An optimization method for regenerator based on local non-thermal equilibrium coupling model

Abstract

The optimization method of a regenerator based on a local non-thermal equilibrium coupling model belongs to the field of comprehensive performance optimization of regenerators. The implementation method of the present invention is as follows: based on the one-dimensional local non-thermal equilibrium model and the three-dimensional local non-thermal equilibrium model of the regenerator, design variables are calculated and iterated to obtain the local non-thermal equilibrium coupling model of the regenerator; the present invention improves the optimization accuracy of the regenerator by establishing a local non-thermal equilibrium coupling model of the free piston Stirling generator regenerator to replace the previous single idealized model; the regenerator optimization problem is constructed with the objective function including the flow pressure drop and heat conduction loss optimization targets combined with the regenerator performance constraint conditions; according to the regenerator optimization problem, the multi-objective optimization of the design variables of the regenerator is performed under preset working conditions, and the flow resistance loss and heat conduction loss generated by the regenerator are suppressed according to the structural parameters of the optimized regenerator, thereby improving the suppression accuracy and efficiency of the flow resistance loss and heat conduction loss of the regenerator.

Description

Technical Field

[0001] The present invention relates to a regenerator optimization method based on a local non-thermal equilibrium coupling model, and in particular to a comprehensive performance optimization design method for a free piston Stirling generator regenerator based on a local non-thermal equilibrium coupling model, belonging to the field of comprehensive performance optimization of regenerators. Background Art

[0002] As a core component of a free-piston Stirling generator, the regenerator is composed of stainless steel wire mesh woven in a plain or other pattern. Its primary function is to store heat from high-temperature gas flowing through it and release it when low-temperature gas flows through it, thereby achieving heat exchange. The flow resistance and thermal conductivity losses during this heat exchange process are the main factors limiting the regenerator's overall performance, which in turn determines the power generation performance of the free-piston Stirling generator. Current research methods for regenerators are relatively inaccurate, especially in wire mesh regenerators, where the flow resistance and thermal conductivity losses caused by the porous structure are more pronounced. When gas flow rates are high or when different working gases are used, this relatively fixed structure is difficult to meet the requirements of the regenerator in these diverse scenarios, nor can it meet the growing performance requirements of free-piston Stirling generators. Therefore, there is an urgent need for more precise and flexible design and optimization strategies for regenerators. Summary of the Invention

[0003] In order to solve the problem of large flow resistance loss and heat conduction loss caused by low research accuracy and inflexible design and optimization of existing free piston Stirling generator regenerators, the purpose of the present invention is to provide a regenerator optimization method based on a local non-thermal equilibrium coupling model. This method replaces the previous single idealized model by establishing a local non-thermal equilibrium coupling model of the free piston Stirling generator regenerator, thereby improving the optimization accuracy of the regenerator and improving the regenerator performance. At the same time, this method also addresses the problem of immature optimization schemes caused by the unified structure of the regenerator, and uses a more flexible and adaptable optimization method to reduce the flow resistance loss and heat conduction loss of the free piston Stirling generator regenerator, reduce the design cost of the regenerator, and shorten the design cycle.

[0004] The purpose of the present invention is achieved through the following technical solutions.

[0005] The present invention discloses a method for optimizing a regenerator based on a local non-thermal equilibrium coupling model, comprising the following steps:

[0006] Step 1: Based on the regenerator design requirements, determine the design variables and their value ranges for the free piston Stirling generator regenerator shell and filling matrix, as well as the regenerator operating conditions. The shell design variable is the shell diameter; the filling matrix design variables are the wire mesh diameter and porosity; the operating conditions include the initial operating pressure, engine speed, and hot end temperature.

[0007] Step 2: establishing a one-dimensional local non-thermal equilibrium model and a three-dimensional local non-thermal equilibrium model of a free piston Stirling generator regenerator based on the initial design variables determined in step 1;

[0008] Step 3: Calculate and iterate the design variables using the one-dimensional local non-thermal equilibrium model and the three-dimensional local non-thermal equilibrium model of the regenerator in step 2 to obtain a coupled model of the local non-thermal equilibrium of the regenerator. The specific iterative process is as follows: first, calculate the temperature and pressure distribution in the regenerator using the one-dimensional local non-thermal equilibrium model, and input the results as boundary conditions into the three-dimensional local non-thermal equilibrium model; then, use the three-dimensional local non-thermal equilibrium model to perform more detailed flow and heat transfer calculations to obtain new temperature and pressure data; feed these data back to the one-dimensional local non-thermal equilibrium model, recalculate and iterate; after multiple iterations, when the temperature and pressure change errors of the one-dimensional and three-dimensional simulations are less than a preset percentage threshold, it is determined that the iterative convergence condition is met;

[0009] Preferably, when the temperature and pressure variation errors of the one-dimensional and three-dimensional simulations are less than 5%, it is determined that the iterative convergence condition is met.

[0010] Step 4: Perform fluid dynamics and thermodynamics analysis on the coupled model in step 3, and obtain the flow resistance loss and heat conduction loss of the regenerator to evaluate its overall performance. The flow resistance loss expression is:

[0011]

[0012] Where D is the regenerator diameter, v is the average flow velocity of the gas, and ΔP is the flow pressure drop, which is expressed as follows:

[0013]

[0014] Where L is the regenerator length, ρ is the gas density, and D h is the equivalent diameter, f is the friction coefficient of gas flowing through the regenerator, and the calculation formula is:

[0015]

[0016] Where, is the porosity, d s is the wire mesh diameter, Re m is the dynamic Reynolds number, expressed as follows:

[0017]

[0018] Where μ is the dynamic viscosity of the gas;

[0019] The heat loss expression is:

[0020]

[0021] Among them, k m is the heat transfer coefficient of the gas flowing through the wire mesh packing in the regenerator, T h is the hot end temperature, T c is the cold end temperature, A m is the cross-sectional area of ​​the metal filler and is expressed as follows:

[0022]

[0023] The comprehensive performance evaluation index of the regenerator is expressed by comprehensive performance parameters, and the heat loss coefficient h is introduced on this basis. R Calculations were performed to further quantify the impact of heat loss on regenerator performance and improve the accuracy of comprehensive performance evaluation of regenerators, as follows:

[0024]

[0025] Where σ is the specific surface area, which is related to the porosity and mesh diameter, and h R is the heat loss coefficient, which are expressed as follows:

[0026]

[0027] Where m is the mass flow rate of gas, c p is the specific heat capacity of the gas;

[0028] Arranging the above formulas (8) and (10), we can obtain the expression of the comprehensive performance parameters of the regenerator as follows:

[0029]

[0030] Step 5: With the objective function including the optimization objectives of flow pressure drop and heat conduction loss, combined with the constraint conditions described in Equation (12), a regenerator optimization problem based on the local non-thermal equilibrium coupling model is constructed. According to the regenerator optimization problem based on the local non-thermal equilibrium coupling model, a multi-objective optimization of the design variables of the regenerator is performed under the working conditions of Step 1 to obtain the optimized structural parameters of the regenerator. The flow resistance loss and heat conduction loss generated by the regenerator in Step 4 are suppressed based on the optimized structural parameters of the regenerator; wherein, the objective function includes flow pressure drop and heat conduction loss, and there are a total of 4 constraints, including 3 regenerator performance constraints. The constraint expressions are expressed as follows:

[0031]

[0032] The method further includes step 6: bringing the structural parameters obtained in step 5 into step 3 to obtain a new coupling model, and then obtaining the regenerator performance evaluation index Rosc through step 4, and improving the optimization accuracy of the regenerator structural parameters based on the updated regenerator performance evaluation index Rosc.

[0033] The method further includes step 7: changing the design variables and their ranges and working conditions of the regenerator in step 1, repeating steps 1 to 5, and obtaining the structural parameter values ​​of the regenerator with the optimal comprehensive performance under the conditions.

[0034] Beneficial effects:

[0035] 1. The present invention discloses a regenerator optimization method based on a local non-thermal equilibrium coupling model. By establishing a local non-thermal equilibrium coupling model of a free piston Stirling generator regenerator to replace the previous description of it by a single model, the optimization accuracy and efficiency of the regenerator can be improved.

[0036] 2. The present invention discloses a method for optimizing a regenerator based on a local non-thermal equilibrium coupling model. The method calculates the temperature and pressure distribution within the regenerator using a one-dimensional local non-thermal equilibrium model and inputs the results as boundary conditions into a three-dimensional model. The three-dimensional model is then used to perform more refined flow and heat transfer calculations to obtain new temperature and pressure data. This data is fed back into the one-dimensional local non-thermal equilibrium model for recalculation and iteration. Multiple design variable calculations and iterations are performed. When the temperature and pressure variation errors between the one-dimensional and three-dimensional simulations are less than a preset percentage threshold, the iterative convergence condition is determined to be satisfied, thereby obtaining a local non-thermal equilibrium coupling model of the regenerator. A regenerator optimization problem based on the local non-thermal equilibrium coupling model is constructed using an objective function including flow pressure drop and heat conduction loss optimization objectives, combined with regenerator performance constraints. Based on the regenerator optimization problem based on the local non-thermal equilibrium coupling model, multi-objective optimization of the design variables of the regenerator is performed under the operating conditions of step 1 to obtain optimized structural parameters of the regenerator. The optimized structural parameters of the regenerator are used to suppress the flow resistance loss and heat conduction loss generated in the regenerator, thereby improving the accuracy and efficiency of suppressing the flow resistance loss and heat conduction loss of the regenerator.

[0037] 3. The present invention discloses a regenerator optimization method based on a local non-thermal equilibrium coupling model, in which the iterative convergence condition is selected as the temperature and pressure variation error of the one-dimensional and three-dimensional simulations is less than 5%. This convergence condition can take into account both the optimization accuracy and efficiency of the regenerator structural parameters.

[0038] 4. The present invention discloses a regenerator optimization method based on a local non-thermal equilibrium coupling model. The method performs fluid dynamics and thermodynamics analysis on the local non-thermal equilibrium coupling model of the regenerator, obtains expressions for the flow resistance loss and heat conduction loss of the regenerator, and quantitatively evaluates the comprehensive performance of the regenerator. The comprehensive performance evaluation index of the regenerator is expressed using comprehensive performance parameters, and on this basis, the heat loss coefficient h is introduced. R Calculations are performed to further quantify the impact of heat loss on regenerator performance and improve the accuracy of comprehensive performance evaluation of regenerators.

[0039] 5. The present invention discloses a regenerator optimization method based on a local non-thermal equilibrium coupling model. This method addresses the problem of immature optimization schemes caused by the unified structure of the regenerator, and reduces the flow resistance loss and heat conduction loss of the free piston Stirling generator regenerator with a more flexible and adaptable optimization method. This overcomes the problems of immature research schemes for existing regenerators and low versatility of design optimization methods, solves the problems of low accuracy and design efficiency of conventional design methods, reduces design costs, and shortens the design cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a rendering of a parameterized model of a regenerator according to an embodiment of the present invention;

[0041] Figure 2 Establishing a flow chart for the local non-thermal equilibrium coupling model of an embodiment of the present invention;

[0042] Figure 3 This is a flow chart of the regenerator effectiveness optimization strategy according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0044] Existing research on regenerators suffers from low research accuracy, fixed structural designs, and an inability to meet diverse usage scenarios. These issues lead to insufficient heat transfer and flow performance during actual use, resulting in significant losses. This method aims to improve the research and optimization of regenerators to reduce various losses in the flow and heat transfer processes.

[0045] First, a more accurate simulation model is established to describe the flow resistance loss and heat conduction loss of the regenerator. Second, during the optimization process, a more flexible optimization method is adopted in combination with the existing regenerator structure and design variables. That is, within a specific design parameter range, the regenerator is optimized through multi-objective comprehensive performance optimization to achieve the optimal balance in terms of flow resistance loss, heat conduction loss and overall performance, thereby achieving the redesign purpose.

[0046] The optimization method for a regenerator based on a local non-thermal equilibrium coupling model disclosed in this embodiment is specifically implemented in the following steps:

[0047] Step 1: According to the design requirements, determine the design variables and value ranges of the free piston Stirling generator regenerator shell and filling matrix, and the working conditions of the regenerator; the specific design variables are porosity Screen diameter d s (mm), regenerator diameter D (mm), where the range of design variables is 0.02≤d s ≤0.09, 30≤D≤60; the initial values ​​are: d s =0.06mm, D=30mm; working conditions include: working pressure of 3MPa, initial hot end temperature of 700K, initial cold end temperature of 300K, and working frequency of 50Hz;

[0048] Step 2: Based on the initial design variables determined in step 1, establish the one-dimensional and three-dimensional local non-thermal equilibrium models of the free piston Stirling generator regenerator, as shown in the attached figure. Figure 1 ;

[0049] Step 3: Use the one-dimensional and three-dimensional local non-thermal equilibrium models of the regenerator in step 2 to calculate and iterate the design variables to obtain the coupled model of the local non-thermal equilibrium of the regenerator. The specific iterative process is as follows: First, calculate the temperature and pressure distribution in the regenerator through the one-dimensional model, and input the results as boundary conditions into the three-dimensional model; then, use the three-dimensional model to perform more detailed flow and heat transfer calculations to obtain new temperature and pressure data; feed these data back to the one-dimensional model, recalculate and iterate; after multiple iterations, when the temperature and pressure change error of the two is less than 5%, it is considered that the iterative convergence condition is met. The iterative process of the one-dimensional and three-dimensional models is shown in the attached figure. Figure 2 ;

[0050] Step 4: Perform fluid mechanics and thermodynamics analysis on the coupled model in step 3, and obtain the velocity of the gas flowing through the regenerator as 5.40 m / s. By calculating formulas (13)(14)(15)(16)(17), the values ​​of each parameter are obtained as Re m =63.99, D h =0.09mm, f=1.3139, ΔP=3.0316×10 5 Pa, and finally the flow resistance loss Q in the regenerator is calculated P =6.245×10 3 J; By calculating formula (18) (19), the cross-sectional area A of the metal filler is obtained m =2.827×10 - 4 m2 , heat loss Q loss =6.8602×10 4 J. Here, the model coupling specifically uses GT-power software and ANSYS Fluent software, and the comprehensive performance parameter of the regenerator Rosc = 35.91% is calculated by formula (20) to evaluate the comprehensive performance of the regenerator;

[0051]

[0052]

[0053] Among them, the density of the gas ρ is 4.7467Kg / m 3 , the dynamic viscosity of the gas is 2.20029×10 -5 Pa·s, porosity is 0.6, the wire mesh diameter d s is 0.06mm, the regenerator length is 30mm, and the heat transfer coefficient k of the gas flowing through the wire mesh is m 1.82×10 4 W / m 2 , the specific heat capacity cp of the gas is 5194.2 J / Kg·K, the mass flow rate m of the gas is 2.54 Kg / s, and the specific surface area σ is 2.667×10 4 m -1 , hot end temperature T h is 700K, the cold end temperature T c 300K;

[0054] Step 5: With the objective function including the optimization targets of flow pressure drop and heat conduction loss, combined with the constraint conditions described in formula (21), a regenerator optimization problem based on the local non-thermal equilibrium coupling model is constructed. According to the regenerator optimization problem based on the local non-thermal equilibrium coupling model, a multi-objective optimization of the design variables of the regenerator is performed under the working conditions of step 1 to achieve the purpose of suppressing the flow resistance loss and heat conduction loss generated by the regenerator in step 4, and obtain the optimized structural parameters of the regenerator; this embodiment specifically uses the NSLS (Non-dominated Sorting Local Search) algorithm; wherein, the objective function includes flow pressure drop and heat conduction loss, and there are a total of 4 constraints, including 3 regenerator performance constraints. The constraint expressions can be expressed as follows:

[0055]

[0056] By writing the corresponding MATLAB optimization design program, solve and verify whether the optimal solution meets the design requirements;

[0057] The optimization strategy for this example is as follows Figure 3As shown, the porosity after optimization is Screen diameter d s , the optimal solutions for the regenerator diameter D are 0.9, 0.04 mm and 32 mm;

[0058] Step 6: Substitute the structural parameters obtained in step 5 into the new coupling model obtained in step 3, and obtain the velocity of the gas flowing through the regenerator as 5.52 m / s. Then, the values ​​of the parameters calculated in step 4 are the dynamic Reynolds number Re m =52.33, equivalent diameter D h =0.36mm, resistance coefficient f = 1.1213, specific surface area σ = 1×10 4 m -1 , the mass flow rate of gas m=2.72Kg / s, the density, dynamic viscosity and specific heat capacity of the gas remain unchanged, and the pressure drop ΔP=1.224×10 5 Pa, and finally the flow resistance loss Q in the regenerator is calculated P =2.999×10 3 J; By calculating the heat conduction loss, the cross-sectional area A of the metal filler is obtained m =8.043×10 -4 m 2 , heat loss Q loss =1.952×10 4 J; the regenerator performance evaluation index Rosc = 51.97%, and the comparison results of the optimal solution verification and the original solution are shown in Table 1;

[0059] Table 1 Comparison of comprehensive performance of regenerator before and after optimization

[0060]

[0061] Through the comparison in Table 1, it is found that in this embodiment, by optimizing and analyzing the structural parameters within the design variable range of the regenerator, it is found that after optimization, the porosity of the regenerator increases, the wire mesh diameter decreases, and the overall diameter of the regenerator increases. This result shows that in the regenerator, when the gas flow space increases and the wire mesh diameter becomes thinner, it is more conducive to improving the heat exchange effect. Specifically, the increased porosity can provide a larger gas flow channel. At the same time, the smaller wire mesh diameter enhances the contact area between the gas and the solid material. The two interact to improve the heat transfer efficiency. The present invention provides a theoretical reference and practical basis for further improvement of the regenerator, which helps to improve the performance of the regenerator in practical applications.

[0062] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A regenerator optimization method based on a local non-thermal equilibrium coupling model, characterized by: The following steps are included: Step 1: Based on the regenerator design requirements, determine the design variables and their value ranges for the free piston Stirling generator regenerator shell and filling matrix, as well as the regenerator operating conditions. The shell design variable is the shell diameter; the filling matrix design variables are the wire mesh diameter and porosity; the operating conditions include the initial operating pressure, engine speed, and hot end temperature. Step 2: establishing a one-dimensional local non-thermal equilibrium model and a three-dimensional local non-thermal equilibrium model of a free piston Stirling generator regenerator based on the initial design variables determined in step 1; Step 3: Calculate and iterate the design variables using the one-dimensional local non-thermal equilibrium model and the three-dimensional local non-thermal equilibrium model of the regenerator in step 2 to obtain a coupled model of the local non-thermal equilibrium of the regenerator. The specific iterative process is as follows: first, calculate the temperature and pressure distribution in the regenerator using the one-dimensional local non-thermal equilibrium model, and input the results as boundary conditions into the three-dimensional local non-thermal equilibrium model; then, use the three-dimensional local non-thermal equilibrium model to perform more detailed flow and heat transfer calculations to obtain new temperature and pressure data; feed these data back to the one-dimensional local non-thermal equilibrium model, recalculate and iterate; after multiple iterations, when the temperature and pressure change errors of the one-dimensional and three-dimensional simulations are less than a preset percentage threshold, it is determined that the iterative convergence condition is met; Step 4: Perform fluid dynamics and thermodynamics analysis on the coupled model in step 3, and obtain the flow resistance loss and heat conduction loss of the regenerator to evaluate its overall performance. The flow resistance loss expression is: Where D is the regenerator diameter, v is the average flow velocity of the gas, and ΔP is the flow pressure drop, which is expressed as follows: Where L is the regenerator length, ρ is the gas density, and D h is the equivalent diameter, f is the friction coefficient of gas flowing through the regenerator, and the calculation formula is: in, is the porosity, d s is the wire mesh diameter, Re m is the dynamic Reynolds number, expressed as follows: Where μ is the dynamic viscosity of the gas; The heat loss expression is: Among them, k m is the heat transfer coefficient of the gas flowing through the wire mesh packing in the regenerator, T h is the hot end temperature, T c is the cold end temperature, A m is the cross-sectional area of ​​the metal filler and is expressed as follows: The comprehensive performance evaluation index of the regenerator is expressed by comprehensive performance parameters, and the heat loss coefficient h is introduced on this basis. R Calculations were performed to further quantify the impact of heat loss on regenerator performance and improve the accuracy of comprehensive performance evaluation of regenerators, as follows: Where σ is the specific surface area, which is related to the porosity and mesh diameter, and h R is the heat loss coefficient, which are expressed as follows: Where m is the mass flow rate of gas, c p is the specific heat capacity of the gas; Arranging the above formulas (8) and (10), we can obtain the expression of the comprehensive performance parameters of the regenerator as follows: Step 5: With the objective function including the optimization objectives of flow pressure drop and heat conduction loss, combined with the constraint conditions described in formula (12), a regenerator optimization problem based on the local non-thermal equilibrium coupling model is constructed; according to the regenerator optimization problem based on the local non-thermal equilibrium coupling model, multi-objective optimization of the design variables of the regenerator is performed under the working conditions of step 1 to obtain the optimized structural parameters of the regenerator. The flow resistance loss and heat conduction loss generated by the regenerator in step 4 are suppressed based on the optimized structural parameters of the regenerator; wherein, the objective function includes flow pressure drop and heat conduction loss, and there are a total of 4 constraints, including 3 regenerator performance constraints. The constraint expressions are expressed as follows:

2. The method for optimizing a regenerator based on a local non-thermal equilibrium coupling model according to claim 1, wherein: The method further includes step 6: bringing the structural parameters obtained in step 5 into step 3 to obtain a new coupling model, and then obtaining the regenerator performance evaluation index Rosc through step 4, and improving the optimization accuracy of the regenerator structural parameters based on the updated regenerator performance evaluation index Rosc.

3. The method for optimizing a regenerator based on a local non-thermal equilibrium coupling model according to claim 1, wherein: The method further includes step 7: changing the design variables and their ranges and working conditions of the regenerator in step 1, repeating steps 1 to 5, and obtaining the structural parameter values ​​of the regenerator with the optimal comprehensive performance under the conditions.

4. The method for optimizing a regenerator based on a local non-thermal equilibrium coupling model according to claim 1, 2 or 3, wherein: In step 3, when the temperature and pressure variation errors of the one-dimensional and three-dimensional simulations are less than 5%, it is determined that the iterative convergence condition is met.

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