阅读说明：本技术 一种基于布谷鸟算法的热声制冷机回热器参数优化设计方法 (Thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm ) 是由 杜军 徐真杨 赵永杰 任繁 孙淼 于 2021-09-29 设计创作，主要内容包括：本发明公开了一种基于布谷鸟算法的热声制冷机回热器参数优化设计方法,包括S1、基于线性热声理论和板叠近似理论,建立回热器的无因次化制冷量方程和无因次化消耗声功方程；S2、设置制冷量方程和消耗声功方程中优化参数的约束条件；S3、建立布谷鸟算法的适应度函数,利用布谷鸟算法确定最优的一组设计参数的数值。本发明提供的方法操作简单,只需要输入初始参数和约束条件,即可快速得出设计方案,提高了求解的效率。(The invention discloses a thermoacoustic refrigerator regenerator parameter optimization design method based on a cuckoo algorithm, which comprises the steps of S1, establishing a dimensionless refrigerating capacity equation and a dimensionless sound power consumption equation of a regenerator based on a linear thermoacoustic theory and a plate stack approximation theory; s2, setting the constraint conditions of the optimized parameters in the refrigeration quantity equation and the sound power consumption equation; s3, establishing a fitness function of the cuckoo algorithm, and determining the optimal value of a group of design parameters by using the cuckoo algorithm. The method provided by the invention is simple to operate, and the design scheme can be quickly obtained only by inputting the initial parameters and the constraint conditions, so that the solving efficiency is improved.)

1. A thermoacoustic refrigerator regenerator parameter optimization design method based on a cuckoo algorithm is characterized by comprising the following steps:

s1, establishing a dimensionless refrigerating capacity equation and a dimensionless sound power consumption equation of the heat regenerator based on a linear thermoacoustic theory and a plate stacking approximate theory;

s2, setting the constraint conditions of the optimized parameters in the refrigeration quantity equation and the sound power consumption equation;

s3, establishing a fitness function of the cuckoo algorithm, and determining the optimal value of a group of design parameters by using the cuckoo algorithm.

2. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm of claim 1, wherein the dimensionless refrigeration capacity expression established in step S1 is:

the dimensionless consumed sound power expression is as follows:

wherein G is a dimensionless temperature gradient expressed as:

wherein L is_snTo dimensionless regenerator length, X_snDimensionless regenerator position, B porosity, D_rIs the drive ratio; delta_knDimensionless heat penetration thickness, Δ;_mnthe dimensionless temperature difference is shown, sigma is a Plantt number, and gamma is a specific heat ratio.

3. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm according to claim 1, wherein step S2 specifically comprises:

s21 regenerator length constraint: the thermoacoustic effects are generated between the pressure antinode and the node of the sound wave, so that two ends of the heat regenerator can not exceed the pressure antinode and the pressure node, and the first constraint condition is determined;

and S22 constraint of the center position of the regenerator: because the most intense part of the thermoacoustic effect occurs between the pressure antinode and the pressure node, the central position of the regenerator must be within the pressure node and the antinode to achieve the best result of the thermoacoustic effect, and the second constraint condition is determined;

constraint of porosity of S23: when the distance between the heat regenerator plates is 2-4 heat penetration thicknesses, the heat-sound conversion effect is the best, and the heat-sound conversion effect is determined as a third constraint condition;

constraint of S24 drive ratio: the driving ratio is the ratio of dynamic pressure amplitude to average pressure, the driving sound pressure is small, the energy generated by unit volume is small, the driving sound pressure is too large, the gas working medium is caused to generate turbulent flow, and the fourth constraint condition is determined.

4. The thermoacoustic refrigerator regenerator parameter optimization design method based on the cuckoo algorithm according to claim 3, wherein the first constraint condition is:

wherein L is_SIs the regenerator length and λ is the acoustic wavelength.

5. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm according to claim 3, wherein the second constraint condition is:

wherein, X_SIs the regenerator center position and λ is the acoustic wavelength.

6. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm according to claim 3, wherein the third constraint condition is:

2δ_k<y₀<4δ_k；

wherein, y₀Is the heat regenerator plate spacing, which is the porosity, delta, after dimensionless processing_kIs the heat penetration thickness of the working medium.

7. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm according to claim 3, wherein the fourth constraint condition is:

0.015<Dr<0.03；

wherein Dr is the drive ratio, and the value range of Dr is derived from experimental empirical values.

8. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm of claim 1, wherein the fitness function of the cuckoo algorithm established in step S3 is:

fmin＝1/COP (4)；

COP＝Q_cn/W_acn (5)；

where COP is the refrigeration coefficient of the regenerator, Q_cnAnd W_acnThe dimensionless refrigerating capacity and the dimensionless consumed sound power are respectively.

9. The thermoacoustic refrigerator regenerator parameter optimization design method based on cuckoo algorithm of claim 1, wherein the design parameters in step S3 include dimensionless regenerator length, dimensionless regenerator position, porosity and drive ratio, and the process of determining an optimal set of dimensionless regenerator length, dimensionless regenerator position, porosity and drive ratio using cuckoo algorithm comprises:

s31, initializing a cuckoo algorithm;

setting relevant parameters of the cuckoo algorithm, including a search space dimension D and a maximum iteration number g_maxStep size alpha of location update and probability P of finding cuckoo_a；

S32, initializing a population, and randomly generating N groups of bird nests X ═ X₁,x₂,x₃,x₄}，x₁To dimensionless regenerator position X_sn，x₂To dimensionless regenerator length L_sn，x₃Is a porosity of 1, x₄Is the drive ratio Dr;

s33, calculating N groups of nest fitness function values in k iterations, comparing the fitness function values with the optimal solutions respectively, and if the fitness function values are better, updating the optimal solution f of the current N groups of nests_minThe corresponding nest position is the optimal nest position X_best；

S34, generating a k +1 generation bird nest position by using a Levy flight formula, wherein the specific formula is as follows: x_k+1＝X_k+α.*Levy(β)，X_k+1Is the nest position of the k +1 generation, X_kIs the k generation nest position, alpha is the step size, Levy (beta) is the probability density function, beta is the random number, beta belongs to [0,2 ]](ii) a With probability P_aDiscarding partial solutions and generating, as a complement, a new solution of the same number as the discarded solution in a random walk manner, i.e. with a random number r e [0,1 ∈]And P_aComparison, if r>P_aAbandon the original nest and regenerate new birdThe fossa is a new solution, and the specific formula is as follows: x_k+1＝X_k+r*(X_i-X_j)，X_iAnd X_jAre any two solutions at k iterations;

s35, judging whether the iteration number reaches the maximum iteration number g_maxIf not, repeating the steps S33 and S34, otherwise executing the step S36;

and S36, outputting the global optimal position of the bird nest as a fitness function optimization result to obtain the optimal length of the dimensionless regenerator, the central position of the dimensionless regenerator, the porosity and the drive ratio.

Technical Field

The invention relates to an optimization design technology of a thermoacoustic refrigerator, in particular to an optimization design method of a thermoacoustic refrigerator heat regenerator based on a cuckoo algorithm.

Background

The thermoacoustic refrigerator is a new refrigeration technology based on thermoacoustic effect, it utilizes the transmission of sound-driven heat to realize energy conversion, and has the following advantages: (1) no mechanical motion component, solved the part mechanical motion wearing and tearing loss problem, long service life: (2) the refrigerator generally adopts inert gases such as air and the like, does not generate harmful gases to pollute the environment, and is green and environment-friendly; (3) the operation structure is simple, and the repair and maintenance are convenient; (4) the size of the equipment can be adjusted according to the frequency of the driving device, and the higher the frequency, the smaller the volume and the lighter the weight, and the equipment can be used for heat dissipation of electronic equipment. The advantages attract the attention of researchers at home and abroad, and the thermoacoustic refrigeration technology conforms to the development trend of new energy, thereby providing more possibilities for the diversified development of the new energy.

However, the thermoacoustic refrigerator has low energy utilization rate, and the difference in refrigeration coefficient is also a difficulty that cannot be ignored in large-scale application of thermoacoustic refrigeration technology, so that optimization of the thermoacoustic system and a core component regenerator thereof is one of the centers of gravity of current research. The heat regenerator is an important component of the thermoacoustic refrigerator, and can improve the system refrigeration coefficient by improving the performance of the heat regenerator, but the independent variables involved in the operation of the heat regenerator are more than 14, the variables are mutually restricted and influenced, the calculated amount is huge, errors easily occur, and an optimal design scheme is difficult to obtain.

Disclosure of Invention

The purpose of the invention is as follows: the invention aims to provide a thermoacoustic refrigerator regenerator optimization design method based on a cuckoo algorithm, and solves the problems that the traditional design method of the thermoacoustic refrigerator regenerator is complex in calculation and an optimal design scheme is not easy to obtain.

The technical scheme is as follows: a thermoacoustic refrigerator regenerator parameter optimization design method based on a cuckoo algorithm comprises the following steps:

s1, establishing a dimensionless refrigerating capacity equation and a dimensionless sound power consumption equation of the heat regenerator based on a linear thermoacoustic theory and a plate stacking approximate theory;

s2, setting the constraint conditions of the optimized parameters in the refrigeration quantity equation and the sound power consumption equation;

s3, establishing a fitness function of the cuckoo algorithm, and determining the optimal value of a group of design parameters by using the cuckoo algorithm.

Further, the dimensionless cooling capacity expression established in step S1 is:

the dimensionless consumed sound power expression is as follows:

wherein G is a dimensionless temperature gradient expressed as:

wherein L is_snTo dimensionless regenerator length, X_snTo dimensionless regenerator position, D_RPorosity B and drive ratio; delta_knFor dimensionless heat penetration thickness, Δ T_mnThe dimensionless temperature difference is shown, sigma is a Plantt number, and gamma is a specific heat ratio.

Further, step S2 is specifically:

s21 regenerator length constraint: the thermoacoustic effects are generated between the pressure antinode and the node of the sound wave, so that two ends of the heat regenerator can not exceed the pressure antinode and the pressure node, and the first constraint condition is determined;

and S22 constraint of the center position of the regenerator: because the most intense part of the thermoacoustic effect occurs between the pressure antinode and the pressure node, the central position of the regenerator must be within the pressure node and the antinode to achieve the best result of the thermoacoustic effect, and the second constraint condition is determined;

constraint of porosity of S23: when the distance between the heat regenerator plates is 2-4 heat penetration thicknesses, the heat-sound conversion effect is the best, and the heat-sound conversion effect is determined as a third constraint condition;

constraint of S24 drive ratio: the driving ratio is the ratio of dynamic pressure amplitude to average pressure, the driving sound pressure is small, the energy generated by unit volume is small, the driving sound pressure is too large, the gas working medium is caused to generate turbulent flow, and the fourth constraint condition is determined.

Wherein the first constraint condition is as follows:

wherein L is_SIs the regenerator length and λ is the acoustic wavelength.

Wherein the second constraint condition is:

wherein, X_SIs the regenerator center position and λ is the acoustic wavelength.

Wherein the third constraint condition is:

2δ_k<y₀<4δ_k；

wherein, y₀Is the heat regenerator plate spacing, which is the porosity, delta, after dimensionless processing_kIs the heat penetration thickness of the working medium.

Wherein the fourth constraint condition is:

0.015<Dr<0.03；

wherein Dr is the drive ratio, and the value range of Dr is derived from experimental empirical values.

Further, the fitness function of the cuckoo algorithm established in step S3 is:

fmin＝1/COP (4)；

COP＝Q_cn/W_acn (5)；

where COP is the refrigeration coefficient of the regenerator, Q_cnAnd W_acnThe dimensionless refrigerating capacity and the dimensionless consumed sound power are respectively.

Further, the design parameters in step S3 include the dimensionless regenerator length, the dimensionless regenerator position, the porosity, and the drive ratio, and the process of determining the dimensionless regenerator length, the dimensionless regenerator position, the porosity, and the drive ratio for the optimal set using the cuckoo algorithm includes:

s31, initializing a cuckoo algorithm;

setting relevant parameters of the cuckoo algorithm, including a search space dimension D and a maximum iteration number g_maxStep size alpha of location update and probability P of finding cuckoo_a；

S32, initializing a population, and randomly generating N groups of bird nests X ═ X₁,x₂,x₃,x₄}，x₁To dimensionless regenerator position X_sn，x₂To dimensionless regenerator length L_sn，x₃Is porosity B, x₄Is the drive ratio Dr;

s33, calculating N groups of fossa fitness function values during k iterations, comparing the fitness function values with the optimal solutions (the minimum value of the fitness function values of the N groups of fossas during the last iteration) respectively, and if the fitness function values are better, updating the optimal solution f of the current N groups of fossas_minThe corresponding nest position is the optimal nest position X_best；

S34, generating a k +1 generation bird nest position by using a Levy flight formula, wherein the specific formula is as follows: x_k+1＝X_k+α.*Levy(β)，X_k+1Is the nest position of the k +1 generation, X_kIs the k generation nest position, alpha is the step size measured by 0.01, Levy (beta) is the probability density function, beta is a random number, beta belongs to [0,2 ]](ii) a With probability P_aDiscarding partial solutions and generating, as a complement, a new solution of the same number as the discarded solution in a random walk manner, i.e. with a random number r e [0,1 ∈]And P_aComparison, P_aTake 0.25, if r>P_aAnd abandoning the original nest to regenerate a new nest, namely a new solution, wherein the specific formula is as follows: x_k+1＝X_k+r*(X_i-X_j)，X_iAnd X_jAre any two solutions at k iterations;

s35, judging whether the iteration number reaches the maximum iteration number g_maxIf not, repeating the steps S33 and S34, otherwise executing the step S36;

and S36, outputting the global optimal position of the bird nest as a fitness function optimization result to obtain the optimal length of the dimensionless regenerator, the central position of the dimensionless regenerator, the porosity and the drive ratio.

Has the advantages that: compared with the prior art, the invention has the following advantages:

(1) the parameter optimization adopts the latest cuckoo algorithm, can optimize a differential equation set with huge calculation amount, and the specific nest parasitic behavior and the Levy flight characteristic thereof ensure that the optimization process does not fall into the predicament of local optimization and have stronger global search capability.

(2) The modeling of the heat regenerator of the thermoacoustic refrigerator selects the length, the central position, the porosity and the driving ratio of the heat regenerator as optimization variables, rather than only taking the length and the central position of the heat regenerator as variables, and further researches the influence of the whole structure and the micro part of the heat regenerator on the refrigeration performance of the system.

(3) The invention has simple operation, is convenient to understand and skillfully use, can quickly obtain the optimal design scheme of the thermoacoustic refrigerator, and is suitable for designers in the thermoacoustic field.

Drawings

FIG. 1 is a schematic view of a thermoacoustic refrigerator;

FIG. 2 is a flow chart of the method of the present invention;

FIG. 3 is a flow chart of the basic steps of a cuckoo optimization algorithm;

fig. 4 is a schematic view of a square-hole regenerator, wherein (a) is an axial sectional view and (b) is a cross-sectional view.

Detailed Description

The invention is further described with reference to the following figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.

According to the thermoacoustic refrigerator regenerator parameter optimization design method based on the cuckoo algorithm, the length, the central position, the porosity and the drive ratio of the regenerator are optimized, so that the consumed acoustic power is reduced as much as possible under the condition of ensuring that the refrigerating capacity is improved, and the refrigerating coefficient of the system is improved.

As shown in fig. 1, the thermoacoustic refrigerator model in this embodiment mainly includes five portions, namely, an acoustic driver 1, a resonance tube 2, a heat regenerator 3, a hot-side exchanger 4, and a cold-side exchanger 5, where the hot-side exchanger is disposed between the acoustic driver and the heat regenerator, and the cold-side exchanger is disposed between the heat regenerator and the resonance tube. The invention is mainly characterized in that the refrigeration coefficient of a thermoacoustic refrigerator system is optimally designed, and for the whole system, a heat regenerator is a main place for generating thermoacoustic conversion. Therefore, the optimized design can be reduced to the optimized design of the heat regenerator of the thermoacoustic refrigerator.

As shown in fig. 2, the method for optimally designing parameters of a heat regenerator of a thermoacoustic refrigerator based on a cuckoo algorithm of the invention comprises the following steps:

s1, establishing a dimensionless refrigerating capacity equation and a dimensionless sound power consumption equation of the heat regenerator based on a linear thermoacoustic theory and a plate stacking approximate theory;

the dimensionless refrigerating capacity expression is as follows:

the dimensionless consumed sound power expression is as follows:

wherein G is a dimensionless temperature gradient expressed as:

wherein the optimized parameter is the dimensionless regenerator length L_snDimensionless regenerator position X_snPorosity B and drive ratio D_R(ii) a The operating parameters and the working condition parameters are as follows: dimensionless heat penetration thickness delta_knDimensionless temperature difference Δ T_mnPrandtl number σ, specific heat ratio γ.

S2, setting the constraint conditions of the optimized parameters in the refrigeration quantity equation and the sound power consumption equation; the method specifically comprises the following steps:

s21 regenerator length constraint: the thermoacoustic effects are generated between the pressure antinode and the node of the sound wave, so that two ends of the heat regenerator can not exceed the pressure antinode and the pressure node, and the first constraint condition is determined;

the first constraint is:

wherein L is_SIs the regenerator length and λ is the acoustic wavelength.

And S22 constraint of the center position of the regenerator: because the most intense part of the thermoacoustic effect occurs between the pressure antinode and the pressure node, the central position of the regenerator must be within the pressure node and the antinode to achieve the best result of the thermoacoustic effect, and the second constraint condition is determined;

the second constraint is:

wherein, X_SIs the regenerator center position and λ is the acoustic wavelength.

Constraint of porosity of S23: when the distance between the heat regenerator plates is 2-4 heat penetration thicknesses, the heat-sound conversion effect is the best, and the heat-sound conversion effect is determined as a third constraint condition;

the third constraint is:

2δ_k<y₀<4δ_k；

wherein, y₀Is the heat regenerator plate spacing, which is the porosity, delta, after dimensionless processing_kIs the heat penetration thickness of the working medium.

Constraint of S24 drive ratio: the driving ratio is the ratio of dynamic pressure amplitude to average pressure, the driving sound pressure is small, the energy generated by unit volume is small, the driving sound pressure is too large, the gas working medium is caused to generate turbulent flow, and the fourth constraint condition is determined.

The fourth constraint is:

0.015<Dr<0.03；

wherein Dr is the drive ratio, and the value range of Dr is derived from experimental empirical values.

S3, establishing a fitness function of the cuckoo algorithm, and determining the optimal value of a group of design parameters by using the cuckoo algorithm;

the fitness function of the cuckoo algorithm is as follows:

fmin＝1/COP (4)；

COP＝Q_cn/W_acn (5)；

where COP is the refrigeration coefficient of the regenerator, Q_cnAnd W_acnThe dimensionless refrigerating capacity and the dimensionless consumed sound power are respectively.

As shown in fig. 3, the process of determining an optimal set of dimensionless regenerator length, dimensionless regenerator position, porosity, and drive ratio using the cuckoo algorithm includes:

s31, initializing a cuckoo algorithm;

setting relevant parameters of the cuckoo algorithm, including a search space dimension D and a maximum iteration number g_maxStep size alpha of location update and probability P of finding cuckoo_a；

S32, initializing a population, and randomly generating N groups of bird nests X ═ X₁,x₂,x₃,x₄}，x₁To dimensionless regenerator position X_sn，x₂To dimensionless regenerator length L_sn，x₃Is porosity B, x₄Is the drive ratio Dr;

s33, calculating k iterationsComparing the fitness function values of the N groups of nests with the optimal solution (the minimum value of the fitness function values of the N groups of nests in the last iteration) respectively, and if the fitness function values are better, updating the optimal solution f of the current N groups of nests_minThe corresponding nest position is the optimal nest position X_best；

S34, generating a k +1 generation bird nest position by using a Levy flight formula, wherein the specific formula is as follows: x_k+1＝X_k+α.*Levy(β)，X_k+1Is the nest position of the k +1 generation, X_kIs the k generation nest position, alpha is the step size measured by 0.01, Levy (beta) is the probability density function, beta is a random number, beta belongs to [0,2 ]]In this embodiment, β ═ 1.5; with probability P_aDiscarding partial solutions and generating, as a complement, a new solution of the same number as the discarded solution in a random walk manner, i.e. with a random number r e [0,1 ∈]And P_aComparison, P_aTake 0.25, if r>P_aAnd abandoning the original nest to regenerate a new nest, namely a new solution, wherein the specific formula is as follows: x_k+1＝X_k+r*(X_i-X_j)，X_iAnd X_jAre any two solutions at k iterations;

s35, judging whether the iteration number reaches the maximum iteration number g_maxIf not, repeating the steps S33 and S34, otherwise executing the step S36;

and S36, outputting the global optimal position of the bird nest as a fitness function optimization result to obtain the optimal length of the dimensionless regenerator, the central position of the dimensionless regenerator, the porosity and the drive ratio.

The axial sectional view and the cross-sectional view of the final optimized regenerator model are shown in fig. 4 (a) and (b).

In conclusion, the method takes the highest refrigeration coefficient as an optimization target, firstly establishes a mathematical model of the heat regenerator, the mathematical model comprises a dimensionless refrigeration capacity equation and dimensionless consumed acoustic power, takes the length, the central position, the porosity and the drive ratio of the heat regenerator as optimization variables and adds corresponding constraint conditions; searching for the optimal position and the optimal solution of a bird nest by adopting a cuckoo algorithm; outputting a global optimal solution when the conditions are met; and obtaining the optimal design scheme of the heat regenerator of the thermoacoustic refrigerator by using the obtained global optimal solution to correspond to the optimal parameters of the heat regenerator of the thermoacoustic refrigerator. The cuckoo algorithm adopted by the invention is a group intelligent search technology integrating the brooding behavior and the Levy flight mode of cuckoos, and an optimal bird nest is obtained by searching in a random walk mode to hatch the bird egg. The method can quickly and effectively find the optimal solution of the problem or the equation, and the global optimization capability is strong. The method provided by the invention is simple to operate, and the design scheme can be quickly obtained only by inputting the initial parameters and the constraint conditions, so that the solving efficiency is improved.