Finite element-based ultrasonic rolling, kneading and pickling beef brine mass transfer modeling and application

Abstract

The invention relates to the technical field of processing of fresh meat and animal products, in particular to a finite element-based ultrasonic rolling, kneading and pickling beef brine mass transfer modeling method and application, which comprises the following steps: measuring the content change of salt and moisture in a beef sample under different ultrasonic power conditions, and combining with a Fick second law diffusion model, so as to determine the salt content and moisture content of the beef sample; corresponding salt and water mass transfer coefficients are obtained; establishing a three-dimensional physical field model and a beef sample geometric model by utilizing finite element analysis software, and establishing a simulation model of salt and moisture diffusion; establishing a function relationship between different ultrasonic powers and mass transfer coefficients of salt and moisture; and finally, the two models are combined for use, so that the spatial and temporal distribution conditions of the salinity and the moisture under any ultrasonic power condition can be visually presented. The model method has the characteristics of convenience in operation and dynamic visualization, the permeation condition of the pickling liquid in the beef in the pickling process can be observed, and the development of an ultrasonic synergistic tumbling pickling technology is facilitated.

Description

Technical Field

[0001] This invention relates to the field of fresh meat and livestock product processing technology, specifically to a finite element-based modeling and application of brine mass transfer in ultrasonic tumbling and marinating of beef. Background Technology

[0002] Marinating beef is a crucial step in meat processing, its core lying in the migration of salt and water within muscle tissue. Salt penetration not only imparts the basic flavor of the product but also significantly impacts protein solubility, changes in muscle structure, and water retention. Meanwhile, water migration is closely related to marinating uniformity, textural properties, and final edible quality. Therefore, effectively improving the mass transfer efficiency of salt and water is a key research focus in the field of meat processing.

[0003] Conventional tumbling and marinating processes promote the penetration of the marinade through physical compression and impact. However, for large pieces of meat, this method still suffers from problems such as long marinating time and uneven salt distribution, making it difficult to meet the demands of modern meat processing for high efficiency and stable quality. In recent years, ultrasonic technology has been applied to meat marinating due to its cavitation effect, microjet effect, and tissue disruption effect. Existing studies have shown that ultrasonic treatment can increase the porosity of muscle tissue and accelerate the diffusion of salt and water, especially when combined with tumbling, it can significantly shorten marinating time and improve marinating efficiency. For example, Zhang et al. found that ultrasonic synergistic tumbling can significantly improve the permeability of the marinade and the water retention of the product within the same time. However, existing research mainly focuses on the observation of experimental results and the determination of quality indicators, and the mechanism of salt and water diffusion in beef marinated by ultrasonic synergistic tumbling remains unclear.

[0004] Currently, scholars both domestically and internationally have attempted to simulate the marinating process using methods such as the Fick diffusion model and empirical regression models. However, these models only provide single predicted values ​​and cannot visualize the dynamic diffusion of salt and moisture during the marinating process. Finite element analysis, as a numerical simulation method capable of handling complex boundaries and heterogeneous materials, can visualize the physical and chemical changes during material processing and has been applied in heat and mass transfer research in food engineering. However, mature methods and application examples are still lacking in modeling salt and moisture mass transfer during ultrasonic synergistic tumbling marinating of beef.

[0005] Therefore, there is an urgent need to establish a finite element-based model for the mass transfer of brine in ultrasonic tumbling and marinating of beef. By simulating the diffusion law of salt and water in beef during ultrasonic tumbling and marinating, a scientific basis and technical support can be provided for process optimization, quality improvement and industrial application. Summary of the Invention

[0006] The purpose of this invention is to propose a finite element method (FEM)-based modeling and application of brine mass transfer in ultrasonic tumbling marinating of beef, addressing the issues of unclear mass transfer mechanisms and the lack of visualization of salt and moisture diffusion processes in existing models within ultrasonic tumbling marinating technology. By measuring the changes in salt and moisture content in beef samples under different ultrasonic power conditions and combining this with Fick's second law diffusion model, the corresponding salt and moisture mass transfer coefficients are obtained. Based on this, a three-dimensional physical field model and a geometric model of the beef sample are constructed using finite element analysis software. A simulation model of salt and moisture diffusion is established by inputting the mass transfer coefficients and setting boundary conditions. Simultaneously, a functional relationship between different ultrasonic powers and the mass transfer coefficients of salt and moisture is established. Combining these two models allows for the visualization of the spatiotemporal distribution of salt and moisture under arbitrary ultrasonic power conditions, thus providing technical support for optimizing marinating process parameters and controlling product quality.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] A finite element method for modeling the mass transfer of brine in ultrasonically tumbling marinated beef, the method comprising:

[0009] Step 1: Prepare beef samples with marinating times of 30, 60, 90, 120 and 180 min and ultrasonic power of 0, 100, 300, 500 and 700 W respectively using ultrasonic synergistic tumbling marinating technology.

[0010] Step 2: Determine the salt and moisture content of beef under different treatment times and different ultrasonic powers;

[0011] Step 3: Based on Fick's second law diffusion model, calculate the mass transfer coefficients of salt and moisture in beef under different processing conditions using experimentally measured salt and moisture content. and value;

[0012] Step 4: Establish a three-dimensional physical field model and a geometric model of the beef sample in COMSOL software through finite element analysis;

[0013] Step 5: Adjust the salt mass transfer coefficient. With water mass transfer coefficient By combining with finite element analysis and setting appropriate boundary conditions, a simulation model of salt and moisture diffusion is constructed.

[0014] Step Six: Based on the relationship between ultrasonic power and the mass transfer coefficients of salt and water, establish the relationship between different ultrasonic powers and the salt mass transfer coefficient. Water mass transfer coefficient The exponential function model between them;

[0015] Step 7: Combine the simulation model from Step 5 with the mathematical model from Step 6 to achieve a visual simulation of the three-dimensional diffusion distribution of salt and moisture in beef under different ultrasonic power conditions.

[0016] Preferably, step two includes:

[0017] The determination of salt content includes: weighing 10 g of marinated beef, adding 13 times the volume of primary water, homogenizing and mixing thoroughly with a homogenizer, and centrifuging at 13,200×g for 10 min; collecting the supernatant and determining the salt content using a salinity meter.

[0018] The determination of the moisture content includes: weighing 5g of marinated beef, placing it in a constant temperature oven, setting the oven temperature to 103℃ and maintaining it for 4.5 h, transferring it to a desiccator to cool for 1 h until the sample quality is stable, weighing it and calculating the moisture content.

[0019] Preferably, step three includes:

[0020] Using the salt and moisture content data of beef at different processing times as input values, and incorporating Fick's second law diffusion equation, the salt mass transfer coefficient at corresponding time points was solved under different ultrasonic power conditions. and water mass transfer coefficient Furthermore, the salt and moisture content in the equilibrium state was obtained by tumbling the beef for 30 hours.

[0021] The diffusion equation according to Fick's second law is:

[0022] ;

[0023] ;

[0024] in, and These represent the initial salt and moisture content, respectively. and These represent the salt and moisture content at different time points. and These represent the salt and moisture content at the corresponding salinity equilibrium state, respectively. and These represent the salt and water diffusion coefficients, respectively. This indicates the thickness of the beef sample.

[0025] Preferably, step four includes:

[0026] A three-dimensional physical field model and a geometric model of the beef sample were established in COMSOL software using finite element analysis. The physical field selected was the "Dilute Mass Transfer" physical field interface, which was used to describe the diffusion behavior of salt and water in the beef tissue.

[0027] The geometric model is constructed based on the size and shape of the actual beef sample, creating a corresponding three-dimensional geometric model to reflect the spatial structural characteristics of the sample. The sample material properties are arbitrary tissue types, and the sample mesh is divided into conventional physical field controlled meshes.

[0028] Preferably, step five includes:

[0029] The experimentally measured salt diffusion coefficient and moisture diffusion coefficient Input the data into the model and adjust the mass transfer coefficient according to the ultrasonic power conditions; in addition, the rare matter transfer is a transient process; the boundary conditions are set to be transient external convection flux types for all 6 surfaces;

[0030] The initial salt content is the salt content of fresh beef shank itself, the initial moisture content is the moisture content of fresh beef shank itself, and the external concentration is the salt concentration in the marinade.

[0031] The transient equation for mass transfer of salt and water is:

[0032] ;

[0033] ;

[0034] The concentration boundary is: ;

[0035] The boundary flux is: ;

[0036] Where D represents the effective diffusion coefficient of salt or moisture. This represents the initial concentration at a given inflow surface. Indicates the mass transfer factor. Indicates the concentration of the bulk solution outside the model;

[0037] Subsequently, using COMSOL's finite element numerical solver, the migration of salt and water in beef tissue under different ultrasonic powers and processing times was visualized.

[0038] Preferably, step six includes:

[0039] By comparing the ultrasonic power with the experimentally obtained diffusion coefficient and A functional relationship was established and fitted using an exponential function. The fitted functional equation was then used as a mathematical model to calculate the diffusion coefficients of salt and water in beef under different ultrasonic power conditions.

[0040] Preferably, step seven includes:

[0041] By combining the salt and moisture diffusion simulation in step five with the exponential function model in step six, a modeling system for studying the migration patterns of salt and moisture in beef under ultrasonic synergistic tumbling and marinating is constructed. The salt diffusion coefficient under different ultrasonic powers is determined based on the exponential function model. and moisture diffusion coefficient This was incorporated into a simulation model to achieve a visual simulation of the diffusion and distribution of salt and moisture in beef under different ultrasonic powers during synergistic tumbling.

[0042] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0043] This invention combines Fick's second law diffusion model with finite element analysis to achieve a three-dimensional visualization of the diffusion process of salt and moisture inside beef, thereby effectively revealing the mass transfer mechanism in the ultrasonic synergistic tumbling and marinating process.

[0044] This invention establishes a mathematical model between ultrasonic power and mass transfer coefficient, which can calculate the mass transfer coefficients of salt and water under different ultrasonic treatment conditions, intuitively predict the dynamic migration and distribution of salt and water, and provide a scientific basis for the regulation and optimization of pickling process.

[0045] This invention can be used not only for experimental research, but also to provide theoretical guidance and technical support for quality control and industrial production in meat processing, and has good prospects for promotion and application. Attached Figure Description

[0046] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0047] Figure 1 This invention provides a rapid determination model and application flowchart for the salt and moisture content of marinated beef.

[0048] Figure 2 This is a graph showing the changes in salt and moisture content in beef under different ultrasonic powers and times according to the present invention.

[0049] Figure 3 This invention is a three-dimensional geometric model constructed based on beef sample materials;

[0050] Figure 4This is a three-dimensional streamline diagram of the diffusion of salt and moisture in beef under different processing conditions according to the present invention;

[0051] Figure 5 Simulation diagram of the diffusion process of salt and moisture in beef under different treatment conditions according to the present invention;

[0052] Figure 6 This is a correlation analysis graph showing the relationship between ultrasonic power and the mass transfer rates of salt and water in this invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Please see Figures 1-6 The present invention provides the following technical solution:

[0055] Example 1: As Figure 1 As shown, this invention provides a finite element-based modeling and application of brine mass transfer in ultrasonic tumbling marinated beef, comprising the following steps:

[0056] Step 1: Prepare beef samples with marinating times of 30, 60, 90, 120 and 180 min and ultrasonic power of 0, 100, 300, 500 and 700 W respectively using ultrasonic synergistic tumbling marinating technology.

[0057] Step 2: Determine the salt and moisture content of beef under different treatment times and different ultrasonic powers;

[0058] Step 3: Based on Fick's second law diffusion model, calculate the mass transfer coefficients of salt and moisture in beef under different processing conditions using experimentally measured salt and moisture content. and value;

[0059] Step 4: Establish a three-dimensional physical field model and a geometric model of the beef sample in COMSOL software through finite element analysis;

[0060] Step 5: Adjust the salt mass transfer coefficient. With water mass transfer coefficient By combining with finite element analysis and setting appropriate boundary conditions, a simulation model of salt and moisture diffusion is constructed.

[0061] Step Six: Based on the relationship between ultrasonic power and the mass transfer coefficients of salt and water, establish the relationship between different ultrasonic powers and the salt mass transfer coefficient. Water mass transfer coefficient The exponential function model between them;

[0062] Step 7: Combine the simulation model from Step 5 with the mathematical model from Step 6 to achieve a visual simulation of the three-dimensional diffusion distribution of salt and moisture in beef under different ultrasonic power conditions.

[0063] In step one, the experimental sample is taken from the hindquarters of a Simmental bull.

[0064] First, remove the visible fat and tendons from the surface of the beef, then cut the beef into several cubes (10 × 10 × 10 cm). 3 The processed beef was then placed in an ultrasonic tumbling apparatus along with the marinade at a mass ratio of 100:35. The marinade consisted of an aqueous solution of sodium tripolyphosphate, sodium pyrophosphate, sodium hexametaphosphate, and sodium chloride. The drum speed was set to 10 rpm, the inner drum vacuum was controlled at -0.08 MPa, the temperature was maintained at 4℃, and the tilt angle was kept at 55°. The ultrasonic power was set to 0, 100, 300, 500, and 700 W, and the ultrasonic time was set to 30, 60, 90, 120, 150, and 180 min. After marinating, the sample was immediately removed from the tumbling drum and the surface was wiped dry with absorbent paper for subsequent analysis.

[0065] In step two, the sodium chloride content of the sample is determined using a salinity meter. The specific procedure is as follows:

[0066] Weigh 10 g of marinated beef, add 13 times its volume of primary water, homogenize thoroughly using a homogenizer, let stand overnight, and centrifuge at 13,200 × g for 10 min at 4℃. Collect the supernatant and determine its salt content using a salinity meter. Each experimental group was repeated 3 times. The salt content is expressed as g / 100 g. For moisture content analysis, take 5 g of marinated beef, place it in a glass weighing bottle, tilt the cap at the bottle opening, and place it in a constant temperature drying oven at 103℃ for 4.5 h. After heating, immediately transfer it to a desiccator to cool for 45 min until the sample mass stabilizes, weigh it, and calculate the moisture content.

[0067] In step three, the salt and moisture content data of beef at different processing times are used as input values. Fick's second law diffusion equation is introduced to solve for the salt mass transfer coefficient at the corresponding time points under different ultrasonic power conditions. and water mass transfer coefficient Furthermore, the salt and moisture content at equilibrium was obtained by tumbling beef for 30 hours. The expression for the Fick's second law diffusion equation is as follows:

[0068] ;

[0069] ;

[0070] in, and These represent the initial salt and moisture content (g / 100 g), respectively. and These represent the salt and moisture content at different time points (s), respectively. and These represent the salt and moisture content (m² / s) at the corresponding salinity equilibrium state. and These represent the salt and water diffusion coefficients, respectively. This indicates the thickness (m) of the beef sample.

[0071] In step four, a three-dimensional physical field model and a geometric model of the beef sample are established in COMSOL software using finite element analysis. The physical field is selected in COMSOL Multiphysics software using the "Dilute Mass Transport (Tds module)" interface to describe the diffusion behavior of salt and water in beef tissue. The geometric model is constructed based on the actual size and shape of the beef sample (10 × 10 × 10 cm). 3 A cube is used to construct a corresponding three-dimensional geometric model to reflect the spatial structural characteristics of the sample. The results are as follows: Figure 3 As shown. The sample material properties are of arbitrary tissue type, and the sample mesh is divided into a conventional physical field controlled mesh.

[0072] In step five, the experimentally measured salt diffusion coefficient will be used. and moisture diffusion coefficient The data is input into the model, and the mass transfer coefficient is adjusted according to the ultrasonic power conditions. Furthermore, the rarefied mass transfer is a transient process; the boundary conditions are set to transient external convection flux types for all six surfaces. The initial salt content is the intrinsic salt content of fresh beef shank, the initial moisture content is the intrinsic water content of fresh beef shank, and the external concentration is the salt concentration in the marinade.

[0073] The transient equation for mass transfer of salt and water is:

[0074] ;

[0075] ;

[0076] The concentration boundary is: ;

[0077] The boundary flux is: ;

[0078] Where D represents the effective diffusion coefficient of salt or moisture (m 2 / s), This represents the initial concentration at the given inflow surface (mol / m³). 3 ), This represents the mass transfer coefficient (m / s). The concentration of the bulk solution outside the model (mol / m³) 3 );

[0079] Subsequently, using COMSOL's finite element numerical solver, the migration of salt and water in beef tissue under different ultrasonic powers and processing times was visualized.

[0080] In step six, the ultrasonic power is compared with the diffusion coefficient obtained experimentally. and A functional relationship was established, and referring to Lenart's (1980) research, an exponential function was selected for fitting. The fitted functional equation was further used as a mathematical model to calculate the diffusion coefficients of salt and water in beef under different ultrasonic power conditions.

[0081] Step seven combines the salt and moisture diffusion simulation from step five with the mathematical model from step six to construct a modeling system for studying the migration patterns of salt and moisture in beef under ultrasonic synergistic tumbling and marinating. The salt diffusion coefficient under different ultrasonic powers is determined based on the mathematical model. and moisture diffusion coefficient This was incorporated into a simulation model to achieve a visual simulation of the diffusion and distribution of salt and moisture in beef under different ultrasonic powers during synergistic tumbling.

[0082] Example 2: Salt content, moisture content, and diffusion coefficient of beef in the example and The visualization of the three-dimensional diffusion process and the results of the mathematical model fitting are as follows:

[0083] (1) Salt and moisture content of beef under different ultrasonic powers and processing times:

[0084] like Figure 2 As shown, the salt and moisture contents in beef samples changed under different ultrasonic power and processing time conditions. The results indicate that the diffusion behavior of salt and moisture in beef is affected by ultrasonic power and tumbling time. With increasing ultrasonic power and processing time, the salt and moisture contents in the samples both showed an upward trend. This suggests that the synergistic effect of ultrasound and tumbling can accelerate the penetration and diffusion of salt and moisture, thereby improving the marinating efficiency of beef.

[0085] (2) Diffusion coefficients of salt and moisture in beef under different ultrasonic powers:

[0086] Substituting the marinating time, salt content, and moisture content of the beef into Fick's second law diffusion equation, the diffusion coefficients obtained are as follows. Table 1 shows the salt diffusion coefficients calculated based on Fick's second law diffusion equation. exist Between m² / s, the moisture diffusion coefficient exist Between m² / s. Significant differences exist in the salt or water mass transfer coefficients under different ultrasonic power treatment conditions ( Compared with the control group without ultrasound treatment, after ultrasound treatment... and The values ​​all increased significantly, and showed a continuous upward trend with the increase of ultrasound power. ).

[0087] Table 1. Diffusion coefficients of salt and moisture in beef under different ultrasonic powers.

[0088]

[0089] Note: Different letters "ad" indicate that the diffusion coefficients of salt and water in beef vary significantly under different ultrasonic powers. ).

[0090] (3) Visualization of the diffusion of salt and moisture in beef under different ultrasound powers:

[0091] All surfaces of the beef samples were designated as inflow surfaces for the marinade, and the diffusion coefficients of each treatment group were incorporated into the geometric model to simulate the salt and moisture diffusion process. Figure 4 As shown, the three-dimensional streamline diagram clearly presents the transient behavior of salt and moisture diffusion under different ultrasonic synergistic tumbling curing conditions. It is evident that in the initial stage of curing, the salt and moisture streamlines exhibit irregular distribution and counter-current flow. These results indicate that the salt and moisture within the beef exhibit a multidirectional, irregular, and transient process in the initial stage of curing. With prolonged curing time, the salt and moisture streamlines tend to diffuse towards the center of the beef sample. This is due to the concentration difference between the inside and outside of the beef, as well as the unidirectional transport of the curing solution along the curing direction.

[0092] also, Figure 5This paper presents a 3D simulation of salt and moisture diffusion in beef samples after different ultrasonic synergistic tumbling and marinating processes. Linear color scales represent the salt and moisture content of the beef. In the initial stage of marinating, the edges of the beef cross-section appear red, while the central area is predominantly blue. This phenomenon indicates that the transfer of salt and moisture occurs very rapidly when the marinade comes into contact with the beef. As the ultrasonic power and tumbling time increase, the color of the beef cross-section gradually changes from blue to red, indicating that the salt and moisture content in the beef exhibits a dynamic distribution and a continuously increasing trend. Furthermore, the simulation of the marinating process revealed that the ultrasonically treated beef samples were redder than the non-ultrasonic treated samples, with the 700W ultrasonic treatment group showing the most vibrant red color. This indicates that the diffusion behavior of salt and moisture in beef is significantly affected by ultrasonic power, and ultrasonic synergistic tumbling treatment can effectively improve the diffusion rate of the marinade. These results demonstrate that this simulation method can dynamically simulate the diffusion behavior of salt and moisture during beef marinating and optimize marinating process parameters accordingly.

[0093] (4) Correlation analysis between ultrasonic power and the mass transfer rates of salt and water:

[0094] According to Lenart (1980), during ultrasonic-assisted tumbling and marinating, the ultrasonic power has an exponential relationship with the diffusion coefficients of salt and moisture in beef. Figure 6 It can be seen that the goodness of fit R² between ultrasonic power and salt diffusion coefficient is 0.997, while the goodness of fit R² between ultrasonic power and moisture diffusion coefficient is 0.971, proving that the fitting accuracy of the two is high, indicating that there is a clear correspondence between ultrasonic power and the diffusion coefficients of salt and moisture.

[0095] (5) Application of model methods:

[0096] A specific ultrasonic power is determined based on meat processing requirements. Then, at this power, the corresponding salt or water mass transfer coefficient is derived using the mathematical model from step six. Furthermore, the obtained salt or water mass transfer coefficient is substituted into the diffusion simulation model from step five, and the migration of salt and water in beef tissue at different time stages under this ultrasonic power is visualized using COMSOL's finite element numerical solver.

[0097] In summary, this patent utilizes ultrasonic synergistic tumbling and marinating technology, taking beef shank as the experimental subject. By measuring the changes in salt and moisture content in beef samples under different ultrasonic power conditions, and combining this with Fick's second law diffusion model, the corresponding salt and moisture mass transfer coefficients are obtained. Based on this, a three-dimensional physical field model and a geometric model of the beef sample are constructed using finite element analysis software. A simulation model of salt and moisture diffusion is established based on the input mass transfer coefficients and set boundary conditions. Simultaneously, a functional relationship between different ultrasonic powers and the mass transfer coefficients of salt and moisture is established. The combined use of these two models can visualize the spatiotemporal distribution of salt and moisture under arbitrary ultrasonic power conditions. This modeling method is characterized by its ease of operation and dynamic visualization, allowing observation of the penetration of marinade into the beef during the marinating process. It provides a scientific basis and technical support for the optimization of meat product processes, quality improvement, and industrial application, demonstrating promising application prospects and contributing to the promotion of ultrasonic synergistic tumbling and marinating technology in meat marinating.

[0098] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A finite element method for modeling the mass transfer of brine in ultrasonically tumbling marinated beef, characterized in that: The method includes: Step 1: Prepare beef samples with marinating times of 30, 60, 90, 120 and 180 min and ultrasonic power of 0, 100, 300, 500 and 700 W respectively using ultrasonic synergistic tumbling marinating technology. Step 2: Determine the salt and moisture content of beef under different treatment times and different ultrasonic powers; Step 3: Based on Fick's second law diffusion model, calculate the mass transfer coefficients of salt and moisture in beef under different processing conditions using experimentally measured salt and moisture content. and value; Step 4: Establish a three-dimensional physical field model and a geometric model of the beef sample in COMSOL software through finite element analysis; Step 5: Adjust the salt mass transfer coefficient. With water mass transfer coefficient By combining with finite element analysis and setting appropriate boundary conditions, a simulation model of salt and moisture diffusion is constructed. Step Six: Based on the relationship between ultrasonic power and the mass transfer coefficients of salt and water, establish the relationship between different ultrasonic powers and the salt mass transfer coefficient. Water mass transfer coefficient The exponential function model between them; Step 7: Combine the simulation model from Step 5 with the mathematical model from Step 6 to achieve a visual simulation of the three-dimensional diffusion distribution of salt and moisture in beef under different ultrasonic power conditions.

2. The method for modeling the mass transfer of brine in ultrasonic tumbling marinated beef based on finite element method as described in claim 1, wherein step two includes: The determination of salt content includes: weighing 10 g of marinated beef, adding 13 times the volume of primary water, homogenizing and mixing thoroughly with a homogenizer, and centrifuging at 13,200×g for 10 min; collecting the supernatant and determining the salt content using a salinity meter. The determination of the moisture content includes: weighing 5 g of marinated beef, placing it in a constant temperature oven, setting the oven temperature to 103℃ and maintaining it for 4.5 h, transferring it to a desiccator to cool for 1 h until the sample quality is stable, weighing it and calculating the moisture content.

3. The method for modeling the mass transfer of brine in ultrasonic tumbling marinated beef based on finite element method as described in claim 1, wherein step three includes: Using the salt and moisture content data of beef at different processing times as input values, and incorporating Fick's second law diffusion equation, the salt mass transfer coefficient at corresponding time points was solved under different ultrasonic power conditions. and water mass transfer coefficient Furthermore, the salt and moisture content in the equilibrium state was obtained by tumbling the beef for 30 hours. The diffusion equation according to Fick's second law is: ； ； in, and These represent the initial salt and moisture content, respectively. and These represent the salt and moisture content at different time points. and These represent the salt and moisture content at the corresponding salinity equilibrium state, respectively. and These represent the salt and water diffusion coefficients, respectively. This indicates the thickness of the beef sample.

4. The method for modeling the mass transfer of brine in ultrasonic tumbling marinated beef based on finite element method as described in claim 1, wherein step four includes: A three-dimensional physical field model and a geometric model of the beef sample were established in COMSOL software using finite element analysis. The "Dilute Mass Transfer" physical field interface was selected to describe the diffusion behavior of salt and moisture in the beef tissue. The geometric model is constructed based on the size and shape of the actual beef sample, creating a corresponding three-dimensional geometric model to reflect the spatial structural characteristics of the sample. The sample material properties are arbitrary tissue types, and the sample mesh is divided into conventional physical field controlled meshes.

5. The method for modeling the mass transfer of brine in ultrasonic tumbling marinated beef based on finite element method as described in claim 1, wherein step five includes: The experimentally measured salt diffusion coefficient and moisture diffusion coefficient Input the data into the model and adjust the mass transfer coefficient according to the ultrasonic power conditions; in addition, the rare matter transfer is a transient process; the boundary conditions are set to be transient external convection flux types for all 6 surfaces; The initial salt content is the salt content of fresh beef shank itself, the initial moisture content is the moisture content of fresh beef shank itself, and the external concentration is the salt concentration in the marinade. The transient equation for mass transfer of salt and water is: ； ； The concentration boundary is: ; The boundary flux is: ; Where D represents the effective diffusion coefficient of salt or moisture. This represents the initial concentration at a given inflow surface. Indicates the mass transfer factor. Indicates the concentration of the bulk solution outside the model; Subsequently, using COMSOL's finite element numerical solver, the migration of salt and water in beef tissue under different ultrasonic powers and processing times was visualized.

6. The method for modeling the mass transfer of brine in ultrasonic tumbling marinated beef based on finite element method as described in claim 1, wherein step six includes: By comparing the ultrasonic power with the experimentally obtained diffusion coefficient and A functional relationship was established and fitted using an exponential function. The fitted functional equation was then used as a mathematical model to calculate the diffusion coefficients of salt and water in beef under different ultrasonic power conditions.

7. The method for modeling the mass transfer of brine in ultrasonic tumbling marinated beef based on finite element method as described in claim 1, wherein step seven includes: By combining the salt and moisture diffusion simulation in step five with the exponential function model in step six, a modeling system for studying the migration patterns of salt and moisture in beef under ultrasonic synergistic tumbling and marinating is constructed. The salt diffusion coefficient under different ultrasonic powers is determined based on the exponential function model. and moisture diffusion coefficient This was incorporated into a simulation model to achieve a visual simulation of the diffusion and distribution of salt and moisture in beef under different ultrasonic powers during synergistic tumbling.

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