Liquid ammonia spraying numerical simulation method and system considering flash boiling

Abstract

The invention provides a liquid ammonia spraying numerical simulation method and system considering flash boiling, and relates to the technical field of liquid ammonia numerical simulation, the simulation process is divided into a plurality of time steps, each time step executes the following operations, and the current spraying field state is finally output: obtaining the initial spraying field state of the current time step; an aerodynamic liquid drop breaking calculation method is adopted, liquid drops meeting the dynamic breaking condition are broken into a plurality of small liquid drops, and the current spraying field state is updated; the liquid drops meeting the flash boiling breaking condition are broken into a plurality of small liquid drops by adopting an internal bubble development method in the liquid drop flash boiling process, and the current spraying field state is updated; on the basis of an aerodynamic breaking mechanism, simulation of the development process of bubbles in liquid drops generated due to flash boiling in the spraying process is added, so that numerical simulation of liquid ammonia is perfected, the breaking mechanism of liquid ammonia spraying is fully researched, and the combustion characteristics and performance of an engine are evaluated.

Description

Technical Field

[0001] The invention belongs to the technical field of liquid ammonia numerical simulation, and in particular relates to a liquid ammonia spray numerical simulation method and system taking flash boiling into consideration. Background Art

[0002] With the rapid development of the engine industry, zero-carbon fuels have become a new focus of attention in the engine industry. Among them, hydrogen fuel and ammonia fuel, as the primary zero-carbon fuels, have good application prospects; ammonia fuel, as a renewable zero-carbon fuel, has certain advantages in storage, transportation, emissions, etc., and is easy to use in automobile engines; although studies have shown that ammonia can be used as a zero-carbon fuel to replace traditional petroleum fuels to reduce carbon emissions, in actual engine applications, due to ammonia's disadvantages such as high ignition energy and low laminar flame speed, it is difficult to use it alone as a fuel in the engine. Therefore, existing technologies tend to mix ammonia with other carbon-containing fuels (such as diesel). For engines with ammonia direct injection, certain means can be used to enhance its atomization effect.

[0003] Numerical simulation of liquid ammonia is an important means to evaluate combustion characteristics and performance, and can provide a reference for the practical application of certain settings. In the numerical simulation process, the application of fluid mechanics models will have a great impact on the reliability of the simulation results. Liquid ammonia is a fuel that is more likely to be in an overheated state under the working environment of the engine. Its fragmentation and evaporation during the spray process are very different from those of traditional fuels. However, there are currently few algorithmic processes for liquid ammonia spray that can be applied to numerical simulation software.

[0004] At present, relevant research generally believes that there are two competing breakup mechanisms in the breakup of superheated spray: the breakup caused by aerodynamics and the breakup caused by flash boiling. The former can be characterized as the breakup caused by the instability of the droplets themselves, while the latter is the breakup caused by the explosion of bubbles after flash boiling occurs in the droplets.

[0005] Compared with other liquid fuels, liquid ammonia has a lower saturation pressure under the same conditions, so its flash boiling degree is more intense. In terms of traditional fragmentation, there are relatively mature models that can be well applied in numerical simulations (such as KH-RT model, TAB model, LISA model, etc.) to describe the aerodynamic fragmentation mechanism. However, in terms of flash boiling fragmentation, the existing technology lacks a description of this fragmentation mechanism, resulting in inaccurate numerical simulation of liquid ammonia. Summary of the invention

[0006] In order to overcome the deficiencies of the above-mentioned prior art, the present invention provides a method and system for numerical simulation of liquid ammonia spray taking into account flash boiling. On the basis of the aerodynamic breakup mechanism, the method and system increase the simulation of the development process of bubbles inside droplets generated by flash boiling during the spray process, thereby improving the numerical simulation of liquid ammonia, helping to fully study the breakup mechanism of liquid ammonia spray and evaluate the combustion characteristics and performance of the engine.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] A first aspect of the present invention provides a liquid ammonia spray numerical simulation method taking into account flash boiling.

[0009] A numerical simulation method for liquid ammonia spray considering flash boiling is proposed. The simulation process is divided into multiple time steps. Each time step performs the following operations and finally outputs the current spray field state:

[0010] Get the initial spray field state of the current time step, including the number of droplets, droplet diameter and droplet temperature;

[0011] Based on the initial spray field state, the aerodynamic droplet breakup calculation method is used to break the droplets that meet the dynamic breakup conditions into several small droplets, and the current spray field state is updated;

[0012] Based on the current spray field state, the internal bubble development method of the droplet flash boiling process is adopted to break the droplets that meet the flash boiling breakup conditions into several small droplets, and the current spray field state is updated;

[0013] Among them, the method for the development of bubbles inside the droplet flash boiling process is to quantify the number of bubble nucleations inside the droplet, combine it with the bubble growth model, predict the droplet porosity, and judge whether the flash boiling breakup conditions are met based on the porosity.

[0014] Furthermore, the dynamic breakup condition is that the instability wavelength of the droplets is greater than the droplet diameter.

[0015] Furthermore, the aerodynamic droplet breakup calculation method takes all droplets as calculation objects, and the specific steps are as follows:

[0016] Calculate the Reynolds number of the droplet in the flow field based on the droplet diameter and droplet temperature;

[0017] Based on the Reynolds number, calculate the drag coefficient;

[0018] Based on the drag coefficient, the acceleration is calculated, and then the instability wavelength is calculated;

[0019] The droplets that meet the flash boiling breakup conditions are aerodynamically broken and randomly broken into several small droplets with the same radius.

[0020] Furthermore, the flash boiling breakup condition is that the current void fraction of the droplets is greater than a threshold value.

[0021] Furthermore, the method for developing internal bubbles in the droplet flash boiling process takes all droplets as calculation objects, and the specific steps are as follows:

[0022] Based on the droplet temperature, the number of internal bubble nuclei in the droplet flash boiling process is calculated;

[0023] The radius change rate of each bubble nucleated is calculated through the bubble growth model, so that the volume of each bubble is calculated in real time;

[0024] According to the volume of the bubble and the volume of the droplet, the current void fraction of the droplet is calculated;

[0025] The droplets that meet the flash boiling breakup conditions undergo bubble explosion and break into several small droplets.

[0026] Furthermore, the bubble growth model adopts the Rayleigh-Plesset equation solved from the sphere momentum equation, and uses a numerical solution method to iteratively calculate the radius change rate of the bubble.

[0027] Furthermore, during the iterative calculation process, the current void fraction is used to correct the physical property parameters in the Rayleigh-Plesset equation.

[0028] A second aspect of the present invention provides a liquid ammonia spray numerical simulation system taking flash boiling into consideration.

[0029] A liquid ammonia spray numerical simulation system considering flash boiling divides the simulation process into multiple time steps. Each time step performs the following operations and finally outputs the current spray field state, including a state acquisition module, a first crushing module and a second crushing module:

[0030] The state acquisition module is configured to: obtain the initial spray field state of the current time step, including the number of droplets, droplet diameter and droplet temperature;

[0031] The first breakup module is configured to: based on the initial spray field state, use an aerodynamic droplet breakup calculation method to break the droplets that meet the dynamic breakup conditions into a plurality of small droplets, and update the current spray field state;

[0032] The second fragmentation module is configured to: based on the current spray field state, adopt the internal bubble development method of the droplet flash boiling process to fragment the droplets that meet the flash boiling fragmentation conditions into a plurality of small droplets, and update the current spray field state;

[0033] Among them, the method for the development of bubbles inside the droplet flash boiling process is to quantify the number of bubble nucleations inside the droplet, combine it with the bubble growth model, predict the droplet porosity, and judge whether the flash boiling breakup conditions are met based on the porosity.

[0034] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in a method for numerical simulation of liquid ammonia spray taking into account flash boiling as described in the first aspect of the present invention.

[0035] The fourth aspect of the present invention provides an electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in a method for numerical simulation of liquid ammonia spray taking into account flash boiling as described in the first aspect of the present invention are implemented.

[0036] One or more of the above technical solutions have the following beneficial effects:

[0037] 1. On the basis of the aerodynamic breakup mechanism, the simulation of the development process of bubbles inside the droplets generated by flash boiling during the spray process is added. The high-intensity flash boiling of ammonia during spraying is taken into account, which can better simulate the phenomena in the flash boiling process, thereby improving the numerical simulation of liquid ammonia, which is helpful to fully study the breakup mechanism of liquid ammonia spray and evaluate the combustion characteristics and performance of the engine.

[0038] 2. Based on the existing single bubble hypothesis, the porosity and breakup timing are predicted more accurately by quantifying the number of bubble nuclei, especially in the area near the nozzle at the beginning of spraying where flash boiling is more intense.

[0039] 3. By introducing the droplet void ratio, the droplet physical properties in the process are corrected, which improves the accuracy of describing the bubble radius growth.

[0040] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0042] Figure 1 This is a flow chart of the method of the first embodiment.

[0043] Figure 2 This is a diagram of the crushing process based on flash boiling in the first embodiment. DETAILED DESCRIPTION

[0044] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0045] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0046] Embodiment 1

[0047] In one embodiment of the present disclosure, a method for numerical simulation of liquid ammonia spray considering flash boiling is provided, wherein the simulation process is divided into multiple time steps, and the following operations are performed in each time step, and finally the current spray field state is outputted:

[0048] Step S1: Obtain the initial spray field state at the current time step, including the number of droplets, droplet diameter, and droplet temperature.

[0049] Step S2: Based on the initial spray field state, an aerodynamic droplet breakup calculation method is used to break the droplets that meet the dynamic breakup conditions into a number of small droplets, and the current spray field state is updated.

[0050] Furthermore, the dynamic breakup condition is that the instability wavelength of the droplets is greater than the droplet diameter.

[0051] Furthermore, the aerodynamic droplet breakup calculation method takes all droplets as calculation objects, and the specific steps are as follows:

[0052] Calculate the Reynolds number of the droplet in the flow field based on the droplet diameter and droplet temperature;

[0053] Based on the Reynolds number, calculate the drag coefficient;

[0054] Based on the drag coefficient, the acceleration is calculated, and then the instability wavelength is calculated;

[0055] The droplets that meet the flash boiling breakup conditions are aerodynamically broken and randomly broken into several small droplets with the same radius.

[0056] Step S3: Based on the current spray field state, the droplets meeting the flash boiling breakup conditions are broken into several small droplets using the internal bubble development method of the droplet flash boiling process, and the current spray field state is updated.

[0057] Among them, the method for the development of bubbles inside the droplet flash boiling process is to quantify the number of bubble nucleations inside the droplet, combine it with the bubble growth model, predict the droplet porosity, and judge whether the flash boiling breakup conditions are met based on the porosity.

[0058] Furthermore, the flash boiling breakup condition is that the current void fraction of the droplets is greater than a threshold value.

[0059] Furthermore, the method for developing internal bubbles in the droplet flash boiling process takes all droplets as calculation objects, and the specific steps are as follows:

[0060] Based on the droplet temperature, the number of internal bubble nuclei in the droplet flash boiling process is calculated;

[0061] The radius change rate of each bubble nucleated is calculated through the bubble growth model, so that the volume of each bubble is calculated in real time;

[0062] According to the volume of the bubble and the volume of the droplet, the current void fraction of the droplet is calculated;

[0063] The droplets that meet the flash boiling breakup conditions undergo bubble explosion and break into several small droplets.

[0064] Furthermore, the bubble growth model adopts the Rayleigh-Plesset equation solved from the sphere momentum equation, and uses a numerical solution method to iteratively calculate the radius change rate of the bubble.

[0065] Furthermore, during the iterative calculation process, the current void fraction is used to correct the physical property parameters in the Rayleigh-Plesset equation.

[0066] The following is a detailed description of the implementation process of a numerical simulation method for liquid ammonia spray considering flash boiling in this embodiment.

[0067] The simulation process is divided into multiple time steps, with the time step dt as a simulation cycle, to simulate the breakup caused by aerodynamics and the breakup caused by flash boiling. Considering that the flash boiling breakup has a smaller time scale, the time step dt is divided into several parts, which are counted as the time scale dt of the flash boiling breakup. f ; In a simulation cycle dt, the current simulation time is t f , 0<=t f ≤dt.

[0068] Based on the above time setting, a specific implementation example is provided, such as Figure 1 As shown, specifically:

[0069] 1. Get the spray field state at the current time step, including the current number of droplets and the diameter R and temperature T of all droplets.

[0070] The following steps will use physical parameters such as droplet density, kinematic viscosity, and surface tension. Considering that the temperature changes dramatically during the spraying process, the physical properties of the droplets will change with the temperature. These physical parameter values ​​are retrieved from the physical property table based on the temperature; among them, the temperature is calculated in real time based on fluid mechanics.

[0071] 2. Perform calculations for aerodynamic fragmentation

[0072] Aerodynamic calculations can be considered to be caused by the resistance of the droplets. Taking all droplets as the calculation object, the steps of aerodynamic fragmentation are as follows:

[0073] (1) Based on the droplet diameter and droplet temperature, calculate the Reynolds number Re of the droplet in the flow field:

[0074]

[0075] Among them, d is the droplet diameter, ρ is the droplet density, μ represents the kinematic viscosity of the droplet, and u is the movement speed of the droplet, which is calculated in real time based on fluid mechanics.

[0076] (2) Calculate the drag coefficient C based on the Reynolds number Re d :

[0077]

[0078] (3) Based on the drag coefficient C d , calculate the acceleration a, and then calculate the instability wavelength ω:

[0079]

[0080] Where σ represents the surface tension of the droplet, ρ g and ρ l Represent the density of gas phase and liquid phase respectively, a is the acceleration caused by aerodynamics, and the calculation formula is:

[0081]

[0082] Among them, C d is the resistance coefficient, ρ g and ρ l They represent the density of the gas phase and the liquid phase respectively, which are pre-set constants; u is the movement speed of the droplet, which is calculated in real time based on fluid mechanics; and r represents the radius of the droplet.

[0083] (4) When the instability wavelength ω is larger than the droplet diameter d, the droplet undergoes aerodynamic breakup and randomly breaks into 1-10 small droplets with the same radius; otherwise, return to step (1), considering that the droplet diameter will decrease with evaporation in the spray field, which will cause the Reynolds number Re to increase, and then cause the drag coefficient Cd to decrease, further causing the acceleration a to decrease, so the instability wavelength ω is an increasing process. Therefore, return to step (1) to recalculate the Reynolds number, and repeat this cycle until breakup.

[0084] 3. Perform calculations for flash boiling and breaking

[0085] The fragmentation caused by flash boiling is the fragmentation caused by the explosion of bubbles after flash boiling occurs in the droplets. The fragmentation process is as follows: Figure 2 As shown in the figure, a number of white bubbles are generated inside the blue droplet. As the bubbles grow, their volume gradually increases until they explode and the droplet breaks into multiple small droplets. The specific calculation process is:

[0086] (1) Taking each droplet as an object, the number of internal bubble nuclei ND in the droplet flash boiling process is calculated based on the droplet temperature:

[0087]

[0088] Here, Δθ is the superheat, which is defined as the difference between the droplet temperature and the saturation temperature.

[0089] One of the key steps in the development of bubbles in a droplet is nucleation, that is, the generation of bubbles. Assume that a number of initial bubbles with a radius of initial radius Rc are generated in the current time step, where the calculation formula for the initial radius is:

[0090]

[0091] Among them, P ∞ Represents the ambient pressure at a specific temperature, P s represents the saturation pressure at a specific temperature, and σ represents the surface tension of the droplet.

[0092] (2) If the current simulation time t f When dt is exceeded, the calculation ends and the next time step begins.

[0093] (3) If the current simulation time t f If dt is not exceeded, the dt is calculated by the Rayleigh-Plesset equation. f The radius of the bubbles within the time step, thus calculating the volume of each bubble.

[0094] Specifically, each flash boiling breakup time scale dt fThe droplet in the flow field traverses once, and the bubble growth model is applied. The Rayleigh-Plesset equation (RPE) obtained by solving the sphere momentum equation is used to describe the growth of the bubble radius R(t). The change law of the bubble radius with time is obtained, and the physical parameters appearing in the equation are corrected by considering the void fraction. The numerical solution is used to iteratively calculate each step length dt f The rate of change of bubble radius, Rayleigh-Plesset equation (RPE) is as follows:

[0095]

[0096] Among them, P v (T) and P ∞ They represent the saturation pressure and ambient pressure at a specific temperature, respectively; R(t) is the bubble radius at time t; ρ represents the density of the droplet-bubble system; and σ represents the surface tension of the droplet.

[0097] In this step, the physical property parameters are corrected considering the physical property effect brought by the porosity. Taking density as an example, the correction method is as follows:

[0098]

[0099] in, represents the void ratio, ρ g and ρ l are the densities of the gas phase and the liquid phase, respectively.

[0100] Taking viscosity as an example, the correction method is:

[0101]

[0102] in, represents the void ratio, v g With v l are the viscosities of the gas phase and the liquid phase, respectively.

[0103] (4) Calculation of void ratio The formula is:

[0104]

[0105] Among them, V b is the volume of the bubble, V l is the volume of the droplet, and the volumes of the bubbles and droplets are calculated using the regular sphere approximation.

[0106] (5) If the current void ratio exceeds the threshold, the bubble explodes and the droplet breaks, randomly breaking into 1-5 droplets with the same radius. The calculation ends and the number of droplets and the droplet radius R are updated. In this embodiment, the threshold is set to 0.55.

[0107] (6) If the current porosity does not exceed the threshold, enter the next flash boiling and crushing time step dt f , return to step (3).

[0108] Embodiment 2

[0109] In one embodiment of the present disclosure, a liquid ammonia spray numerical simulation system considering flash boiling is provided, wherein the simulation process is divided into multiple time steps, and the following operations are performed in each time step, and finally the current spray field state is output, including a state acquisition module, a first crushing module, and a second crushing module:

[0110] The state acquisition module is configured to: obtain the initial spray field state of the current time step, including the number of droplets, droplet diameter and droplet temperature;

[0111] The first breakup module is configured to: based on the initial spray field state, use an aerodynamic droplet breakup calculation method to break the droplets that meet the dynamic breakup conditions into a plurality of small droplets, and update the current spray field state;

[0112] The second fragmentation module is configured to: based on the current spray field state, adopt the internal bubble development method of the droplet flash boiling process to fragment the droplets that meet the flash boiling fragmentation conditions into a plurality of small droplets, and update the current spray field state;

[0113] Among them, the method for the development of bubbles inside the droplet flash boiling process is to quantify the number of bubble nucleations inside the droplet, combine it with the bubble growth model, predict the droplet porosity, and judge whether the flash boiling breakup conditions are met based on the porosity.

[0114] Embodiment 3

[0115] The purpose of this embodiment is to provide a computer-readable storage medium.

[0116] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in a method for numerically simulating liquid ammonia spray taking into account flash boiling as described in the first embodiment of the present disclosure.

[0117] Embodiment 4

[0118] The purpose of this embodiment is to provide an electronic device.

[0119] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in a numerical simulation method for liquid ammonia spray considering flash boiling as described in Embodiment 1 of the present disclosure are implemented.

[0120] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for numerical simulation of liquid ammonia spray considering flash boiling, characterized in that: The simulation process is divided into multiple time steps. The following operations are performed in each time step, and the current spray field state is finally output: Get the initial spray field state of the current time step, including the number of droplets, droplet diameter and droplet temperature; Based on the initial spray field state, the aerodynamic droplet breakup calculation method is used to break the droplets that meet the dynamic breakup conditions into several small droplets, and the current spray field state is updated; Based on the current spray field state, the internal bubble development method of the droplet flash boiling process is adopted to break the droplets that meet the flash boiling breakup conditions into several small droplets, and the current spray field state is updated; Among them, the method for the development of bubbles inside the droplet flash boiling process is to quantify the number of bubble nucleations inside the droplet, combine it with the bubble growth model, predict the droplet porosity, and judge whether the flash boiling breakup conditions are met based on the porosity.

2. A method for numerical simulation of liquid ammonia spray considering flash boiling as claimed in claim 1, characterized in that: The dynamic breakup condition is that the instability wavelength of the droplets is greater than the droplet diameter.

3. A method for numerical simulation of liquid ammonia spray considering flash boiling as claimed in claim 1, characterized in that: The aerodynamic droplet breakup calculation method takes all droplets as calculation objects, and the specific steps are as follows: Calculate the Reynolds number of the droplet in the flow field based on the droplet diameter and droplet temperature; Based on the Reynolds number, calculate the drag coefficient; Based on the drag coefficient, the acceleration is calculated, and then the instability wavelength is calculated; The droplets that meet the flash boiling breakup conditions are aerodynamically broken and randomly broken into several small droplets with the same radius.

4. The method for numerical simulation of liquid ammonia spray considering flash boiling according to claim 1, characterized in that: The flash boiling breakup condition is that the current void fraction of the droplets is greater than a threshold value.

5. The method for numerical simulation of liquid ammonia spray considering flash boiling according to claim 1, characterized in that: The method for developing internal bubbles in the droplet flash boiling process takes all droplets as calculation objects, and the specific steps are as follows: Based on the droplet temperature, the number of internal bubble nuclei in the droplet flash boiling process is calculated; The radius change rate of each bubble nucleated is calculated through the bubble growth model, so that the volume of each bubble is calculated in real time; According to the volume of the bubble and the volume of the droplet, the current void fraction of the droplet is calculated; The droplets that meet the flash boiling breakup conditions undergo bubble explosion and break into several small droplets.

6. A method for numerical simulation of liquid ammonia spray considering flash boiling as claimed in claim 5, characterized in that: The bubble growth model adopts the Rayleigh-Plesset equation solved from the sphere momentum equation and uses a numerical solution method to iteratively calculate the radius change rate of the bubble.

7. A method for numerical simulation of liquid ammonia spray considering flash boiling as claimed in claim 6, characterized in that: During the iterative calculation process, the current void fraction is used to correct the physical property parameters in the Rayleigh-Plesset equation.

8. A liquid ammonia spray numerical simulation system considering flash boiling, characterized in that: The simulation process is divided into multiple time steps. Each time step performs the following operations and finally outputs the current spray field state, including the state acquisition module, the first crushing module and the second crushing module: The state acquisition module is configured to: obtain the initial spray field state of the current time step, including the number of droplets, droplet diameter and droplet temperature; The first breakup module is configured to: based on the initial spray field state, use an aerodynamic droplet breakup calculation method to break the droplets that meet the dynamic breakup conditions into a plurality of small droplets, and update the current spray field state; The second breaking module is configured to: based on the current spray field state, break the droplets that meet the flash boiling breaking conditions into a plurality of small droplets by using the internal bubble development method of the droplet flash boiling process, and update the current spray field state; Among them, the method for the development of bubbles inside the droplet flash boiling process is to quantify the number of bubble nucleations inside the droplet, combine it with the bubble growth model, predict the droplet porosity, and judge whether the flash boiling breakup conditions are met based on the porosity.

9. An electronic device, comprising: a memory for non-transitory storage of computer readable instructions; a processor for executing the computer-readable instructions; Wherein, when the computer-readable instructions are executed by the processor, the method according to any one of claims 1 to 7 is executed.

10. A storage medium, characterized in that: The computer-readable instructions are non-transitorily stored, wherein when the computer-readable instructions are executed by a computer, the method of any one of claims 1 to 7 is performed.

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