High-density-ratio bubble rising behavior numerical calculation method based on LSMPS

Abstract

The invention discloses a high-density-ratio bubble rising behavior numerical calculation method based on LSMPS. The method is specifically implemented according to the following steps that 1, a two-dimensional axisymmetric single bubble rising calculation model is established based on a meshless moving particle semi-implicit method; 2, calculating the temporary speed of the particles; 3, calculating the pressure of gas particles and interface node particles; step 4, calculating pressure jump of interface node particles; 5, calculating the pressure of the liquid particles; step 6, correcting the speed of the particles; 7, updating the positions of the particles and the interface node particles; and step 8, analog calculation and result export. According to the method, an axial symmetry model is adopted, rising behaviors of air bubbles in water and nitrogen bubbles in lead-bismuth alloy are numerically simulated, evolution of a bubble interface can be accurately captured, the total rising speed of the bubbles and the change rule of the speeds of the tops and the bottoms of the bubbles are analyzed, and the evolution process of the mass center height, the size, the surface area and the aspect ratio of the bubbles along with time is obtained.

Description

Technical Field

[0001] This invention belongs to the field of fluid mechanics technology, specifically relating to a numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS. Background Technology

[0002] Rising bubble motion is widespread in various engineering fields, such as marine engineering, chemical engineering, energy engineering, and environmental engineering. High density ratio phenomena in gas-liquid two-phase flows often occur during bubble ascent. For example, rising air bubbles in water and rising inert gas bubbles in liquid metal systems have gas-liquid density ratios approaching a thousand or even ten thousand times. Under these conditions, due to the discontinuity of fluid properties, abrupt jumps / drops in density and pressure typically occur at the interface. Due to the combined effects of buoyancy, inertial forces, viscous forces, and surface tension, bubble dynamics become highly nonlinear, making the interface prone to instability and severe deformation. Therefore, in-depth research into the motion laws of high-density-ratio bubbles is of great significance for revealing the fundamental mechanisms of multiphase flow. Summary of the Invention

[0003] The purpose of this invention is to provide a numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS, which can accurately capture the evolution of the bubble interface.

[0004] The technical solution adopted in this invention is a numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS, which is implemented according to the following steps: Step 1. Establish a two-dimensional axisymmetric single-bubble ascent computational model based on the meshless moving particle semi-implicit method; Step 2. Calculate the temporary velocity of the particle; Step 3. Calculate the pressure of gas particles and interface node particles; Step 4. Calculate the pressure jump of particles at the interface nodes; Step 5. Calculate the pressure of the liquid particles; Step 6. Correct the particle velocity; Step 7. Update the positions of particles and interface node particles; Step 8. Simulation calculation and result export.

[0005] The invention is further characterized by: In step 1, during the initial arrangement of gas and liquid phase particles, the particle arrangement near the phase interface adopts multi-resolution technology, that is, different regions use different particle spacing and different resolutions. The closer to the phase interface, the smaller the particle spacing and the denser the particle distribution. The farther away from the phase interface, the larger the particle spacing and the sparser the particle distribution.

[0006] In step 2, the temporary velocity is calculated explicitly, and a particle velocity correction term and an artificial viscosity term are added: (1) In the formula, It is the time step. It's a temporary speed. Convection term, velocity correction It is the particle's velocity. This is the artificial viscosity item, indicated by the superscript. Indicates the calculation steps, subscript i Represents particles i .

[0007] In step 3, for gas particles and interface nodes, consider the following pressure equation: For gas particles: (2) For UI nodes: (3).

[0008] In step 4, a pressure jump occurs at the interface node between the gas and liquid phases. The formula for calculating the pressure jump is: (4) in, It is a gas interface node i Pressure It is a liquid interface node i Pressure, superscript and All of these represent calculation steps.

[0009] In step 5, the pressure jump calculated in step 4 is used as the Dirichlet boundary condition for the calculation of liquid phase particle pressure. The liquid phase particle pressure is calculated using the following formula: (5).

[0010] The particle velocity correction calculation formula in step 6 is as follows: (6).

[0011] The formula for calculating the positions of updated particles and interface node particles in step 7 is as follows: (7).

[0012] The beneficial effects of this invention are: This invention presents a numerical calculation method for the rising behavior of high-density ratio bubbles based on LSMPS. Employing a two-dimensional axisymmetric model, it studies the rising behavior of bubbles under high density ratios and can simulate bubble motion in air-water and nitrogen-lead-bismuth alloy systems, as well as other gas-liquid two-phase flows with high density ratios. The numerical algorithm accurately captures the evolution of the bubble interface, and the calculated data can be used to analyze bubble rising characteristics, including total rising velocity, bubble top velocity, bubble bottom velocity, centroid height, bubble volume, surface area, and aspect ratio. This invention helps to elucidate the characteristics of bubble rising behavior under high density ratios and verifies that the meshless LSMPS method can effectively simulate gas-liquid two-phase flows. Attached Figure Description

[0013] Figure 1 This is a flowchart of the numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to the present invention; Figure 2a This invention relates to a two-dimensional axisymmetric model and boundary condition diagram of single bubble rise in a numerical calculation method for high density ratio bubble rise behavior based on LSMPS. Figure 2b This is a computational region diagram in the numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS in this invention; Figure 3 This is a diagram showing the arrangement of nodes at the moving interface between the gas and liquid phases in the numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS in this invention. Figure 4 This is a multi-resolution transition region diagram in the numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS in this invention; Figure 5 This is a schematic diagram of the simulation results of a single air bubble with an initial radius of 0.0025m rising in water in the numerical calculation method of high density ratio bubble rising behavior based on LSMPS of the present invention; Figure 6 This is a schematic diagram of the simulation results of a single air bubble with an initial radius of 0.00375m rising in water in the numerical calculation method of high density ratio bubble rising behavior based on LSMPS of the present invention; Figure 7 This is a schematic diagram of the simulation results of a single air bubble with an initial radius of 0.005m rising in water in the numerical calculation method of high density ratio bubble rising behavior based on LSMPS of the present invention; Figure 8 This is a schematic diagram illustrating the variation of the total rising velocity of bubbles with time under different initial radii in the numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS of this invention. Figure 9 This is a schematic diagram comparing the numerical results with the Grace plot in the numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS of this invention. Detailed Implementation

[0014] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0015] This invention relates to a numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS, such as... Figure 1 As shown, please follow these steps: Step 1. Establish a two-dimensional axisymmetric single-bubble ascent computational model based on the meshless moving particle semi-implicit method; Step 2. Calculate the temporary velocity of the particle; Step 3. Calculate the pressure of gas particles and interface node particles; Step 4. Calculate the pressure jump of particles at the interface nodes; Step 5. Calculate the pressure of the liquid particles; Step 6. Correct the particle velocity; Step 7. Update the positions of particles and interface node particles; Step 8. Simulation calculation and result export.

[0016] Example 1 A numerical calculation method for the rising behavior of high-density ratio bubbles based on LSMPS is used. In step 1, the computational domain is a two-dimensional axisymmetric model, where a single hemispherical bubble rises in a static liquid under the influence of buoyancy. The computational model consists of liquid particles, gas particles, wall particles, and interface node particles. The topology of the gas-liquid interface is described by the positions of the interface node particles. Figures 2a-2b As shown, the computational domain has a height of H, a width of L, and a distance h from the bubble center to the bottom. In this invention, L is greater than twice the initial bubble radius, and h is twice the initial bubble radius. The upper and lower walls use no-slip boundary conditions, while the sides use free-slip boundary conditions.

[0017] like Figure 3 As shown, when the gas and liquid phase particles are initially arranged, the particle arrangement near the phase interface adopts multi-resolution technology, that is, different regions use different particle spacing and different resolutions. The closer to the phase interface, the smaller the particle spacing and the denser the particle distribution. The farther away from the phase interface, the larger the particle spacing and the sparser the particle distribution.

[0018] like Figure 4 As shown, a transition region is introduced near the interface, where the particle size... Linear interpolation is performed as a function of the distance to the interface. (1) in, Represents particles Distance to the interface r a andr b These are parameters for the transition region across multiple spatial resolutions. This indicates the spatial resolution ratio.

[0019] Example 2 A numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS is used, wherein in step 2, the temporary velocity is calculated explicitly, and a particle velocity correction term and an artificial viscosity term are added: (2) In the formula, It is the time step. It's a temporary speed. Convection term, velocity correction It is the particle's velocity. This is the artificial viscosity item, indicated by the superscript. Indicates the calculation steps, subscript i Represents particles i .

[0020] Example 3 A numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS is used, wherein in step 3, the following pressure equation is considered for gas particles and interface nodes: For gas particles: (3) For UI nodes: (4).

[0021] Example 4 A numerical calculation method for the rising behavior of high density-ratio bubbles based on LSMPS is used, wherein in step 4, pressure jumps occur at the interface nodes between the gas and liquid phases, and the pressure jump calculation formula is as follows: (5) in, It is a gas interface node i Pressure It is a liquid interface node i Pressure, superscript and All of these represent calculation steps.

[0022] Example 5 A numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS is used, in step 5, where the pressure jump calculated in step 4 is used as the Dirichlet boundary condition for the calculation of liquid phase particle pressure. The liquid phase particle pressure is calculated using the following formula: (6).

[0023] Example 6 A numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS, wherein in step 6, the particle velocity correction calculation formula adopts the following formula: (7).

[0024] Example 7 A numerical calculation method for high density ratio bubble rising behavior based on LSMPS, wherein step 7 uses the following formula to update the particle and interface node particle positions: (8).

[0025] Example 8 The numerical calculation method for high density ratio bubble rising behavior based on LSMPS involves step 8, which uses C++ to program and output data documents, and then uses Paraview software to display the calculation results in the form of images.

[0026] Example 9 This embodiment yields simulation results of the upward motion of a single air bubble with an initial radius of 0.0025m in water, as follows: Figure 5-7 As shown.

[0027] During the bubble's ascent, the terminal ascent speed after the bubble stabilizes It is a key parameter characterizing bubble flow in a liquid. The terminal velocity of the bubble is determined using Clift's empirical formula: (9) In this invention, when the initial radii of the bubble are 0.0025 m, 0.00375 m and 0.005 m, the terminal velocities obtained from empirical formulas are 0.236 m / s, 0.240 m / s and 0.255 m / s, respectively.

[0028] like Figure 8 The variation of the total rising velocity of the bubble with time under different initial radii is shown. The formula for calculating the total rising velocity of the bubble in this invention is expressed as follows: (10) in, v c It is the total velocity of the bubbles. N g It is the number of gas phase particles. v i It is a particle i speed, r i It is a particle i The location.

[0029] Bubble shape is defined by three dimensionless numbers: the Morton number, the Eötvös number, and the Reynolds number. (11) (12) (13) In this invention, the Morton number, Eötvös number, and Reynolds number are listed in Table 1, as shown in the table: Table 1. Parameters of air bubble rise in water

[0030] The differences between the speeds obtained from the empirical formulas and the speeds obtained from the numerical simulations of this invention are 5.9%, 12.5%, and 17.6%, respectively. Overall, the calculation results agree well with the experimentally obtained empirical formula predictions.

[0031] like Figure 9 As shown, the bubble terminal rising velocity calculated using this invention, along with the corresponding Morton number, Eötvös number, and Reynolds number, matches well with the results predicted by the Grace plot. The bubble eventually exhibits a wobbling shape.

[0032] This invention presents a numerical calculation method for the rising behavior of high-density ratio bubbles based on LSMPS. It employs a two-dimensional axisymmetric model of single-bubble motion, adding moving interface particles for coupling between gas and liquid phase particles. Combining techniques such as particle dynamic multi-resolution schemes, particle movement schemes, and artificial viscosity schemes, it numerically simulates the rising motion characteristics of bubbles at high density ratios and accurately captures changes in the bubble interface. Using an axisymmetric model, the rising behavior of air bubbles in water and nitrogen bubbles in lead-bismuth alloys was numerically simulated. This accurately captures the evolution of the bubble interface, analyzes the changes in the total rising velocity of the bubbles and the velocities at the top and bottom of the bubbles, and obtains the evolution of the bubble's centroid height, volume, surface area, and aspect ratio over time.

Claims

1. A numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS, characterized in that, The specific steps are as follows: Step 1. Establish a two-dimensional axisymmetric single-bubble ascent computational model based on the meshless moving particle semi-implicit method; Step 2. Calculate the temporary velocity of the particle; Step 3. Calculate the pressure of gas particles and interface node particles; Step 4. Calculate the pressure jump of particles at the interface nodes; Step 5. Calculate the pressure of the liquid particles; Step 6. Correct the particle velocity; Step 7. Update the positions of particles and interface node particles; Step 8. Simulation calculation and result export.

2. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, In step 1, when the gas and liquid phase particles are initially arranged, the particle arrangement near the phase interface adopts multi-resolution technology, that is, different regions use different particle spacing and different resolutions. The closer to the phase interface, the smaller the particle spacing and the denser the particle distribution. The farther away from the phase interface, the larger the particle spacing and the sparser the particle distribution.

3. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, In step 2, the temporary velocity is calculated explicitly, and a particle movement velocity correction term and an artificial viscosity term are added: （1） In the formula, It is the time step. It's a temporary speed. Convection term, velocity correction It is the particle's velocity. This is the artificial viscosity item, indicated by the superscript. Indicates the calculation steps, subscript i Represents particles i .

4. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, In step 3, for gas particles and interface nodes, consider the following pressure equation: For gas particles: （2） For UI nodes: （3）。 5. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, In step 4, a pressure jump occurs at the interface node between the gas and liquid phases. The pressure jump calculation formula is as follows: （4） in, It is a gas interface node i Pressure It is a liquid interface node i Pressure, superscript and All of these represent calculation steps.

6. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, In step 5, the pressure jump calculated in step 4 is used as the Dirichlet boundary condition for the liquid phase particle pressure calculation. The liquid phase particle pressure calculation uses the following formula: （5）。 7. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, The particle velocity correction calculation formula in step 6 is as follows: （6）。 8. The numerical calculation method for the rising behavior of high density ratio bubbles based on LSMPS according to claim 1, characterized in that, The formula for calculating the positions of updated particles and interface node particles in step 7 is as follows: （7）。

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