Simulation apparatus and program

Abstract

To provide a simulation device capable of analyzing a flow of a liquid containing bubbles without dividing an analysis space into lattices.SOLUTION: To analyze the motion of a liquid containing a plurality of bubbles by using a particle method. Simulation conditions are input to the input unit. The processing unit performs calculation based on the simulation condition input to the input unit. The processing unit has a function of discretizing a liquid using a plurality of computational particles based on an input simulation condition, a function of representing each of air bubbles by one computational particle based on the input simulation condition, a function of calculating an interaction between a computational particle of the liquid and a computational particle of the air bubble based on the input simulation condition, a function of solving a governing equation of the discretized liquid in consideration of the interaction, and a function of solving a governing equation of the air bubble in consideration of the interaction.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a simulation device and a program. [Background technology]

[0002] Slurry bubble column reactors have attracted attention as a key device for realizing the production of carbon-recycled liquid synthetic fuels (Fischer-Tropsch synthesis (FT synthesis)). In a slurry bubble column reactor, a complex flow occurs in which liquid, powder, and bubbles coexist. To improve the efficiency of liquid fuel synthesis, it is desirable to predict the flow conditions inside the reactor and find the conditions under which FT synthesis occurs actively.

[0003] One method for predicting the flow inside a reactor is to conduct verification experiments using actual or test equipment. However, there are limitations to conducting verification experiments using actual or test equipment, such as the difficulty of preparing experimental equipment, the large number of conditions that need to be verified, and the fact that some quantities cannot be measured experimentally. For this reason, numerical experiments are often conducted to simulate the flow field on a computer for verification. Computational fluid dynamics simulation equipment is used in these simulations.

[0004] The FT synthesis process produces liquid fuel by bringing CO2-containing synthesis gas into contact with a catalyst. Liquid fuel containing catalyst powder is stored in a reactor, and synthesis gas is injected into the reactor via a bubble generator. To simulate such a reactor, two possible approaches are to apply direct numerical calculation of the governing equations for gas and liquid, and to couple the governing equations for powder. In this case, a very fine computational grid must be created to adequately resolve the bubbles, resulting in a huge number of computational grid points. Therefore, it is extremely difficult to simulate the flow field over a period long enough to confirm the flow state of the FT synthesis process (e.g., 5 to 10 minutes).

[0005] Another possible approach is to treat the liquid containing bubbles as a mixed fluid and couple the governing equations for the mixed fluid with the governing equations for the powder. In this case, it is not possible to directly solve the bubble motion, making it difficult to accurately simulate the bubble motion.

[0006] The following Patent Document 1 discloses a method for analyzing with high accuracy a flow field in which bubbles are dispersed in a liquid phase in a gas-liquid mixture simulation. In this method, the analysis space is divided into multiple grids (cells), and the governing equations are discretized and solved on the divided computational grids. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Japanese Patent Application Laid-Open No. 2013-45423 Summary of the Invention [Problem to be solved by the invention]

[0008] In conventional methods of dividing the space into grids, it is necessary to generate a computational grid according to the shape of the reactor and the multiple components present within the reactor. The technology for generating grids is complicated and affects the quality of the simulation, making it difficult for anyone other than an experienced engineer to obtain high-quality simulation results. The object of the present invention is to provide a simulation device and program capable of analyzing the flow of a liquid containing bubbles without dividing the analysis space into grids. [Means for solving the problem]

[0009] According to one aspect of the present invention, A simulation device that analyzes the movement of a liquid containing a plurality of bubbles using a particle method, an input section for inputting simulation conditions; a processing unit that performs calculations based on the simulation conditions inputted to the input unit; Equipped with The processing unit a function of discretizing the liquid using a plurality of calculation particles based on input simulation conditions; A function of representing each of the bubbles as one calculation particle based on input simulation conditions; a function of calculating interactions between the liquid computational particles and the bubble computational particles based on input simulation conditions; A function of solving a governing equation of the discretized liquid taking into account the interaction; A function of solving a governing equation of the bubbles taking into account the interaction; A simulation device is provided having:

[0010] According to another aspect of the present invention, A program that causes a computer to perform a function of analyzing the movement of a liquid containing a plurality of bubbles using a particle method, A function to acquire simulation conditions, a function of discretizing the liquid using a plurality of calculation particles based on the acquired simulation conditions; A function of representing each of the bubbles as one calculation particle based on the acquired simulation conditions; a function of calculating an interaction between the liquid calculation particles and the bubble calculation particles based on the acquired simulation conditions; A function of solving a governing equation of the discretized liquid taking into account the interaction; A function of solving a governing equation of the bubbles taking into account the interaction; A program for realizing this on a computer is provided. [Effects of the Invention]

[0011] The liquid is discretized using multiple computational particles, and each bubble is represented by a single computational particle, so analysis can be performed without dividing the analysis space into grids. By calculating the interaction between the liquid computational particles and the bubble computational particles, the behavior of the liquid and the bubbles can be analyzed. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 1 is a schematic diagram of the simulation target. [Figure 2] FIG. 2 is a schematic diagram showing a state in which liquid calculation particles 11P, bubble calculation particles 12P, and powder calculation particles 13P are mixed together, for explaining a method of calculating the liquid volume fraction α. [Figure 3] FIG. 3 is a block diagram of the simulation device according to this embodiment. [Figure 4] FIG. 4 is a flowchart showing the procedure of a simulation executed by the simulation device according to an embodiment. [Figure 5] FIG. 5 is a flowchart showing a procedure executed by a simulation device according to another embodiment. [Figure 6] FIG. 6 is a schematic diagram of the simulation target. [Figure 7] FIG. 7 is a graph showing the distribution of the average axial velocity of the calculated particles of the powder at a height position of z=700 mm obtained by simulation, in comparison with the experimental results. [Figure 8] FIG. 8 is a graph showing the distribution of the average axial velocity of the calculated particles of the bubble at a height of z=700 mm obtained by simulation, compared with the experimental results. DETAILED DESCRIPTION OF THE INVENTION

[0013] A simulation device and a program according to an embodiment will be described with reference to FIGS.

[0014] 1 is a schematic diagram of a simulation target. A liquid 11 is contained in a container 10 having an opening at the top. A plurality of gas bubbles 12 and powder particles 13 are dispersed in the liquid 11. In this example, the liquid 11 is discretized using a plurality of computational particles, and each of the plurality of gas bubbles 12 is represented by one computational particle, and each of the plurality of powder particles 13 is represented by one computational particle.

[0015] The interactions between the computational particles of the liquid 11, the computational particles of the bubbles 12, and the computational particles of the powder 13 are calculated, and a numerical analysis method is applied to each computational particle to perform a simulation. The SPH (Smoothed Particle Hydrodynamics) method is applied to the numerical analysis of the computational particles of the liquid 11. Note that it is also possible to apply other particle methods such as the MPS (Moving Particle Simulation) method.

[0016] [Overview of particle methods] Next, we will briefly explain the general SPH (Smoothed Particle Hydrodynamics) method. The SPH method is a Lagrangian-type numerical calculation method that discretizes the continuum using a set of multiple computational particles and calculates the time evolution of the flow field.

[0017] In the SPH method, the mass m of a computational particle is distributed around its periphery by a kernel function W, and the density field is given as a superposition of the mass m and the density field. That is, the position x of the i-th computational particle is given as i Density ρ at i is expressed by the following formula:

number

[0018] For example, the following function can be used as the kernel function W. The following function is called the C2Wendland kernel.

number

[0019] h is the smoothing length, also called the kernel width. The kernel width h is equal to the diameter of an equivalent sphere obtained by replacing each of multiple calculation particles with a sphere of the same mass and physical density. In this specification, the kernel width h may also be referred to as the diameter of a calculation particle.

[0020] Any position x i The value of any scalar quantity A and vector quantity A in can be expressed by the following equation by superposing kernel functions:

number

[0021] The gradient of any scalar quantity A is expressed by the following equation using the superposition of the differential coefficients of the kernel function:

number

number

[0022] Here, ∇W(x ij , h) is the derivative of the kernel function, and when the C2Wendland kernel is used as the kernel function, it is expressed by the following equation:

number

[0023] The divergence for any vector quantity A can be expressed by the following equation, similar to equation (4).

number

[0024] The second derivative with respect to any scalar quantity A can be calculated, for example, using the following formula:

number

[0025] [Governing equations of liquid] The governing equations for a liquid discretized using the SPH method can be expressed, for example, as follows:

number

number

number

number

[0026] Equation (12) is an equation of state derived under the assumption that the fluid is weakly compressible, where c represents the virtual speed of sound and ρ0 represents the reference density. The value of the virtual speed of sound c can be set, for example, to about 10 times the representative velocity of the flow field. The reference density ρ0 can be set, for example, to the density of the fluid. α represents the volume fraction of the liquid.

[0027] A method for calculating the liquid volume fraction α will be described with reference to Fig. 2. Fig. 2 is a schematic diagram showing a state in which liquid calculation particles 11P, bubble calculation particles 12P, and powder calculation particles 13P are mixed together, for explaining the method for calculating the liquid volume fraction α. ​​The bubble calculation particles 12P and powder calculation particles 13P are distributed within the liquid calculation particles 11P.

[0028] The center position of the i-th calculation particle 11P representing the liquid is x i and its diameter is h i (kernel width). The center position of the bth calculation particle 12P, which represents the bubble, is xb and its diameter is d b The center position of the sth calculation particle 13P representing the powder is denoted as x s and its diameter is d s It is marked as follows.

[0029] The liquid volume fraction α is a quantity that represents the ratio of the liquid to the volume of the liquid calculation particle 11P, and can be calculated using, for example, the following formula.

number

number

[0030] [Governing equations of powder] The governing equation for powder can be written, for example, as follows:

number

number

number

[0031] The force Fs and torque Ts can be calculated using, for example, a spring-dashpot model, which is widely used in the DEM (Discrete Element Method) method and will not be described in detail here.

[0032] [Governing equation of bubbles] The motion of bubbles can be modeled using discrete elements, similar to that of powder. The governing equation for bubbles can be written as follows, for example:

number

number

[0033] [Calculation method for the force acting on a powder from a liquid] The forces that powder particles receive from a liquid can be divided into three: pressure gradient force, viscous force, and drag force, which can be written as follows:

number

number

[0034] The drag force can be calculated, for example, using the following formula:

number

number

[0035] Porosity ε at the position of the ath calculated particle of the powder a can be calculated using the following formula:

number

[0036] u in equation (22) a represents the velocity vector of the fluid at the position of the a-th calculated particle of the powder, and can be calculated, for example, by the following equation:

number

[0037] β in Equation (22) a is given by the following formula:

number

number

number

[0038] The force acting on the powder particles from the liquid is expressed as the force s aAs a reaction to this, it can be calculated using the following formula:

number

[0039] [Calculation method for the force acting on a bubble from a liquid] The force b acting on the calculated particle of the bubble from the liquid is, for example, the virtual mass force b VM , drag b D , lift b L , wall lubrication force b W and is given by the following formula:

number

[0040] Virtual mass force b VM is expressed by the following formula:

number

[0041] drag b D is expressed by the following formula:

number

number

number

number

[0042] Lift b L is expressed by the following formula:

number

number

number

[0043] Wall lubrication force b W is expressed by the following formula:

number

number

[0044] The force acting on the liquid particle from the bubble can be calculated using the following equation as a reaction to the force acting on the liquid particle of the bubble shown in equation (30).

number

[0045] [Forces acting on powder from bubbles and forces acting on bubbles from powder] The forces acting on the powder from the bubbles and on the bubbles from the powder can be calculated using a spring-dashpot model, as can the forces generated by the interactions between bubbles and between powder particles.

[0046] Next, the simulation device of this embodiment will be described. 3 is a block diagram of a simulation device according to this embodiment. The simulation device according to this embodiment includes an input unit 30, a processing unit 31, an output unit 32, and a storage unit 33. Simulation conditions and the like are input from the input unit 30 to the processing unit 31. Furthermore, various instructions (commands) and the like are input from the user to the input unit 30. The input unit 30 is composed of, for example, a communication device, a removable media reader, a keyboard, a pointing device, and the like.

[0047] The processing unit 31 executes a simulation using the particle method based on the input simulation conditions and commands. Furthermore, it outputs the simulation results to the output unit 32. The simulation results include information representing the state of particles in the particle system that is the simulation target, changes in the physical quantities of the particle system over time, etc. The processing unit 31 includes, for example, a central processing unit (CPU) of a computer. A program for causing the computer to execute the simulation using the particle method is stored in the storage unit 33. The output unit 32 includes a communication device, a removable media writing device, a display, etc.

[0048] Next, the procedure of the simulation executed by the simulation device according to this embodiment will be described with reference to Fig. 4. Fig. 4 is a flowchart showing the procedure of the simulation executed by the simulation device.

[0049] First, the processing unit 31 acquires simulation conditions input by the user (step SA1). The simulation conditions include information defining the liquid, bubbles, and powder to be simulated, boundary conditions, initial conditions, etc. The information defining the liquid, bubbles, and powder includes physical property values ​​such as density and viscosity of the liquid and gas, and physical property values ​​of the powder. The boundary conditions include information specifying the shape and size of the analysis space, a method for handling liquid calculation particles near the boundary, and a method for handling powder and bubble calculation particles near the boundary. The initial conditions include a method for specifying the initial distribution and initial physical property values ​​of liquid calculation particles, a method for specifying the initial distribution and initial physical property values ​​of powder and bubble calculation particles, and information for arranging multiple calculation particles in the analysis space.

[0050] Next, based on the input simulation conditions, multiple computational particles of liquid, bubbles, and powder are placed in the analysis space (step SA2). Note that if an initial condition in which bubbles do not exist is given, computational particles of liquid and powder are placed in the analysis space.

[0051] Next, the interaction between the liquid, bubbles, and powder particles is calculated (step SA3). Specifically, the force s that the powder receives from the liquid is calculated. a (Equation (20)), the force S acting on the liquid from the powder i (Equation (29)), the force b acting on the bubble from the liquid a (Equation (30)), the force Φ acting on the liquid from the bubbles i (Equation (41)), and calculate the force that the powder receives from the bubbles and the force that the bubbles receive from the powder. The force that the powder receives from the bubbles and the force that the bubbles receive from the powder can be calculated using, for example, a spring-dashpot model.

[0052] Next, the positions and physical quantities of the liquid computational particles are updated by applying a numerical analysis method to the liquid computational particles (step SA4). Specifically, the governing equations of the liquid expressed by equations (9) to (11) are solved.

[0053] Next, the positions and physical quantities of the calculated particles of the powder are updated by applying a numerical analysis method to the calculated particles of the powder (step SA5). Specifically, the governing equations of the powder expressed by equations (15) to (17) are solved.

[0054] Next, the positions and physical quantities of the computational particles of the bubble are updated by applying a numerical analysis method to the computational particles of the bubble (step SA6). Specifically, the governing equations of the bubble expressed by equations (18) and (19) are solved.

[0055] Next, bubbles are introduced into the analysis space based on the input simulation conditions (step SA7). This corresponds to, for example, the process of introducing bubbles into a slurry bubble column reactor. The procedures from step SA3 to step SA7 are repeated until the calculation termination condition is met. The calculation termination condition is given as a simulation condition.

[0056] When the calculation end condition is met, the calculation result is output (step SA9).

[0057] Next, the excellent effects of this embodiment will be described. In this embodiment, the flow of an object to be analyzed, which is a mixture of liquid, bubbles, and powder, can be analyzed without dividing the analysis space into grids, so the user does not need to have the skill to divide the grid appropriately.

[0058] In the above embodiment, a mixture of liquid, bubbles, and powder was analyzed, but it is also possible to analyze a mixture of liquid and bubbles without powder.

[0059] Next, a simulation device and a program according to another embodiment will be described with reference to Figures 5 to 8. Below, a description of the configuration common to the embodiment described with reference to Figures 1 to 4 will be omitted.

[0060] Fig. 5 is a flowchart showing the procedure executed by the simulation device according to this embodiment. The procedure from step SB1 to step SB3 is the same as the procedure from step SA1 to SA3 shown in Fig. 4. In the embodiment shown in Fig. 4, in step SA4 to step SA6, the numerical analysis method is applied to the calculation particles of the liquid, powder, and bubbles in order. In other words, the time step widths for updating the positions and physical quantities of the calculation particles of the liquid, powder, and bubbles are all the same.

[0061] In contrast, in the embodiment shown in Figure 5, in steps SB4 and SB5, a numerical analysis method is applied to the calculation particles of the powder and bubbles, and the positions and physical quantities of the calculation particles are updated. The positions and physical quantities of the calculation particles of the powder and bubbles are updated a specified number of times (step SB6). Note that each time the positions and physical quantities of the calculation particles of the powder and bubbles are updated, the interactions between the calculation particles of the liquid, powder, and bubbles are calculated (step SB3). At this time, the positions and physical quantities of the calculation particles of the liquid remain unchanged.

[0062] After updating the positions and physical quantities of the powder and bubble calculation particles a specified number of times, a numerical analysis method is applied to the liquid calculation particles to update the positions and physical quantities of the liquid calculation particles (step SB7). Then, based on the simulation conditions, the bubble calculation particles are caused to flow into the analysis space (step SB8). The procedure from step SB3 to step SB8 is repeated until the calculation termination condition is met (step SB9). When the calculation termination condition is met, the calculation results are output (step SB10).

[0063] Next, the results of an actual simulation performed using the simulation device according to this embodiment will be described.

[0064] Figure 6 is a schematic diagram of the object to be simulated. A cylindrical container 10 with a diameter of 152 mm is filled with a liquid 11 to a height of 1000 mm. A plurality of powders 13 are dispersed in the liquid 11. A sparger 15 with a diameter of 30 mm and a height of 50 mm is installed at the bottom of the container 10, and air bubbles 12 are injected into the liquid 11 from the sparger 15. A cylindrical coordinate system is defined with the origin at the top end of the sparger 15 in the center of the container 10. The radial direction is labeled r, and the height direction is labeled z.

[0065] As an initial state, the liquid 11 is in a stationary state. The density of the liquid 11 is 1048.5 kg / m 3 The viscosity coefficient is 0.985×10 -3 The powder 13 had a diameter of 3 mm and a density of 1050 kg / m 3 20,000 calculated particles of powder were uniformly dispersed in the liquid 11. Air bubbles 12 with an average diameter of 1.5 mm and a standard deviation of 0.3 mm were introduced from the sparger 15 at a flow rate of 0.8 L / min. The density of the air bubbles 12 was 1.204 kg / m 3 The viscosity coefficient is 1.85×10 -5 The value was set as Pa·s.

[0066] The kernel width of the liquid calculation particle is 5×2 1 / 2 mm, the virtual speed of sound is 32.1 m / s, and the time step size is 1.56 × 10 -4 s. The time step width for updating the positions and physical quantities of the calculation particles of the powder and bubbles was set to 1 / 5 of the time step width for updating the positions and physical quantities of the calculation particles of the liquid. In other words, the number of times specified for step SB6 in Figure 5 was set to 5. The gravitational acceleration g was set to 9.81 m / s 2 It was decided.

[0067] The simulation was performed from 0 seconds in the initial state to 400 seconds. The average values ​​of each physical quantity were calculated from 100 seconds to 400 seconds.

[0068] Figures 7 and 8 are graphs showing the distribution of the average axial velocity of calculated particles of powder and bubbles at a height of z = 700 mm obtained by simulation, respectively, compared with the experimental results. These experimental results are disclosed in Gan, ZW, 2013, "Holdup and velocity profiles of monosized spherical solids in a three-phase bubble column," Chemical Engineering Science 94, 291-301.

[0069] The horizontal axis of the graphs shown in Figures 7 and 8 represents the ratio of the radial position r to the radius R of the cylindrical container 10 (Figure 6), and the vertical axis represents the axial velocity in units of m / s. In the graphs, square symbols with solid lines represent simulation results, and circle symbols represent experimental results. As shown in Figures 7 and 8, it can be seen that the simulation results are in good agreement with the experimental results. This comparison confirms that the simulation device according to this embodiment can simulate the flow of a liquid containing bubbles and powder with high accuracy.

[0070] Next, the effect of making the time step size for the powder and bubbles smaller than the time step size for the liquid, as shown in Figure 5, will be described. Due to constraints on calculation conditions, the time step size for the powder or bubbles may need to be made smaller than the time step size for the liquid. For example, matching the time step size for the powder or bubbles to the time step size for the liquid may result in a calculation failure. Conversely, matching the time step size for the liquid to the time step size for the powder or bubbles increases the amount of calculation. As shown in Figure 5, by making the time step size for the powder and bubbles smaller than the time step size for the liquid, it is possible to avoid calculation failure and suppress an increase in the amount of calculation.

[0071] Each embodiment is merely an example, and it goes without saying that partial substitution or combination of the configurations shown in different embodiments is possible. Similar effects resulting from similar configurations of multiple embodiments will not be mentioned sequentially for each embodiment. Furthermore, the present invention is not limited to the above-described embodiments. For example, it will be obvious to those skilled in the art that various modifications, improvements, combinations, etc. are possible. [Explanation of symbols]

[0072] 10 containers 11 liquid 11P Liquid Computational Particles 12 Bubbles 12P Calculation particle of bubbles 13 Powder 13P Calculation particle size of powder 15 Sparger 30 Input section 31 Processing section 32 Output section 33 Storage section

Claims

1. A simulation device that analyzes the movement of a liquid containing a plurality of bubbles using a particle method, an input section for inputting simulation conditions; a processing unit that performs calculations based on the simulation conditions inputted to the input unit; Equipped with The processing unit a function of discretizing the liquid using a plurality of calculation particles based on input simulation conditions; A function of representing each of the bubbles as one calculation particle based on input simulation conditions; a function of calculating interactions between the liquid computational particles and the bubble computational particles based on input simulation conditions; A function of solving a governing equation of the discretized liquid taking into account the interaction; A function of solving a governing equation of the bubbles taking into account the interaction; A simulation device having:

2. The liquid contains a plurality of powders, The processing unit A function of representing each of the powders as one calculation particle based on input simulation conditions; In the function of calculating the interaction, the interaction between the calculation particle of the liquid, the calculation particle of the bubble, and the calculation particle of the powder is calculated; The simulation device according to claim 1 , further comprising a function of solving a governing equation of the powder taking into account the interaction.

3. A program that causes a computer to perform a function of analyzing the movement of a liquid containing a plurality of bubbles using a particle method, A function to acquire simulation conditions, a function of discretizing the liquid using a plurality of calculation particles based on the acquired simulation conditions; A function of representing each of the bubbles as one calculation particle based on the acquired simulation conditions; a function of calculating an interaction between the liquid calculation particles and the bubble calculation particles based on the acquired simulation conditions; A function of solving a governing equation of the discretized liquid taking into account the interaction; A function of solving a governing equation of the bubbles taking into account the interaction; A program that makes the computer realize this.

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