Optimization method of heat regenerator based on local non-thermal balance coupling model

Abstract

The invention discloses a heat regenerator optimization method based on a local non-thermal balance coupling model, and belongs to the field of heat regenerator comprehensive performance optimization. The implementation method comprises the steps that design variable calculation and iteration are conducted on the basis of a one-dimensional local non-thermal balance model and a three-dimensional local non-thermal balance model of the heat regenerator, and a local non-thermal balance coupling model of the heat regenerator is obtained; according to the method, the local non-thermal balance coupling model of the regenerator of the free piston Stirling generator is established to replace an original single idealized model, and the optimization precision of the regenerator is improved; a heat regenerator optimization problem is constructed by combining a heat regenerator performance constraint condition with an objective function including a flow pressure drop and a heat conduction loss optimization objective; according to the optimization problem of the heat regenerator, multi-objective optimization of design variables is conducted on the heat regenerator under the preset working condition, the flow resistance loss and the heat conduction loss generated by the heat regenerator are restrained according to the optimized structural parameters of the heat regenerator, and the restraining precision and efficiency of the flow resistance loss and the heat conduction loss of the heat regenerator are improved.

Description

Technical Field

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

[0002] As one of the core components of the free piston Stirling generator, the regenerator is composed of stainless steel wire mesh woven in plain or other ways. Its main function is to store the heat when the high-temperature gas flows through the regenerator and release it when the low-temperature gas flows through it, so as to achieve the purpose of heat exchange. The flow resistance loss and heat conduction loss in the flow heat exchange process are the main factors restricting the comprehensive performance of the regenerator, and the quality of the comprehensive performance of the regenerator restricts the power generation performance of the free piston Stirling generator. The current research methods on the regenerator are of low accuracy, especially in the wire mesh type regenerator, the flow resistance loss and heat conduction loss caused by the pore structure are more obvious. When the gas flow rate is too large or different working gases are replaced, this relatively fixed structure is difficult to meet the use requirements of the regenerator in the above different scenarios, and it cannot meet the growing performance requirements of the free piston Stirling generator; therefore, there is an urgent need for a more accurate and flexible design and optimization strategy for the regenerator. 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 an optimization method for a regenerator based on a local non-thermal equilibrium coupling model. The 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 performance of the regenerator. At the same time, the method also 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 adaptive optimization method, thereby reducing the design cost of the regenerator and shortening the design cycle.

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

[0005] The optimization method of the regenerator based on the local non-thermal equilibrium coupling model disclosed in the present invention comprises the following steps:

[0006] Step 1: According to the regenerator design requirements, determine the design variables and their value ranges of the free piston Stirling generator regenerator shell and filling matrix, and the working conditions of the regenerator; the design variable of the shell is the shell diameter; the design variable of the filling matrix is ​​its wire mesh diameter and porosity; the working conditions include the initial working 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 according to 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 into the three-dimensional local non-thermal equilibrium model as boundary conditions; then, use the three-dimensional local non-thermal equilibrium model to perform more sophisticated 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; through multiple iterations, when the temperature and pressure change errors of the one-dimensional and three-dimensional simulations are less than the 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 satisfied.

[0010] Step 4: Perform fluid mechanics 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 the comprehensive performance of the regenerator; 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, expressed as follows:

[0013]

[0014] Where L is the length of the regenerator, 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 The calculations were performed to further quantify the effect of heat loss on the performance of the regenerator and improve the accuracy of the comprehensive performance evaluation of the regenerator, as follows:

[0024]

[0025] Where σ is the specific surface area, which is related to the porosity and wire 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 the gas, c p is the specific heat capacity of the gas;

[0028] Arrange the above formulas (8) and (10) to obtain the expression of the comprehensive performance parameters of the regenerator:

[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 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, the multi-objective optimization of the design variables of the regenerator under the working conditions of step 1 is performed to obtain the structural parameters of the optimized regenerator, and the flow resistance loss and heat conduction loss generated by the regenerator in step 4 are suppressed according to the structural parameters of the optimized regenerator; wherein, the objective function includes flow pressure drop and heat conduction loss, and there are 4 constraints in total, including 3 regenerator performance constraints, and 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 according to 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, and repeating steps 1 to 5 to obtain the structural parameter values ​​of the optimal comprehensive performance of the regenerator under the conditions.

[0034] Beneficial effects:

[0035] 1. The present invention discloses a method for optimizing a regenerator based on a local non-thermal equilibrium coupling model, which can improve the optimization accuracy and efficiency of the regenerator 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.

[0036] 2. The present invention discloses a method for optimizing a regenerator based on a local non-thermal equilibrium coupling model. The temperature and pressure distribution in the regenerator is calculated by a one-dimensional local non-thermal equilibrium model, and the result is input into a three-dimensional model as a boundary condition. Then, the three-dimensional model is used to perform more refined flow and heat transfer calculations to obtain new temperature and pressure data. These data are fed back to the one-dimensional local non-thermal equilibrium model, recalculated and iterated. By performing design variable calculations and iterations for multiple times, when the temperature and pressure variation 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 satisfied, and a local non-thermal equilibrium coupling model of the regenerator is obtained. The objective function includes the optimization objectives of flow pressure drop and heat conduction loss, and the regenerator optimization problem based on the local non-thermal equilibrium coupling model is constructed in combination with the regenerator performance constraint condition. According to the regenerator optimization problem based on the local non-thermal equilibrium coupling model, the multi-objective optimization of the design variables of the regenerator is performed under the working conditions of step 1 to obtain the structural parameters of the optimized regenerator. According to the optimized structural parameters of the regenerator, the flow resistance loss and heat conduction loss generated by the regenerator are suppressed, thereby improving the suppression accuracy and efficiency of the flow resistance loss and heat conduction loss of the regenerator.

[0037] 3. The present invention discloses an optimization method for a regenerator based on a local non-thermal equilibrium coupling model, in which the iterative convergence condition is selected as the temperature and pressure change error of 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 an optimization method for a regenerator based on a local non-thermal equilibrium coupling model, which performs fluid mechanics and thermodynamics analysis on the local non-thermal equilibrium coupling model of the regenerator, obtains the flow resistance loss and heat conduction loss expressions of the regenerator, and quantitatively evaluates the comprehensive performance of the regenerator; the comprehensive performance evaluation index of the regenerator is expressed by a comprehensive performance parameter, and on this basis, the heat loss coefficient h is introduced R Calculations are performed to further quantify the impact of heat loss on the performance of the regenerator and improve the accuracy of the comprehensive performance evaluation of the regenerator.

[0039] 5. The present invention discloses an optimization method for a regenerator based on a local non-thermal equilibrium coupling model. In order to solve the problem of immature optimization schemes caused by the unified structure of the regenerator, a more flexible and adaptable optimization method is used to reduce the flow resistance loss and heat conduction loss of the free piston Stirling generator regenerator, overcome the problems of immature research schemes for existing regenerators and low versatility of design optimization methods, solve the problems of low accuracy and design efficiency of conventional design methods, reduce design costs, and shorten design cycles. 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 A flow chart is established for the local non-thermal equilibrium coupling model of the embodiment of the present invention;

[0042] Figure 3 This is a flow chart of the strategy for optimizing the effectiveness of the regenerator 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] In view of the problems existing in the existing research on regenerators, such as low research accuracy, fixed structural design, and failure to meet diverse usage scenarios, the regenerators have insufficient heat transfer and flow performance during actual use, resulting in large losses. This method aims to improve the research and optimization of regenerators to achieve the purpose of reducing various losses in the flow and heat transfer process.

[0045] Firstly, a more accurate simulation model is established to describe the flow resistance loss and heat conduction loss of the regenerator. Secondly, in 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 comprehensive performance, so as to achieve the redesign purpose.

[0046] The optimization method of the regenerator based on the 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 is 3MPa, initial hot end temperature is 700K, initial cold end temperature is 300K, working frequency is 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: Calculate and iterate the design variables using the one-dimensional and three-dimensional local non-thermal equilibrium models 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 model, and input the results into the three-dimensional model as boundary conditions; 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 errors of the two are less than 5%, it is considered that the iterative convergence conditions are 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 length of the regenerator 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 is T c 300K;

[0054] 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 (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, the 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 structural parameters of the optimized 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, and 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 shown in the attached 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 = 2.72 Kg / s, the density, dynamic viscosity and specific heat capacity of the gas remain unchanged, and the pressure drop ΔP is calculated to be 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%, the optimal solution verification results and the original solution comparison results are shown in Table 1;

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

[0060]

[0061] Through the comparison of 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 the further improvement of the regenerator, which helps to improve the performance of the regenerator in practical applications.

[0062] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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 method for optimizing a regenerator based on a local non-thermal equilibrium coupling model, characterized in that: The following steps are included: Step 1: According to the regenerator design requirements, determine the design variables and their value ranges of the free piston Stirling generator regenerator shell and filling matrix, and the working conditions of the regenerator; the design variable of the shell is the shell diameter; the design variable of the filling matrix is ​​its wire mesh diameter and porosity; the working conditions include the initial working 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 according to 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 into the three-dimensional local non-thermal equilibrium model as boundary conditions; then, use the three-dimensional local non-thermal equilibrium model to perform more sophisticated 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; through multiple iterations, when the temperature and pressure change errors of the one-dimensional and three-dimensional simulations are less than the preset percentage threshold, it is determined that the iterative convergence condition is met; Step 4: Perform fluid mechanics 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 the comprehensive performance of the regenerator; 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, expressed as follows: Where L is the length of the regenerator, 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 are performed to further quantify the impact of heat loss on the performance of the regenerator and improve the accuracy of the comprehensive performance evaluation of the regenerator, as follows: Where σ is the specific surface area, which is related to the porosity and wire mesh diameter, and h R is the heat loss coefficient, which are expressed as follows: Where m is the mass flow rate of the gas, c p is the specific heat capacity of the gas; Arrange the above formulas (8) and (10) to obtain the expression of the comprehensive performance parameters of the regenerator: 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, the multi-objective optimization of the design variables of the regenerator under the working conditions of step 1 is performed to obtain the structural parameters of the optimized regenerator, and the flow resistance loss and heat conduction loss generated by the regenerator in step 4 are suppressed according to the structural parameters of the optimized regenerator; wherein, the objective function includes flow pressure drop and heat conduction loss, and there are 4 constraints in total, including 3 regenerator performance constraints, and 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, characterized in that: 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 according to 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, characterized in that: The method further includes step 7: changing the design variables and their ranges and working conditions of the regenerator in step 1, and repeating steps 1 to 5 to obtain the structural parameter values ​​of the optimal comprehensive performance of the regenerator 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, characterized in that: 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 iteration convergence condition is met.

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