A method for optimizing arrangement of multi-source contact type ultrasonic device in multi-physical field

Abstract

This invention discloses an optimized array method for a multi-source contact ultrasonic device in a multi-physics field, comprising the following steps: constructing a three-dimensional model of the multi-source contact ultrasonic device in a hydrometallurgical experiment coupled with a multi-physics field in a simulation system; setting the structural parameters, operating parameters, physical fields, boundary conditions, and material properties of the hydrometallurgical experiment; meshing the three-dimensional model; and solving the three-dimensional model using a parametric solver and a steady-state solver to obtain the total sound pressure result and total sound pressure distribution map of the hydrometallurgical experiment model coupled with a multi-physics field. This invention visualizes the sound pressure field, effectively quantifies the influence of the acoustic and physical parameters of the multi-source contact ultrasonic device on the sound pressure distribution of the physical field during the multi-physics field coupling process, and can accurately simulate, analyze, and optimize the acoustic characteristics of the multi-source contact ultrasonic device under different conditions with different acoustic parameters, helping to reduce the time and cost of multiple experiments in the laboratory.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic simulation and hydrometallurgical technology, and particularly relates to an optimized array method for multi-source contact ultrasonic devices in multi-physics fields. Background Technology

[0002] Ultrasound is an effective external field intensification method and is currently widely used in hydrometallurgical process intensification. While research has shown that the high temperature, high pressure, and strong jet generated by ultrasound can open inclusions on mineral surfaces, promote mass transfer, and regulate the crystal orientation of metal precipitation processes, thereby enhancing metal extraction, removal of harmful impurities, and metal electrodeposition, the sound field and sound pressure distribution within the reaction chamber during ultrasound application remains unclear. Furthermore, experimental studies have shown that increasing ultrasonic power can improve the leaching rate of valuable elements and shorten the leaching reaction time, but the optimal ultrasonic power and how to maximize its use for intensifying the reaction process are unknown. In addition, determining the optimal number and distribution of ultrasonic reactors within a reaction chamber (reactor) to maximize the output ultrasonic energy for process intensification is also difficult to demonstrate experimentally.

[0003] Experimentally investigating the optimal distribution of ultrasonic reactors in a reactor to maximize the output acoustic energy for hydrometallurgical strengthening processes requires significant time and yields limited systematic results. Numerical analysis, on the other hand, uses computer simulations to calculate established equations and models, addressing scientific problems difficult to characterize experimentally. COMSOL Multiphysics, a finite element analysis-based simulation software widely used in various scientific research fields, can perform calculations on multiphysics coupled models, providing intuitive results and data. Simulating the ultrasonic strengthening process using COMSOL Multiphysics allows for the visualization of sound pressure distribution in the reactor, providing a clear picture of phenomena and results not directly observable in experiments. Especially considering that stirring and temperature significantly impact sound pressure during actual reactions, studying the effects of temperature and stirring fields on sound pressure distribution during contact ultrasound, and optimizing the distribution of multi-source contact ultrasound devices, is highly instructive for enterprise production. Summary of the Invention

[0004] The technical problem solved by this invention is the lack of numerical simulation of ultrasonic enhancement coupled with multi-physics fields in the process and temperature fields in existing technologies. This invention provides an optimized array method for multi-source contact ultrasonic devices in multi-physics fields. Based on actual experimental processes, it studies the influence of different physical parameters of the contact ultrasonic amplitude transformer and the reactor on the sound pressure distribution of the sound field at different stirring speeds and reaction temperatures. The array method of the multi-source ultrasonic amplitude transformer in the ultrasonic enhancement process of hydrometallurgy is optimized to maximize the sound radiation efficiency and achieve maximum energy utilization in the ultrasonic process.

[0005] Technical solution: The present invention provides an optimized arraying method for a multi-source contact ultrasound device in a multi-physics field, the arraying method comprising the following steps:

[0006] Step 1: Construct a three-dimensional model of a hydrometallurgical experiment involving multi-source contact ultrasonic sound field, flow field, and temperature field coupling in the COMSOL Multiphysics simulation system. Select the dynamic mesh, turbulence, and linear Navier-Stokes module tools according to the experimental model requirements, and set the structural and operational parameters of the hydrometallurgical experiment.

[0007] Step 2: Globally define the physical fields, boundary conditions, and material properties of the hydrometallurgical experiment involving multiphysics coupling of acoustic, flow, and temperature fields;

[0008] Step 3: Mesh the three-dimensional model of the hydrometallurgical experiment based on the characteristics of the reactor and the ultrasonic amplitude transformer;

[0009] Step 4: Use the parametric solver and the MUMPS steady-state solver to solve the three-dimensional model of the hydrometallurgical experiment with multi-physics coupling of multi-source contact ultrasonic sound field, flow field and temperature field. Create a model that maps the turbulence calculation results to a linear Navier-Stokes model, obtain the control equations required for the flow field and sound field, and couple them with the temperature field to obtain the total sound pressure result of the multi-physics coupling hydrometallurgical experimental model.

[0010] Step 5: Post-process and visualize the sound field sound pressure results by selecting to add a 3D plotting group or a 2D plotting group to obtain a multi-faceted total sound pressure distribution map; use the color change of the multi-faceted total sound pressure distribution map to analyze the distribution of the operating parameters and structural parameters of the ultrasonic amplitude transformer in the multi-physics coupling model, and obtain the optimal experimental condition parameters.

[0011] Preferably, the specific construction method of step 1 is as follows:

[0012] Step 11: In the COMSOL Multiphysics simulation system, select the acoustic physics module, temperature physics module, fluid physics module, and frequency domain analysis method;

[0013] Step 12: Define the model parameters and model variables for the reaction chamber, ultrasonic amplitude transformer, and stirrer in the hydrometallurgical experiment involving multi-physics coupling of ultrasonic sound field, flow field, and temperature field;

[0014] Step 13: Construct a three-dimensional model of the reaction chamber, ultrasonic amplitude transformer, and stirrer for a hydrometallurgical experiment involving multi-physics coupling of ultrasonic sound field, flow field, and temperature field.

[0015] Preferably, in step 2, when defining the physical fields of the hydrometallurgical experiment involving the coupling of sound field, flow field, and temperature field, the pressure acoustic model in the COMSOL Multiphysics simulation system is used to visualize the sound field of the hydrometallurgical process. The turbulence field effect is mapped to a linear Navier-Stokes model and coupled with the temperature field. The coupling of the temperature field, flow field, and acoustic physical field is achieved using the finite element method, resulting in a multi-source contact ultrasonic sound field-flow field-temperature field coupling model for ultrasonically enhanced hydrometallurgy. Specifically, this includes the following steps:

[0016] Step 21: Define the wave equation calculation formula for the sound field-flow field-temperature field model. Based on the equations of motion, continuity, and state, obtain the wave equation for ultrasonic wave propagation. Define the sound field parameters: ultrasonic amplitude transformer power is 60W / L, frequency is 18~62kHz, ultrasonic amplitude transformer size is 6~30mm, distance from the bottom of the ultrasonic amplitude transformer to the bottom of the reactor is 40~90mm, distance from the center of the circle is 20~130mm, the number of ultrasonic amplitude transformers is 2, 3, 4, or 6, and the distribution of the ultrasonic amplitude transformers includes linear, triangular, quadrilateral, and circular shapes. Define the temperature field parameters: set the experimental temperature to a constant temperature environment of 25~70℃. Define the flow field parameters: reactor volume is 500~2000mL, and stirrer speed is 200~800 rpm.

[0017] Step 22: Couple the flow field, temperature field, and acoustic physical field using the wave equation for ultrasonic propagation to determine the coupling nodes between the flow field, temperature field, and sound field;

[0018] Step 23: Based on the coupling nodes of the flow field, temperature field and sound field, obtain the multi-physics coupling model of the sound field-flow field-temperature field of ultrasonic enhanced hydrometallurgy.

[0019] Preferably, the turbulence model in step 4 combines the k-ε model in free fluid and the k-ω model near the wall, which belongs to the low Reynolds number model. The calculation formula of the turbulence model is as follows:

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] In the formula: ρ is the fluid density, μ is the dynamic viscosity, p is the pressure, F represents the possible source term, K is the turbulent kinetic energy, om is the specific dissipation rate, G is the reciprocal of the wall distance, and I... ref It is a reference length ratio, μ T It is turbulent viscosity.

[0027] Preferably, the complex interaction between the stable flow field and the sound field in step 4 is simulated using a linear Navier-Stokes physics interface. The linear Navier-Stokes equations characterize the linearization of the entire set of governing equations describing compressible, viscous, and non-isothermal fluids, and their calculation formulas are as follows:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula: Φ = ∇u : τ 0 + u 0 : τ It is a viscous dissipation function, where M, F, and Q represent possible source terms. k It is the heat transfer coefficient. α p It is the coefficient of thermal expansion under isobaric conditions. β T It is the isothermal compressibility. p It is the specific heat capacity under constant pressure. iω The multiplier represents the time derivative. μ It is dynamic viscosity. μ B It is volume viscosity.

[0034] Preferably, in step 3, the three-dimensional model of the reactor and the ultrasonic amplitude transformer is meshed. The meshing standard is as follows: in the COMSOL Multiphysics simulation calculation, the CFD meshing sequence is manually edited, and different mesh combinations are used to define the mesh size of different parts of the model to distinguish the mesh size of the main part and the mesh size of the secondary part; the mesh types are free triangle, free quadrilateral, free tetrahedral mesh and boundary layer mesh.

[0035] Preferably, the post-processing and visualization processing in step 5 specifically includes the following steps:

[0036] Step 51: When performing sound field simulation in the COMSOL Multiphysics simulation system, post-processing further processes the calculated pure digital information and converts it into image or animation information;

[0037] Step 52: The post-processing process involves adding a 3D drawing group, selecting the type of graphic to be drawn and specifying the expression under the node, and visualizing the result;

[0038] Step 53: Calculate the absolute sound pressure mean and the relative standard deviation of the sound pressure using the exported numerical results;

[0039] Step 54: Observe and analyze the visualized images and calculation results to measure the uniformity and magnitude of the sound pressure distribution in the sound field; at the same time, selectively optimize the distribution and parameter size of the ultrasonic amplitude transformer, the shape and material of the reactor, and improve the utilization efficiency of the sound field by the multiphysics coupling model.

[0040] Preferably, in the multiphysics coupling model of sound field, flow field and temperature field, the flow field is a flow field with a stirrer, and the stirrer adopts different types of axial impellers, four types of radial impellers or impellers specifically for high viscosity fluids; the sound field adopts an ultrasonic amplitude transformer; the temperature field adopts electromagnetic heating, infrared heating, resistance heating and thermal domain heating.

[0041] Preferably, the reactor in step 2 is made of glass; the flow field material is selected based on the material density, dynamic viscosity, bulk viscosity, thermal conductivity, constant pressure heat capacity, sound velocity and specific heat rate characteristics, and the flow field material is a 5%~20% H2SO4 solution.

[0042] Compared with the prior art, the present invention has at least the following beneficial effects:

[0043] 1. The optimized array method of the multi-source contact ultrasonic device in a multi-physics field of the present invention is based on the numerical simulation method of COMSOL Multiphysics. By using the finite element method to construct an aeroacoustic model of the enhanced hydrometallurgical process coupled with ultrasound, stirring and temperature fields, the sound field and sound pressure are visualized. The influence of the acoustic parameters (ultrasonic power), physical parameters (diameter) of the multi-source contact ultrasonic device and the physical parameters (material and shape) of the reactor on the sound pressure distribution of the physical field in the multi-physics coupling process during the ultrasonic synergistic stirring process is effectively quantified. It can accurately simulate, analyze and optimize the acoustic characteristics of the multi-source contact ultrasonic device under different conditions with different acoustic parameters. The use of COMSOL Multiphysics simulation software can save a lot of experimental time and cost, and solve the problem that the sound field and sound pressure distribution in the reactor during the ultrasonic action process cannot be directly presented.

[0044] 2. Traditional non-contact ultrasonic transducers are adsorbed onto the outer surface of the reactor, so their effectiveness is weakened by the obstruction of the reactor wall. Contact ultrasonic amplitude transformers, on the other hand, act directly on the interior of the solid-liquid mixture, effectively avoiding acoustic energy loss and improving acoustic energy transmission efficiency. They also maximize the application of ultrasonic energy to the mass transfer and process intensification of the reaction. Optimized results obtained by simulating the distribution of multiple ultrasonic amplitude transformers in the same reactor further improve acoustic energy conversion efficiency. Furthermore, contact ultrasonic amplitude transformers reduce resonant impedance, exhibiting fatigue resistance and higher safety and reliability, extending transducer lifespan, facilitating equipment scaling, and making them suitable for widespread enterprise application. Attached Figure Description

[0045] Figure 1 The flowchart shows the optimized arraying method of the multi-source contact ultrasound device in a multi-physics field according to the present invention.

[0046] Figure 2 The total sound pressure distribution of multiple cross-sections is obtained by the arraying method of the optimized multi-source contact ultrasound device in a multi-physics field according to Embodiment 1 and Comparative Example 1 of the present invention.

[0047] Figure 3 The total sound pressure distribution diagrams of multiple planes are obtained by the arraying method of the optimized multi-source contact ultrasound device in a multi-physics field in Embodiment 2 and Comparative Example 2 of the present invention.

[0048] Figure 4 The total sound pressure distribution of multiple cross-sections is obtained by the arraying method of the optimized multi-source contact ultrasound device in a multi-physics field according to Embodiment 3 and Comparative Example 3 of the present invention.

[0049] Figure 5The total sound pressure distribution diagrams of multiple planes are obtained by the arraying method of the optimized multi-source contact ultrasound device in a multi-physics field in Embodiment 4 and Comparative Example 4 of the present invention.

[0050] Figure 6 Line graphs showing the absolute sound pressure and relative standard deviation of Examples 1-4 and Comparative Examples 1-4 of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will be described in conjunction with the accompanying drawings. Figures 1-6 The technical solutions of the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, the present invention provides an optimized arraying method for a multi-source contact ultrasound device in a multi-physics field, the arraying method comprising the following steps:

[0053] Step 1: Construct a 3D model of a hydrometallurgical experiment involving multi-source contact ultrasonic sound field, flow field, and temperature field coupling in the COMSOL Multiphysics simulation system. Select the dynamic mesh, turbulence, and linear Navier-Stokes modules according to the experimental model requirements, and set the structural and operational parameters of the hydrometallurgical experiment. The specific method for constructing the 3D model of the hydrometallurgical experiment is as follows:

[0054] Step 11: In the COMSOL Multiphysics simulation system, select the acoustic physics module, temperature physics module, fluid physics module, and frequency domain analysis method;

[0055] Step 12: Define the model parameters and model variables for the reaction chamber, ultrasonic amplitude transformer, and stirrer in the hydrometallurgical experiment involving multi-physics coupling of ultrasonic sound field, flow field, and temperature field;

[0056] Step 13: Construct a three-dimensional model of the reaction chamber, ultrasonic amplitude transformer, and stirrer for a hydrometallurgical experiment involving multi-physics coupling of ultrasonic sound field, flow field, and temperature field.

[0057] Step 2: Globally define the physical fields, boundary conditions, and material properties of the hydrometallurgical experiment involving the coupling of sound, flow, and temperature fields. When defining the physical fields of the hydrometallurgical experiment, the pressure acoustic model in the COMSOL Multiphysics simulation system is used to visualize the sound field of the hydrometallurgical process. The turbulence field effect is mapped to a linear Navier-Stokes equations and coupled with the temperature field. The coupling of the temperature field, flow field, and acoustic physical field is achieved using the finite element method, resulting in a multi-source contact ultrasonic sound field-flow field-temperature field coupling model for ultrasonically enhanced hydrometallurgy. This specifically includes the following steps:

[0058] Step 21: Define the wave equation calculation formula for the sound field-flow field-temperature field model. Based on the equations of motion, continuity, and state, obtain the wave equation for ultrasonic wave propagation. Construct a multi-physics coupled model of the sound field, flow field, and temperature field. The flow field is a flow field with a stirrer, using different types of axial impellers, four types of radial impellers, or impellers specifically designed for high-viscosity fluids. The sound field uses an ultrasonic amplitude transformer. The temperature field uses electromagnetic heating, infrared heating, resistance heating, and thermal domain heating. The reactor is made of glass. Select the flow field material based on material density, dynamic viscosity, bulk viscosity, thermal conductivity, constant-pressure heat capacity, sound velocity, and specific heat rate characteristics. The flow field material uses a 5%~20% H2SO4 solution. Define the sound field parameters: ultrasonic amplitude transformer power is 60W / L, frequency is 18~62kHz, ultrasonic amplitude transformer size is 6~30mm, and the distance from the bottom of the ultrasonic amplitude transformer to the bottom of the reactor is 40~90mm. mm, distance from the center is 20~130mm, number of ultrasonic amplitude transformers is 2, 3, 4, 6, and the distribution of ultrasonic amplitude transformers includes straight line, triangle, quadrilateral and circle; define temperature field parameters: set the experimental temperature to a constant temperature environment of 25~70℃; define flow field parameters: the volume of the reaction vessel is 500~2000mL, and the stirring speed is 200~800rpm;

[0059] Step 22: Couple the flow field, temperature field, and acoustic physical field using the wave equation for ultrasonic propagation to determine the coupling nodes between the flow field, temperature field, and sound field;

[0060] Step 23: Based on the coupling nodes of the flow field, temperature field and sound field, obtain the multi-physics coupling model of the sound field-flow field-temperature field of ultrasonic enhanced hydrometallurgy.

[0061] Step 3: Mesh the 3D model of the hydrometallurgical experiment based on the characteristics of the reactor and the ultrasonic amplitude transformer. The meshing standard is as follows: In the COMSOL Multiphysics simulation calculation, manually edit the CFD meshing sequence and use different mesh combinations to define the mesh size of different parts of the model to distinguish the mesh size of the main part and the mesh size of the secondary part. The mesh types are free triangle, free quadrilateral, free tetrahedral mesh and boundary layer mesh.

[0062] Step 4: Using a parametric solver and a MUMPS steady-state solver, the three-dimensional model of the multi-physics coupled hydrometallurgical experiment involving multi-source contact ultrasonic sound field, flow field, and temperature field is solved. A mapping is created to the turbulence calculation results onto a linear Navier-Stokes model to obtain the governing equations required for the flow and sound fields. These equations are then coupled with the temperature field to obtain the total sound pressure result of the multi-physics coupled hydrometallurgical experimental model. The turbulence model combines the k-ε model in free fluid and the k-ω model near the wall, belonging to the low Reynolds number model. The calculation formula for the turbulence model is as follows:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] In the formula: ρ is the fluid density, μ is the dynamic viscosity, p is the pressure, F represents the possible source term, K is the turbulent kinetic energy, om is the specific dissipation rate, G is the reciprocal of the wall distance, and I... ref It is a reference length ratio, μ T It is turbulent viscosity.

[0070] The complex interaction between the stable flow field and the sound field in the background is simulated using a linear Navier-Stokes physics interface. The linear Navier-Stokes equations characterize the linearization of the entire set of governing equations describing compressible, viscous, and non-isothermal fluids, and their calculation formulas are as follows:

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] In the formula: Φ = ∇u : τ 0 + u 0 : τ It is a viscous dissipation function, where M, F, and Q represent possible source terms. k It is the heat transfer coefficient. α p It is the coefficient of thermal expansion under isobaric conditions. β T It is the isothermal compressibility. p It is the specific heat capacity under constant pressure. iω The multiplier represents the time derivative. μ It is dynamic viscosity. μ B It is volume viscosity.

[0077] Step 5: Post-process and visualize the sound field sound pressure results by selecting to add a 3D plotting group or a 2D plotting group to obtain a multi-faceted total sound pressure distribution map; use the color changes of the multi-faceted total sound pressure distribution map to analyze the distribution of the ultrasonic amplitude transformer's operating and structural parameters in the multiphysics coupling model, and obtain the optimal experimental condition parameters. The post-processing and visualization specifically include the following steps:

[0078] Step 51: When performing sound field simulation in the COMSOL Multiphysics simulation system, post-processing further processes the calculated pure digital information and converts it into image or animation information;

[0079] Step 52: The post-processing process involves adding a 3D drawing group, selecting the type of graphic to be drawn and specifying the expression under the node, and visualizing the result;

[0080] Step 53: Calculate the absolute sound pressure mean and the relative standard deviation of the sound pressure using the exported numerical results;

[0081] Step 54: Observe and analyze the visualized images and calculation results to measure the uniformity and magnitude of the sound pressure distribution in the sound field; at the same time, selectively optimize the distribution and parameter size of the ultrasonic amplitude transformer, the shape and material of the reactor, and improve the utilization efficiency of the sound field by the multiphysics coupling model.

[0082] Specifically, the optimized multi-source contact ultrasound device array method in a multi-physics field provided by the present invention is compared and illustrated using Examples 1-4 and Comparative Examples 1-4 as follows:

[0083] Example 1: Step S1: In the COMSOL Multiphysics simulation system, select the "3D model" mode to create a 3D model of a 500mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16mm and made of low alloy steel, two ultrasonic amplitude transformers arranged in a straight line, and a stirring speed of 200 rpm.

[0084] Step S2: Select the fluid domain material, construct a 5% (w / w) H2SO4 solution, and define the density and sound velocity; select glass material from the material library for the solid domain reactor material, and select low alloy steel material for the ultrasonic amplitude transformer.

[0085] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 18kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom surface of the reactor is 45mm and 40mm.

[0086] Step S4: Set boundary conditions, reaction temperature is 25℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0087] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0088] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 18kHz, a power density of 60W / L, and a linear distribution are intuitively quantified.

[0089] Example 2: Step S1: In the COMSOL Multiphysics simulation system, select the "3D model" mode to create a 3D model of a 1000 mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16 mm and made of low alloy steel, three ultrasonic amplitude transformers arranged in a triangle, and a stirring speed of 500 rpm.

[0090] Step S2: Select the fluid domain material, construct a 5% (by mass) H2SO4 solution, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor, and select low alloy steel material for the amplitude transformer.

[0091] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 45kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom surface of the reactor is 73mm, 68mm, and 63mm.

[0092] Step S4: Set boundary conditions, reaction temperature is 25℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0093] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0094] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 45kHz, a power density of 60W / L, and a triangular distribution are intuitively quantified.

[0095] Example 3: Step S1: In the COMSOL Multiphysics simulation system, select the "3D model" mode to create a 3D model of a 1500 mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16 mm and made of low alloy steel, four ultrasonic amplitude transformers arranged in a square, and a stirring speed of 500 rpm.

[0096] Step S2: Select the fluid domain material, construct an H2SO4 solution with a mass percentage of 10%, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor material, and select low alloy steel material for the amplitude transformer.

[0097] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 45kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom of the reactor is 82mm.

[0098] Step S4: Set boundary conditions, reaction temperature is 70℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0099] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0100] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 45kHz, a power density of 60W / L, and a square distribution pattern are intuitively quantified.

[0101] Example 4: Step S1: In the COMSOL Multiphysics simulation system, select the "3D model" mode to create a 3D model of a 1000 mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16 mm and made of low alloy steel, 6 ultrasonic amplitude transformers arranged in a circle, and a stirring speed of 500 rpm.

[0102] Step S2: Select the fluid domain material, construct an H2SO4 solution with a mass percentage of 20%, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor material, and select low alloy steel material for the amplitude transformer.

[0103] Step S3: Set the acoustic parameters and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 62 kHz, the power density is 60 W / L, and the distance between the ultrasonic amplitude transformer and the bottom of the reactor is 80 mm.

[0104] Step S4: Set boundary conditions, reaction temperature is 70℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0105] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0106] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 45kHz, a power density of 60W / L, and a circular distribution pattern are intuitively quantified.

[0107] Comparative Example 1: The difference from Example 1 is that the number of ultrasonic amplitude transformers, total power density, frequency, volume of the reactor, stirrer speed, reaction temperature, and solution properties are kept constant. The distance between the ultrasonic amplitude transformers and the center of the reactor is changed. The ultrasonic amplitude transformer on the left is 5 mm away from the center, and the ultrasonic amplitude transformer on the right is 4 mm away from the center. The specific steps are as follows:

[0108] Step S1: In the COMSOL Multiphysics simulation system, select the "3D model" mode to create a 3D model of a 500 mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16 mm and made of low alloy steel, two ultrasonic amplitude transformers arranged in a straight line, and a stirring speed of 200 rpm.

[0109] Step S2: Select the fluid domain material, construct a 5% (by mass) H2SO4 solution, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor, and select low alloy steel material for the amplitude transformer.

[0110] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 18kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom surface of the reactor is 45mm and 40mm.

[0111] Step S4: Set boundary conditions, reaction temperature is 25℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0112] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0113] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 18kHz, a power density of 60W / L, and a linear distribution are intuitively quantified.

[0114] Comparative Example 2: The difference from Example 2 is that the number of ultrasonic amplitude transformers, total power density, reactor volume, stirrer speed, and reaction temperature are kept constant. The frequency of the ultrasonic amplitude transformers is reduced to 18kHz, the sulfuric acid mass percentage is increased to 10%, and the distance from the ultrasonic amplitude transformers to the center of the reactor is changed. The specific steps are as follows:

[0115] Step S1: In the COMSOL Multiphysics simulation system, select the "3D Model" mode to create a 3D model of a 1000 mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16 mm and made of low alloy steel, consisting of 3 ultrasonic amplitude transformers arranged in a triangle, and a stirring speed of 500 rpm.

[0116] Step S2: Select the fluid domain material, construct an H2SO4 solution with a mass percentage of 10%, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor material, and select low alloy steel material for the amplitude transformer.

[0117] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 18kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom surface of the reactor is 73mm, 68mm, and 63mm.

[0118] Step S4: Set boundary conditions, reaction temperature is 25℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0119] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0120] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 18kHz, a power density of 60W / L, and a triangular distribution are intuitively quantified.

[0121] Comparative Example 3: The difference from Example 3 is that the number of ultrasonic amplitude transformers, total power density, frequency, volume of the reactor, stirrer speed, sulfuric acid mass percentage, and temperature are kept constant, while the distance from the ultrasonic amplitude transformers to the bottom of the reactor is changed. The specific steps are as follows:

[0122] Step S1: In the COMSOL Multiphysics simulation system, select the "3D Model" mode to create a 3D model of a 1500 mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16 mm and made of low alloy steel, four ultrasonic amplitude transformers arranged in a square, and a stirring speed of 500 rpm.

[0123] Step S2: Select the fluid domain material, construct an H2SO4 solution with a mass percentage of 10%, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor material, and select low alloy steel material for the amplitude transformer.

[0124] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 45kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom surface of the reactor is 82mm, 82mm, 77mm, and 77mm.

[0125] Step S4: Set boundary conditions, reaction temperature 70℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0126] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0127] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 45kHz, a power density of 60W / L, and a square distribution pattern are intuitively quantified.

[0128] Comparative Example 4: The difference from Example 4 is that the number of ultrasonic amplitude transformers, total power density, frequency, sulfuric acid mass percentage, and reaction temperature are kept constant, the volume of the reaction vessel is increased to 2000 mL, the stirrer speed is increased to 800 rpm, and the distance from three of the ultrasonic amplitude transformers to the bottom of the reaction vessel is changed. The specific steps are as follows:

[0129] Step S1: In the COMSOL Multiphysics simulation system, select the "3D Model" mode to create a 3D model of a 2000mL glass reactor, an ultrasonic amplitude transformer with a diameter of 16mm and made of low alloy steel, 6 ultrasonic amplitude transformers arranged in a circle, and a stirring speed of 800 rpm.

[0130] Step S2: Select the fluid domain material, construct an H2SO4 solution with a mass percentage of 20%, and define the density and velocity of sound; select glass material from the material library for the solid domain reactor material, and select low alloy steel material for the amplitude transformer.

[0131] Step S3: Set the acoustic and structural parameters of the ultrasonic amplitude transformer. The ultrasonic amplitude transformer frequency is 62kHz, the power density is 60W / L, and the distance between the ultrasonic amplitude transformer and the bottom surface of the reactor is 80mm, 72mm, 80mm, 72mm, 80mm, 72mm, 80mm, 72mm.

[0132] Step S4: Set boundary conditions, reaction temperature is 70℃, select the stirring paddle area as the rotation domain, define pressure point constraints on the reactor, select the upper surface of the reactor for pressure (adiabatic), and define the specified speed.

[0133] Step S5: Mesh the three-dimensional models of the fluid domain, ultrasonic amplitude transformer, and stirrer using free tetrahedral, free triangular, and boundary layer mesh types, respectively.

[0134] Step S6: Using three research parameters, including wall distance initialization, mapping, and frequency domain, the turbulence results are mapped to the sound field. By drawing a three-dimensional plotting group, the sound pressure results of the ultrasonic amplitude transformer with a frequency of 45kHz, a power density of 60W / L, and a circular distribution pattern are intuitively quantified.

[0135] Table 1. Specific process parameters for Examples 1-4 and Comparative Examples 1-4:

[0136] Example Ultrasonic amplitude rod distribution method Frequency (kHz) <![CDATA[Mass percentage of H2SO4 (%)]]> Stirring speed (rpm) Reaction temperature (°C) Distance from the bottom of the reactor (mm) Distance from the center of the circle (mm) Example 1 linear 18 5 200 25 66、61 22 Example 2 triangle 18 10 500 25 73、68、63 89、30 Example 3 rectangle 45 10 500 70 82 40 Example 4 round 62 20 500 70 80、72 60 Comparative Example 1 linear 18 5 200 25 61、51 27、26 Comparative Example 2 triangle 45 5 500 25 73、68、63 121、38 Comparative Example 3 rectangle 45 10 500 70 82、77 40 Comparative Example 4 round 62 20 800 70 80 60 .

[0137] Table 1 shows that all reactors are cylindrical in shape, differing only in the parameters and distribution of the ultrasonic amplifiers. The power density of the amplifiers is the same, with frequencies primarily selected from 18 to 62 kHz. Reaction temperatures range from 25 to 70°C, stirrer speeds from 200 to 800 rpm, and the reactor volumes are 500 to 2000 ml. The distance from the bottom of the ultrasonic amplifier to the bottom of the reactor is 50 to 90 mm, the distance from the center is 20 to 130 mm, the amplifier size is 6 to 30 mm, and the sulfuric acid mass percentage is 5% to 20%. The total sound pressure level across multiple sections under different parameters is as follows: Figures 2-5 As shown, the absolute sound pressure and relative standard deviation of each of Examples 1-4 and Comparative Examples 1-4 are as follows: Figure 6 As shown.

[0138] Depend on Figure 2 Comparing Example 1 and Comparative Example 1, it can be seen that, except for the decrease in height from the bottom of the reactor and the increase in distance from the center, other conditions remain unchanged. The results show that the absolute sound pressure of the sound field increases, indicating that changing the height from the bottom of the reactor and the distance from the center will have a beneficial effect on the sound pressure effect. If the array arrangement is not reasonable, it may lead to local high-pressure or low-pressure areas in the sound field, thereby affecting the effect of ultrasound. Placing the ultrasonic amplitude transformer in a suitable position can increase the sound pressure.

[0139] Depend on Figure 2 Comparing Example 2 and Comparative Example 2, it can be seen that, while keeping the power density of the ultrasonic amplitude transformer, the volume of the reactor, the stirring speed, the reaction temperature, and the height from the bottom of the reactor constant, increasing the frequency of the ultrasonic amplitude transformer to 45kHz, reducing the mass percentage of sulfuric acid to 5%, increasing the distance from the center, increasing the absolute sound pressure, and improving the uniformity of the sound field distribution are all beneficial. This is because the higher the frequency, the shorter the wavelength of the sound wave, leading to an increase in sound pressure. The change in the frequency of the ultrasonic amplitude transformer also affects the magnitude of the sound pressure and the distribution range of the cavitation region in the sound field.

[0140] Depend on Figure 3 Comparing Example 3 and Comparative Example 3, it can be seen that, except for the decrease in the height of the two ultrasonic amplitude rods from the bottom of the reactor, the absolute sound pressure increases when other conditions remain unchanged. When the depth of action of the ultrasonic amplitude rods decreases, the plane of ultrasonic action changes, resulting in a change in the ultrasonic effect. The depth of the ultrasonic amplitude rods also affects the sound pressure and cavitation effect of the sound field.

[0141] Depend on Figure 4Comparing Example 4 and Comparative Example 4, it can be seen that when the volume of the reactor is increased to 2L, the stirring speed is increased to 800rpm, and the height of the ultrasonic amplitude transformer from the bottom of the reactor is the same, the absolute sound pressure increases and the sound pressure distribution is more uniform. By adjusting the position of the ultrasonic amplitude transformer, the cavitation area can be increased. At the same time, under the mechanical force of the six ultrasonic amplitude transformers and the stirring paddle, although the volume of the reactor is increased, the uniformity of the sound field sound pressure is better and the absolute sound pressure also increases. Therefore, selecting an appropriate number of ultrasonic amplitude transformers, their distribution position, and an appropriate stirring speed can improve the ultrasonic effect under the same conditions.

[0142] The optimized multi-source contact ultrasonic device array method in a multiphysics field provided by this invention, as shown by comparing Examples 1-4 and Comparative Examples 1-4, reveals that the distance, arrangement, and distance from the bottom of the reactor of the ultrasonic amplitude transformers all affect the sound field. In experiments, a suitable distribution method should be selected to maximize the effect of the ultrasonic amplitude transformers. The actual experimental conditions are simulated using the COMSOL Multiphysics simulation system, providing examples and visualized results for the experiments. This invention provides a digital model for experimental design and helps reduce the time and cost of multiple experiments in the laboratory. It offers an innovative approach to the selection and arraying of the power and frequency of the ultrasonic amplitude transformers in experiments, and has significant theoretical and practical guiding value for developing efficient ultrasonic auxiliary equipment and realizing the industrial application of power ultrasound, thereby achieving the goal of energy saving and consumption reduction.

[0143] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the array arrangement of a multi-source contact ultrasound device in a multi-physics field, characterized in that, The array arrangement method includes the following steps: Step 1: Construct a three-dimensional model of a hydrometallurgical experiment involving multi-source contact ultrasonic sound field, flow field, and temperature field coupling in the COMSOL Multiphysics simulation system. Select the dynamic mesh, turbulence, and linear Navier-Stokes module tools according to the experimental model requirements, and set the structural and operational parameters of the hydrometallurgical experiment. Step 2: Globally define the physical fields, boundary conditions, and material properties of the hydrometallurgical experiment involving multiphysics coupling of acoustic, flow, and temperature fields; Step 3: Mesh the three-dimensional model of the hydrometallurgical experiment based on the characteristics of the reactor and the ultrasonic amplitude transformer; Step 4: Use the parametric solver and the MUMPS steady-state solver to solve the three-dimensional model of the hydrometallurgical experiment with multi-physics coupling of multi-source contact ultrasonic sound field, flow field and temperature field. Create a model that maps the turbulence calculation results to a linear Navier-Stokes model, obtain the control equations required for the flow field and sound field, and couple them with the temperature field to obtain the total sound pressure result of the multi-physics coupling hydrometallurgical experimental model. Step 5: Post-process and visualize the sound field sound pressure results by selecting to add a 3D plotting group or a 2D plotting group to obtain a multi-faceted total sound pressure distribution map; use the color change of the multi-faceted total sound pressure distribution map to analyze the distribution of the operating parameters and structural parameters of the ultrasonic amplitude transformer in the multi-physics coupling model, and obtain the optimal experimental condition parameters.

2. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 1, characterized in that, The specific construction method for step 1 is as follows: Step 11: In the COMSOL Multiphysics simulation system, select the acoustic physics module, temperature physics module, fluid physics module, and frequency domain analysis method; Step 12: Define the model parameters and model variables for the reaction chamber, ultrasonic amplitude transformer, and stirrer in the hydrometallurgical experiment involving multi-physics coupling of ultrasonic sound field, flow field, and temperature field; Step 13: Construct a three-dimensional model of the reaction chamber, ultrasonic amplitude transformer, and stirrer for a hydrometallurgical experiment involving multi-physics coupling of ultrasonic sound field, flow field, and temperature field.

3. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 1, characterized in that, In step 2, when defining the physical fields of the hydrometallurgical experiment involving the coupling of sound, flow, and temperature fields, the pressure acoustic model in the COMSOL Multiphysics simulation system is used to visualize the sound field of the hydrometallurgical process. The turbulence field effect is mapped to a linear Navier-Stokes model and coupled with the temperature field. The coupling of the temperature field, flow field, and acoustic physical field is achieved using the finite element method, resulting in a multi-source contact ultrasonic sound field-flow field-temperature field coupling model for ultrasonically enhanced hydrometallurgy. The specific steps include: Step 21: Define the wave equation calculation formula for the sound field-flow field-temperature field model. Based on the equations of motion, continuity, and state, obtain the wave equation for ultrasonic wave propagation. Define the sound field parameters: ultrasonic amplitude transformer power is 60W / L, frequency is 18~62kHz, ultrasonic amplitude transformer size is 6~30mm, distance from the bottom of the ultrasonic amplitude transformer to the bottom of the reactor is 40~90mm, distance from the center of the circle is 20~130mm, the number of ultrasonic amplitude transformers is 2, 3, 4, or 6, and the distribution of the ultrasonic amplitude transformers includes linear, triangular, quadrilateral, and circular shapes. Define the temperature field parameters: set the experimental temperature to a constant temperature environment of 25~70℃. Define the flow field parameters: reactor volume is 500~2000mL, and stirrer speed is 200~800 rpm. Step 22: Couple the flow field, temperature field, and acoustic physical field using the wave equation for ultrasonic propagation to determine the coupling nodes between the flow field, temperature field, and sound field; Step 23: Based on the coupling nodes of the flow field, temperature field and sound field, obtain the multi-physics coupling model of the sound field-flow field-temperature field of ultrasonic enhanced hydrometallurgy.

4. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 1, characterized in that, In step 4, the turbulence model combines the k-ε model in free fluid and the k-ω model near the wall, belonging to the low Reynolds number model. The calculation formula for the turbulence model is as follows: ； ； ； ； ； ； In the formula: ρ is the fluid density, μ is the dynamic viscosity, p is the pressure, F represents the possible source term, K is the turbulent kinetic energy, om is the specific dissipation rate, G is the reciprocal of the wall distance, and I... ref It is a reference length ratio, μ T It is turbulent viscosity.

5. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 4, characterized in that, In step 4, the complex interaction between the stable flow field and the acoustic field, which serves as the background, is simulated using a linear Navier-Stokes physics interface. The linear Navier-Stokes equations characterize the linearization of the entire set of governing equations describing compressible, viscous, and non-isothermal fluids, and their calculation formulas are as follows: ； ； ； ； ； In the formula: Φ = ∇u : τ 0 + u 0 : τ It is a viscous dissipation function, where M, F, and Q represent possible source terms. k It is the heat transfer coefficient. α p It is the coefficient of thermal expansion under isobaric conditions. β T It is the isothermal compressibility. p It is the specific heat capacity under constant pressure. iω The multiplier represents the time derivative. μ It is dynamic viscosity. μ B It is volume viscosity.

6. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 1, characterized in that, In step 3, the three-dimensional models of the reactor and ultrasonic amplitude transformer are meshed. The meshing standard is as follows: in the COMSOL Multiphysics simulation calculation, the CFD meshing sequence is manually edited, and different mesh combinations are used to define the mesh size of different parts of the model to distinguish the mesh size of the main part and the mesh size of the secondary part; the mesh types are free triangle, free quadrilateral, free tetrahedral mesh and boundary layer mesh.

7. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 1, characterized in that, Step 5, post-processing and visualization, specifically includes the following steps: Step 51: When performing sound field simulation in the COMSOL Multiphysics simulation system, post-processing further processes the calculated pure digital information and converts it into image or animation information; Step 52: The post-processing process involves adding a 3D drawing group, selecting the type of graphic to be drawn and specifying the expression under the node, and visualizing the result; Step 53: Calculate the absolute sound pressure mean and the relative standard deviation of the sound pressure using the exported numerical results; Step 54: Observe and analyze the visualized images and calculation results to measure the uniformity and magnitude of the sound pressure distribution in the sound field; at the same time, selectively optimize the distribution and parameter size of the ultrasonic amplitude transformer, the shape and material of the reactor, and improve the utilization efficiency of the sound field by the multiphysics coupling model.

8. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 1, characterized in that, In the multiphysics coupling model of sound field, flow field and temperature field, the flow field is a flow field with a stirrer. The stirrer adopts different types of axial impellers, four types of radial impellers or impellers specifically for high viscosity fluids; the sound field adopts ultrasonic amplitude rod; the temperature field adopts electromagnetic heating, infrared heating, resistance heating and thermal domain heating.

9. The optimized array method for multi-source contact ultrasound devices in a multi-physics field according to claim 3, characterized in that, In step 2, the reactor is made of glass. The flow field material is selected based on the material density, dynamic viscosity, bulk viscosity, thermal conductivity, constant pressure heat capacity, sound velocity and specific heat rate characteristics. The flow field material is a 5%~20% H2SO4 solution.

Images