized by a processor such as a CPU (Central Processing Unit) and a memory (main storage unit) such as a RAM (Random Access Memory) or a ROM (Read Only Memory).

[0028] The calculation unit 12 estimates the flow rate distribution of the injected material on the injection surface by using a particle method. Specifically, when executing the particle method, the calculation unit 12 uses the injected material as particles. The calculation unit 12 also uses, as the particle interval in the particle inflow region, the inflow particle arrangement interval d', which is obtained from the liquid phase filling rate α in the particle inflow region (see FIG. 1) set in the intermediate region of the injection path of the spray nozzle and the initial inter-particle distance d, which is the inter-particle distance of the injected material immediately after injection.

[0029] The calculation unit 12 also uses a function of the probability of particles being generated in the particle inflow region as a particle generation rate function P. This particle generation rate function P is calculated in advance using a flow rate distribution on a test injection surface that has been measured in advance using a test spray nozzle having the same shape as the spray nozzle. The calculation unit 12 also expresses the coordinates of the injection object in the particle inflow region using the inflow particle arrangement interval d' and the particle generation rate function P. Details of the processing by the calculation unit 12 will be described later.

[0030] The output unit 13 is realized by an output device such as a display, etc. The output unit 13 outputs the calculation results of the calculation unit 12.

[0031] (Flow rate distribution estimation method) The flow rate distribution estimation method executed by the injection object flow rate distribution estimation device according to the embodiment will be described in detail with reference to Fig. 5 and Fig. 6. Fig. 5 shows the Cartesian coordinate space around the spray nozzle (on the particle inflow region). Fig. 6 also shows the initial inter-particle distance d and the inflow particle arrangement interval d' in the particle inflow region.

[0032] In this embodiment, the behavior of the injection material injected from the spray nozzle is numerically analyzed by the particle method, mainly by the calculation unit 12. In the numerical analysis by the particle method, the inflow particle arrangement interval d' is calculated by adjusting the initial inter-particle distance d based on the estimated inflow amount Q in the particle inflow region, and the particles are allowed to flow in according to the particle generation rate function P, thereby estimating the flow rate distribution of the injection material on the injection surface.

[0033] In the particle method, the inflow condition is generally a method in which multiple particles with velocity are uniformly arranged in the particle inflow region. A schematic representation of this conventional particle method concept is shown in Figure 6(a). The particle arrangement interval in this case is defined as the initial inter-particle distance d, as shown in Figure 6(a). Note that in Figure 6(a), the liquid region is the actual liquid region, and in the particle method, this liquid region is divided into multiple regions, and each region is assumed to represent one particle arranged in the center. In Figure 6(a), one particle is represented by a single black circle. In this way, the liquid region is assumed to be multiple particles, as shown in Figure 6(a).

[0034] In the method of uniformly distributing particles in the particle inflow region, as shown in Figure 6(a), the liquid flows in from the particle inflow region as a continuous stream. This means that the particle inflow region is filled with liquid, making it difficult to reproduce the spray state of a spray nozzle. It is also difficult to adjust the amount of liquid flowing in. Furthermore, the liquid is mixed with gas, creating a gas-liquid multiphase flow, so the above assumption does not hold.

[0035] Therefore, in this embodiment, the inventors have come up with the idea of ​​estimating the state of a gas-liquid multiphase flow in which gas is mixed with liquid using a particle method by the following method. (a) The fluid is assumed to be discrete from the time it is sprayed from the spray nozzle until it reaches the spray surface. (b) Assume that the nozzle outlet and spray surface contain only liquid. (c) Assume that the amount of liquid sprayed from the nozzle of the spray nozzle at a particular time is the same as the amount of liquid when it reaches the spray surface. (d) The inflow particle arrangement interval d' (see Fig. 6(b)) that satisfies the above (a) to (c) is set by the initial inter-particle distance d. In addition, the estimated inflow amount Q in the particle inflow region is adjusted according to the size of the inflow particle arrangement interval d'.

[0036] Figure 6(b) is a schematic diagram of the state in the case of a "gas-liquid multiphase fluid." In Figure 6(b), the same squares as in Figure 6(a) indicate liquid regions, and one liquid region is assumed to represent one particle. On the other hand, Figure 6(b) differs from the conventional particle method shown in Figure 6(a) in that it has gas phase regions in addition to liquid regions. In the case of Figure 6(b), the blank areas between the liquid regions indicated by the squares correspond to the gas phase regions. The liquid regions are considered to be arranged at equal intervals, with the inflow particle placement interval d' between them, sandwiching the gas phase regions.

[0037] To determine the inflow particle arrangement interval d' that satisfies the expected inflow volume Q in the particle inflow region, the liquid filling rate α in the particle inflow region is calculated. If the cross-sectional area of ​​the particle inflow region is S and the injection flow velocity is v, the cross-sectional area of ​​the liquid itself is Q / v, so the liquid filling rate α in the particle inflow region can be expressed as the following equation (1).

[0038]

number

[0039] The relationship between the initial inter-particle distance d, the inflow particle arrangement interval d', and the liquid phase filling rate α can be expressed by the following formula (2).

[0040]

number

[0041] By rearranging the above equations (1) and (2), the following equation (3) can be obtained: In the following equation (3), for example, when d=d', the particle inflow region is completely filled with particles, so α=1.

[0042]

number

[0043] However, simply introducing the inflow particle arrangement interval d' makes it difficult to reproduce the flow rate distribution at the injection surface, because particles are uniformly arranged in the particle inflow region. Therefore, in this embodiment, a new particle generation rate function P(x, y) is introduced, and the inflow particle arrangement interval d' is specified for each coordinate in the particle inflow region, thereby making it possible to obtain a desired flow rate distribution at the injection surface.

[0044] The particle generation rate function P is a two-variable function whose variables are the two-dimensional coordinates on the particle inflow region (see Figure 5), and is used to determine whether or not to place a particle at that coordinate during particle placement. The particle generation rate function P can be, for example, a Gaussian function, a power function, or a function defined by the product or sum of these.

[0045] When the particle generation rate function P is introduced, there will be areas in the particle inflow region where particles are not generated, and therefore, with the previously set inflow particle arrangement interval d', the actual inflow volume will be lower than the expected inflow volume Q. Therefore, in this embodiment, a new corrected liquid phase filling rate α' is set and the inflow particle arrangement interval d' is corrected.

[0046] The corrected liquid phase filling rate α' that satisfies the desired assumed inflow volume Q under the particle generation rate function P can be calculated using the following equation (4): In the following equation (4), the normal liquid phase filling rate α is multiplied by the ratio of the value obtained by surface integration within the particle inflow region of the particle generation rate function E(x, y), which is 1 over the entire particle inflow region, to the value obtained by surface integration within the particle inflow region of the particle generation rate function P(x, y).

[0047]

number

[0048] Here, the region D in the above formula (4) is the particle inflow region where particles are generated. In addition, the value obtained by surface integration of the particle generation rate function E(x, y) within the particle inflow region is equal to the cross-sectional area S, so the corrected liquid phase filling rate α' can be expressed as the following formula (5).

[0049]

number

[0050] Furthermore, when the above formula (1) is substituted for α in the above formula (5), the following formula (6) is obtained.

[0051]

number

[0052] By recalculating the inflow particle arrangement interval d' in the above equation (3) using the corrected liquid phase filling rate α' shown in the above equation (6), it is possible to reproduce the spray nozzle flow rate distribution while satisfying the desired assumed inflow volume Q. Specifically, the corrected liquid phase filling rate α' is substituted for the liquid phase filling rate α in equation (3) and then equation (6) is substituted. In other words, the inflow particle arrangement interval d' taking into account the particle generation rate function P(x, y) is expressed by the following equation (7). Note that the corrected liquid phase filling rate α' in the below equation (7) is expressed by the above equation (6).

[0053]

number

[0054] (Pre-calculation of inflow particle placement interval d') FIG. 7 shows the flow of pre-calculation processing of the arrangement interval d' of incoming particles, which is carried out only once before the start of analysis by the particle method in this embodiment.

[0055] In the pre-calculation process for the inflow particle arrangement interval d', first, the particle generation rate function P(x, y) is set (step S1). Here, the variables x and y are points on the xy coordinates in the particle inflow region shown in Figure 5. The particle generation rate function P(x, y) is set from the flow rate distribution on the test injection surface that is measured in advance using a test spray nozzle with the same shape as the spray nozzle. Because the particle generation rate function P(x, y) is a two-variable function in the particle inflow region, the flow rate distribution is also measured two-dimensionally.

[0056] Figure 8 shows an example of a flow rate distribution on a test injection surface that was measured in advance. The flow rate distribution in the x-axis direction shown in Figure 8(a) is trapezoidal, and the flow rate distribution in the y-axis direction shown in Figure 8(b) is normal. These shapes in Figure 8 are taken as functions of x and y, which are set as the particle generation function P(x,y). In this embodiment, since the particle inflow region is set to an elliptical shape, the following equation (8) is set as the particle generation rate function P(x,y).

[0057]

number

[0058] Here, a, b, and γ in the above formula (8) x ,σ y are the radius of the particle inflow region in the x-axis direction, the radius of the particle inflow region in the y-axis direction, the coefficient representing the jet spread in the x-axis direction, and the standard deviation representing the degree of jet spread in the y-axis direction, respectively. These parameters a, b, and γ x ,σ y was fitted from the actually measured flow rate distribution shown in FIG. 8, and the following values ​​were obtained, for example:

[0059] a=300mm b=100mm gamma x =0.01 σ y =30mm

[0060] Note that the parameters a, b, and γ x ,σ y When determining the amount of water remaining in each slit, multiple slits may be placed on the injection surface, and a fitting may be performed based on the amount of water remaining in each slit. Alternatively, a similar fitting may be performed on any surface in the particle inflow region (a surface parallel to the injection surface).

[0061] [Parameter determination method] Parameters a, b, γ x ,σ yA specific method for determining is explained in more detail below. First, an actual spray experiment is carried out under the same conditions as the spray nozzle to be analyzed, and the two-dimensional flow rate distribution is measured on the spray surface or on a plane parallel to the particle inflow region.

[0062] An example of a method for obtaining the results shown in Figure 8 through actual experiments is to set up multiple measurement points in a straight line (in other words, in a row) on the ejection surface and measure the flow rate per unit time at each point. More specifically, measurement slits or containers are placed at equal intervals on the ejection surface, and the amount of liquid collected in each slit within a certain period of time is measured. In this case, measurements are performed multiple times under the same conditions, and the average value is used to reduce measurement error.

[0063] Here, "two-dimensional" refers to two directions, the x-axis and the y-axis, which are perpendicular to each other on the spray surface. The above-mentioned multiple measurement points are arranged in the x-axis direction relative to the spray nozzle, and the flow rate is measured using the above-mentioned method. The above-mentioned multiple measurement points are also arranged in the y-axis direction, and the flow rate is similarly measured using the above-mentioned method. In order to measure the flow rate distribution in each of the x-axis and y-axis directions with sufficient resolution, it is desirable to have 10 or more measurement points in each of the x-axis and y-axis directions.

[0064] Furthermore, it is preferable to perform the above measurements while changing conditions such as the distance from the spray nozzle and the spray angle, and obtain flow rate distribution data under each condition, since this enables the present invention to be applied to a variety of usage environments. Based on the flow rate measurement results at each point, the shape characteristics of the flow rate distribution in each of the x-axis and y-axis directions are grasped.

[0065] When the flow rate distribution in the x-axis direction is trapezoidal as shown in Fig. 8(a), the parameter a corresponds to half of the lower base of the trapezoid, and γ x corresponds to the inclination of the legs of the trapezoid. x can be calculated for each of the two legs and averaged, or can be calculated for either one of the legs. On the other hand, when the flow rate distribution in the y-axis direction is a normal distribution as shown in Figure 8(b), the parameter b corresponds to half the width in the horizontal direction from the point where the flow rate ratio on the vertical axis is 0%, and σy corresponds to the standard deviation of the distribution.

[0066] When determining the optimal particle generation function P that can reproduce Figure 8, the parameters a, b, and γ set by the above method are x ,σ y may be used as initial values ​​and fitted to approximate the shapes shown in (a) and (b) of Figure 8. Various methods can be used for this fitting, such as the nonlinear least squares method and the gradient method.

[0067] For example, to optimize the parameters of equation (8) from measured data, an algorithm can be used that minimizes the sum of squares of the differences between the measured data points and the values ​​calculated from equation (8). In this case, it is efficient to set initial estimates based on the geometric characteristics of the injection pattern and then use these as a starting point for optimization.

[0068] Next, after calculating the corrected liquid phase filling rate α' (step S2), the inflow particle arrangement interval d' is calculated (step S3). The initial inter-particle distance d in the analysis was set to 2 mm. The corrected liquid phase filling rate α' can be expressed as the following equation (9) using the particle generation rate function P(x, y) of the above equation (8).

[0069]

number

[0070] Here, a and γ in the above formula (9) x ,σ y are the radius of the particle inflow region in the x-axis direction, the coefficient representing the jet spread in the x-axis direction, and the standard deviation representing the extent of the jet spread in the y-axis direction, respectively.

[0071] Since it is difficult to obtain an analytical solution for this equation, an approximate solution is obtained by discretizing it in the program. After determining the corrected liquid phase filling rate α', the inflow particle arrangement interval d' is calculated using the following equation (7). This completes the pre-calculation of the inflow particle arrangement interval d'.

[0072] [Number]

[0073] (Particle inflow process) FIG. 9 shows the flow of the particle inflow process that is performed at each step during the analysis by the particle method in the present embodiment.

[0074] In the particle inflow process, first, particles are generated by determination using the particle generation rate function P (step S11). In this case, for example, as shown in FIG. 10, a bounding box that encloses the particle inflow region is created using the x-axis direction radius a and the y-axis direction radius b of the particle inflow region. Then, one of the four vertices of this bounding box is used as the initial coordinates for particle placement. In the example of FIG. 10, the lower left vertex of the bounding box is used as the initial coordinates.

[0075] After determining the initial coordinates, the region is scanned at the inflowing particle placement interval d'. At that time, particles are generated at the coordinates only when each coordinate (x, y) within the bounding box is "within the elliptical particle inflow region" and "the particle generation rate function P returns True".

[0076] Here, "the particle generation rate function P returns True" means that "a function that returns True or False based on the value of the particle generation rate function P returns True". In this case, for example, a random number rand in the range from 0 to 1 is generated, and if the value is smaller than the return value of the particle generation rate function P(x, y) at the coordinates (x, y), True is returned. For example, when the particle generation rate function P(x, y) = 1 (P(x, y) = E(x, y)), since rand < P(x, y) always holds, True is returned for any coordinates (x, y) (= particles are uniformly arranged). Note that as the above random number, a random number with a certain degree of accuracy may be used. For example, a random number that divides the range from 0 to 1 into at least 100 parts and selects one of them may be used.

[0077] Next, the flow velocity is calculated from the coordinates of each generated particle (step S12). The absolute value of the flow velocity is set in advance, and the direction is set to the direction from the spray nozzle outlet to the coordinates of the particle. This completes the particle inflow process, as the coordinates and flow velocity of each particle in the particle inflow region are determined.

[0078] [How to set the absolute value of the flow velocity] A method for setting the absolute value of the flow velocity in advance will be described. The flow velocity may be calculated by experimental measurement. For example, a method can be used in which the state during spray injection is photographed with a high-speed camera and the flow velocity is measured using PIV (Particle Image Velocimetry). Alternatively, the flow velocity can be measured directly using an instrument such as a laser Doppler velocimeter. The absolute value of the flow velocity may also be calculated in advance using numerical simulation. The initial velocity of the particles in the present invention may also be set based on the obtained flow velocity. In this embodiment, the direction of the flow velocity is defined as a vector directed from the spray nozzle outlet to the particle coordinates, and is automatically calculated in the present invention according to the position of each particle, so there is no need to set it in advance.

[0079] (Calculation of flow distribution) Next, by assigning a flow velocity to each generated particle, the flow rate distribution of the ejected material on the ejection surface is estimated. Figure 11 shows an example of the analysis results of the flow rate distribution. In Figure 11, the solid line shows the actually measured flow rate distribution, the dashed line shows the analysis results of the present invention, and the dashed line shows the analysis results of the prior art. As shown in Figure 11, with the present invention, very good agreement with the measured values ​​was obtained, and it can be seen that the analysis accuracy is significantly improved compared to the results of the conventional analysis method.

[0080] According to the method for estimating the flow rate distribution of a sprayed material according to the embodiment described above, even for a gas-liquid multiphase fluid, the flow rate distribution on the spray surface of a sprayed material sprayed from a spray nozzle can be accurately estimated using the particle method, which has a proven track record as a numerical simulation method.

[0081] Furthermore, the method for estimating the flow rate distribution of a jetted material according to the embodiment can also estimate the flow rate distribution of a jetted material on the jetting surface of a printing target when using a printing device equipped with a spray nozzle. This can, for example, reduce jetting unevenness and improve print quality.

[0082] (Modification 1 of this embodiment) There are cases where the spray nozzle to be analyzed has an elliptical injection surface and takes on a different particle generation function P(x,y). Examples of particle generation functions P(x,y) other than those shown in Figure 8(a) and (b) are shown below. Note that the parameters included in the equations described below with the same symbols as those in the above equations are the same parameters, so their explanation will be omitted.

[0083] (a) x-axis: normal distribution, y-axis: normal distribution

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[0084] Here, σ in the above formula (10) x is the standard deviation that represents the extent of the jet spread in the x-axis direction.

[0085] (b) x-axis: normal distribution, y-axis: trapezoidal

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[0086] (c) x-axis: trapezoid, y-axis: trapezoid

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[0087] Here, γ in the above formula (12) y is a coefficient that represents the spray spread in the y-axis direction.

[0088] (d) x-axis: trapezoid, y-axis: trigonometric function

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[0089] (Modification 2 of this embodiment) On the other hand, if the spray nozzle to be analyzed has a shape other than elliptical, the particle inflow region is set to the same shape as the shape of the spray nozzle's injection surface. As a result, the particle generation function P(x, y) is also set to a function that can reflect that shape. For example, the corrected liquid phase filling rate α' and inflow particle arrangement interval d' for each major shape are as shown in the following examples. Note that parameters included in the equations described below with the same symbols as those in the above equations are the same parameters, so explanations will be omitted.

[0090] (a) When the particle inflow region is circular The x-axis and y-axis directions are set perpendicular to each other in the radial direction of the circle. In this case, the above formula (8) has a normal distribution on the x-axis and a normal distribution on the y-axis, so the following formula (14) is obtained. In the following formula (14), σ x is the standard deviation that represents the extent of the injection spread in the x-axis direction, and σ y is the standard deviation that represents the degree of injection spread in the y-axis direction, and r is the radius of the circle in the inflow region. Note that the above equations (7) and (9) are the same as those in Figure 8.

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[0091] (b) When the particle inflow region is rectangular The x-axis direction is taken along one pair of parallel sides of the above rectangle, and the y-axis direction is taken along the other pair of sides. Note that the x-axis and y-axis directions may be taken in reverse. In this case, equation (8) becomes a trapezoid with the x-axis and the y-axis in a trapezoidal shape, so the following equation (15) is taken. In equation (15) below, a is the half width of the rectangle in the x-axis direction, b is the half width of the rectangle in the y-axis direction, and γ x is the coefficient that represents the spray spread in the x-axis direction, γ y is a coefficient that represents the spread of the jet in the y-axis direction. Note that the above formulas (7) and (9) are the same as those in Figure 8.

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[0092] (c) When the particle inlet region has an arbitrary shape For the above arbitrary shape, the x-axis and y-axis directions are taken to be perpendicular to each other. For an inflow region D of any shape, the x-axis is normal distribution and the y-axis is normal distribution, so in this case, equation (8) is taken as the following equation (16). In the following equation (16), σ x is the standard deviation that represents the extent of the injection spread in the x-axis direction, and σ y is the standard deviation that represents the degree of spray spread in the y-axis direction. Note that the above formulas (7) and (9) are the same as those in Figure 8.

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[0093] (Method for estimating temperature distribution of an object) The method for estimating the flow rate distribution of a jetted object according to the embodiment can also be applied to estimating the temperature distribution of an object. In this case, when using a heating device or a cooling device equipped with a spray nozzle, the method for estimating the temperature distribution of an object estimates the flow rate distribution of the jetted object on the spray surface using the above-described method for estimating the flow rate distribution of a jetted object, and estimates the temperature distribution of the object to be heated or cooled based on the estimation result. This makes it possible to accurately estimate the temperature distribution of the object based on the appropriately estimated flow rate distribution of the jetted object.

[0094] (Spray nozzle design method) Furthermore, the method for estimating the flow rate distribution of a jetted object according to the embodiment can also be applied to the design of a spray nozzle. In this case, the method for designing a spray nozzle estimates the flow rate distribution of a jetted object on a jetting surface using the above-described method for estimating the flow rate distribution of a jetted object, and determines the arrangement and number of spray nozzles based on the estimation results. This makes it possible to determine the optimal arrangement and number of spray nozzles based on the appropriately estimated flow rate distribution of the jetted object.

[0095] (How to create a trained model) Furthermore, the method for estimating the flow rate distribution of a sprayed object according to the embodiment can also be applied to creating a trained model. In this case, the method for creating a trained model estimates multiple flow velocities in the normal direction and multiple flow velocities in the tangential direction relative to the spray surface of the coolant sprayed from the spray nozzle using the above-described method for estimating the flow rate distribution of a sprayed object. Then, model training is performed using the multiple normal flow velocities and multiple tangential flow velocities as input values ​​and the amount of heat dissipation as an output value. This makes it possible to create a model that accurately estimates the amount of heat dissipation based on the multiple flow velocities in the normal direction and the tangential direction that have been appropriately estimated.

[0096] The method for estimating the flow rate distribution of a jet object, the method for estimating the temperature distribution of an object, the method for designing a spray nozzle, and the method for creating a trained model according to the present invention have been specifically described above using a description of the preferred embodiment and examples, but the scope of the present invention is not limited to these descriptions and should be broadly interpreted based on the claims. Needless to say, various changes, modifications, etc. based on these descriptions are also included in the scope of the present invention. [Explanation of symbols]

[0097] 1 Flow distribution estimation device 11 Input section 12 Arithmetic section 13 Output section

Claims

1. A method for estimating a flow rate distribution of an object sprayed from a spray nozzle onto an ejection surface by a particle method, the method comprising: When executing the particle method, The injection material is made into particles, a particle spacing in the particle inflow region is defined as an inflow particle arrangement spacing d′ obtained from a liquid phase filling rate α in a particle inflow region set in an intermediate region of a spray path of the spray nozzle and an initial inter-particle distance d, which is an inter-particle distance of the sprayed material immediately after spraying, A particle generation rate function P is a function of the probability that the particles are generated in the particle inflow region, The coordinates of the ejection object within the particle inflow region are expressed by the inflow particle arrangement interval d′ and the particle generation rate function P, the particle generation rate function P is calculated in advance using a flow rate distribution on a test injection surface that is measured in advance using a test spray nozzle having the same shape as the spray nozzle; A method for estimating the flow rate distribution of injected material.

2. The method for estimating a flow rate distribution of a jetted material according to claim 1 , wherein the flow rate distribution of the jetted material on a jetting surface of a printing target is estimated when a printing device equipped with the spray nozzle is used.

3. A method for estimating the temperature distribution of an object, which, when using a heating device or a cooling device equipped with the spray nozzle, estimates the flow rate distribution of a sprayed object on a spray surface using the method for estimating the flow rate distribution of a sprayed object described in claim 1, and estimates the temperature distribution of an object to be heated or cooled based on the estimation result.

4. A spray nozzle design method comprising estimating the flow rate distribution of a spray material on a spray surface by the method for estimating flow rate distribution of a spray material according to claim 1, and determining the arrangement and number of spray nozzles based on the estimation result.

5. A method for creating a trained model, which estimates multiple flow velocities in the normal direction and multiple flow velocities in the tangential direction relative to the injection surface of a cooling liquid sprayed from a spray nozzle using the method for estimating the flow rate distribution of an injected object described in claim 1, and trains a model using the multiple flow velocities in the normal direction and the multiple flow velocities in the tangential direction as input values ​​and the amount of heat dissipated as an output value.

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