CN115221786A - Design optimization method of Brayton cycle system matching mobile solid nuclear reactor - Google Patents

Abstract

A Brayton cycle system design optimization method matched with a mobile solid nuclear reactor is characterized by initializing input parameters according to design constraints to perform Brayton cycle thermodynamic calculation, performing system quality and efficiency analysis according to the calculated result, and further performing optimization analysis by adopting an improved non-dominated sorting genetic algorithm (NSGA-II) according to important parameters which are obtained by analysis and influence the system quality to realize optimization of the Brayton cycle system. The invention considers the cycle thermal efficiency and the system output power, obtains the system quality optimal design under different design constraints through parameterization and optimization analysis means, can be applied to the quality optimal design of the Brayton cycle system of the coupled small nuclear reactor, and has certain reference value for optimizing and determining the system parameters to reduce the overall quality of the device.

Description

Design optimization method of Brayton cycle system matching mobile solid nuclear reactor

technical field

The invention relates to a technology in the field of small nuclear reactor device design, in particular to a design optimization method for a Brayton cycle system matching a mobile solid nuclear reactor.

Background technique

As a kind of small modular reactor, the small mobile nuclear reactor usually has an output electric power of not more than 20MWe, and can be flexibly deployed in a place far away from the grid to operate independently. Therefore, reducing the quality of the reactor and the energy conversion system is necessary to meet the mobility of the small nuclear reactor system. Sexuality is very important. The use of a directly cooled gas-cooled reactor in combination with a closed Brayton cycle energy conversion unit can achieve lower system specific mass at power levels on the order of megawatts. However, the current optimization methods for this kind of design route are all aimed at the index of cycle efficiency, without considering the quality index which is more important to improve the maneuverability of the system. Therefore, there is an urgent need for an optimal design method that takes into account the thermal efficiency of the cycle and the output power and minimizes the system quality, so as to provide support for the design of small mobile nuclear reactor devices and the system quality optimization evaluation.

SUMMARY OF THE INVENTION

Aiming at the existing supercritical _CO2 Brayton cycle technology of matching sodium reactor and the Brayton cycle technology based on nonlinear programming, the invention does not consider the optimization of system quality, cannot be applied to the shortcomings of small mobile nuclear reactors, and cannot solve the problem of Brayton cycle System quality optimization problem, a Brayton cycle system design optimization method matching mobile solid nuclear reactor is proposed, taking into account the cycle thermal efficiency and system output power, and obtaining the maximum system quality under different design constraints through parameterization and optimization analysis methods. The optimal design can be used in the quality optimization design of the Brayton cycle system coupled with small nuclear reactors, and has a certain reference value for optimizing the determination of system parameters to reduce the overall quality of the device.

The present invention is achieved through the following technical solutions:

The invention relates to a Brayton cycle system design optimization method matching a mobile solid nuclear reactor. Input parameters are initialized according to design constraints to perform Brayton cycle thermodynamic calculation; The important parameters of quality are further optimized and analyzed by the improved non-dominated sorting genetic algorithm (NSGA-II) to realize the optimization of the Brayton cycle system.

The important parameters that affect the quality of the system include: turbine inlet temperature, heat exchanger efficiency, and average molar mass of ammonia mixed working medium.

The invention relates to a system for realizing the above method, comprising: a Brayton cycle thermodynamics calculation unit, a parameterized analysis unit and an optimization analysis unit, wherein: the Brayton cycle thermodynamics calculation unit performs system loop thermodynamic calculation according to the input parameters of the cycle, and obtains The temperature and pressure distribution of the loop, the component design calculation is completed at the same time, and the system quality information is obtained. The parameterized analysis unit changes According to different input parameter values, the Brayton cycle thermodynamic calculation unit is called to obtain the system efficiency and quality information under different design parameters and optimize. According to the preliminary analysis results of the parameterized analysis unit, the analysis unit establishes the number and range of variables for the optimization analysis, carries out the optimization analysis, and obtains the optimal design solution set of the system.

technical effect

The invention comprehensively considers thermodynamic cycle parameters and equipment size parameters, screens the number of input variables by means of parameterized analysis, determines the range of input variables, and performs optimization analysis on this basis to obtain the quality optimal design interval of the Brayton cycle system of a small nuclear reactor . The invention can significantly improve the maneuverability and rapid deployment capability of the small mobile nuclear reactor.

Description of drawings

Figure 1 is a flow chart of the quality design optimization of the Brayton cycle system matching the mobile solid nuclear reactor;

Figure 2 is a flow chart of Brayton cycle thermodynamic calculation;

Figure 3 is a flow chart of heat exchanger design calculation;

Figure 4 is a schematic diagram of a simple regenerative Brayton cycle;

5 is a schematic diagram of a printed circuit board heat exchanger;

6 is a schematic structural diagram of a gas-cooled reactor fuel assembly;

Fig. 7 is a schematic diagram of a parametric analysis result;

Figure 8 is a schematic diagram of the quality optimization design solution set.

Detailed ways

及入口温度T₇压力P₇，设备参数包括：设备的效率(透平效率η_t、压缩机效率η_c、回热器效率η_rep、预冷器效率η_pre)与换热器堆芯的几何参数。As shown in Figure 4, in order to simply regenerate the Brayton cycle, this form of Brayton cycle is mostly used due to the limitations of mobile small nuclear reactors in terms of weight, volume, and deployment mobility. The system includes heat exchangers (regenerators and precoolers), reactors, Brayton rotating machinery (turbines, compressors, generators) and other equipment. The parameters that affect the thermal efficiency of the cycle and the quality of the device can be divided into cycle parameters and equipment. Parameters, cycle parameters include: turbine inlet temperature T ₁ , compressor inlet pressure P ₄ , compressor pressure ratio PI, average molar mass M of helium and xenon mixed working medium, and flow rate of working medium on the cold side of precooler

and inlet temperature T ₇ pressure P ₇ , equipment parameters include: equipment efficiency (turbine efficiency η _t , compressor efficiency η _c , regenerator efficiency η _rep , precooler efficiency η _pre ) and the heat exchanger core efficiency Geometric parameters.

As shown in Figure 5, the heat exchanger analyzed in this example is a printed circuit board heat exchanger. It has higher efficiency and is suitable for small mobile nuclear reactor systems. The straight channel core and channel geometric parameters include: core length L, width W, height H, channel diameter D, channel spacing P, and plate thickness t _p . In terms of the core, with the design parameters of the components fixed, the height H and radius R of the core are used as input variables, and the structure of the gas-cooled reactor fuel assembly is calculated as shown in Figure 6. The moderator is used as the component matrix, and the Outlet tunnels to accommodate coolant channels and fuel rods.

The power of small mobile nuclear reactors is above the megawatt level. The energy conversion system adopts Brayton cycle to achieve lower system specific mass. The circulating working fluid is also used as the coolant of the core, without intermediate heat exchangers, and the system layout is simpler.

Commonly used working fluids include helium, helium-xenon mixed gas, and supercritical carbon dioxide. In this example, the helium-xenon mixed gas is used as an example for analysis. Compared with the other two working fluids, the input variables consider the composition of the mixed working fluid more.

As shown in FIG. 1 , this embodiment relates to a Brayton cycle system design optimization method matching a mobile solid nuclear reactor. Input parameters are initialized according to design constraints to perform Brayton cycle thermodynamic calculation, and system quality and efficiency analysis is performed according to the calculated results. , according to the important parameters affecting the quality of the system obtained from the analysis, the NSGA-II optimization algorithm is used for further optimization analysis, and the design interval with the optimal system quality under the specified constraints is obtained. This method is applied in the design stage of the small nuclear reactor device. , the core adopts a direct-cooled gas-cooled reactor, and the heat exchanger is a printed circuit board heat exchanger. In addition, it also includes a turbine, a compressor and a generator. The optimization process considers the cycle thermodynamic parameters and the design parameters of each equipment, and finally obtains The thermodynamic cycle parameters of the system after the quality optimization and the design parameters of each equipment.

As shown in FIG. 2 , the Brayton cycle thermodynamic calculation refers to: obtaining loop efficiency, power and quality information through calculation. The overall calculation is based on the energy conservation and steady-state thermodynamic equations of each component, combined with cycle parameters, using empirical relational expressions or geometric design methods for different components to obtain mass estimation results, including the following steps:

Step 1: Initialize the cycle parameters and the geometric parameters of the heat exchanger according to the input, and assume that the pressure drop on the high-pressure side and the low-pressure side of the loop is both 0.1MPa, so as to obtain the inlet pressure P ₁ and outlet pressure P ₂ of the turbine.

Step 2: Calculation of the turbine thermodynamic process. According to the inlet temperature T ₁ and the pressure P ₁ , the inlet entropy value is obtained through the physical property look-up table. According to the isentropic process, the outlet entropy value is equal to the inlet, and the outlet enthalpy value is obtained, S ₁ =S(T ₁ , P ₁ ), h _2s =H (S ₁ , P ₂ ), further combined with the definition of isentropic efficiency, the actual turbine outlet enthalpy and temperature can be calculated, h ₂ =h ₁ -η _t ×(h ₁ -h _2s ), T ₂ =T (h ₂ , P ₂ ), where: the subscript 1 represents the turbine inlet parameter, the subscript 2 represents the turbine outlet parameter, the subscript 2s is the outlet parameter of the isentropic process; S is the entropy of the working fluid, T is the temperature, P is the pressure, h is the specific enthalpy, and η _t is the entropic efficiency of the turbine.

其中：π为压气机压比，N_total为布雷顿旋转单元的数量，α_BRU为系统比质量系数，与透平入口温度T₁相关，具体为

P_e为单个布雷顿旋转单元的输出功率。Step 3: The thermodynamic process calculation of the compressor is similar to that of the turbine. First obtain the outlet enthalpy value h _5s under the isentropic process, and further combine the definition of isentropic efficiency to calculate the actual outlet enthalpy value h ₅ and temperature T ₅ . The turbine, generator and compressor together form the Brayton rotating unit in the system, the mass of which is calculated using the empirical relationship,

Where: π is the compressor pressure ratio, N _total is the number of Brayton rotating units, α _BRU is the system specific mass coefficient, which is related to the turbine inlet temperature T ₁ , specifically

_Pe is the output power of a single Brayton rotating unit.

Step 4: Combine the inlet temperatures T ₅ and T ₂ of the hot and cold sides of the regenerator calculated and determined in Step 3 and Step 2, according to the input regenerator efficiency, carry out the design calculation of the heat exchanger, and calculate the outlet parameters and quality of the heat exchanger Information, as shown in Figure 3, specifically includes:

Step 4.1: According to the definition of the efficiency of the regenerator, calculate the outlet temperatures T ₃ and T ₆ on the hot and cold sides of the regenerator. At this time, the pressure at the outlet of the heat exchanger is obtained by the assumed pressure drop ΔP.

换热器的总换热量，平均分配给每个通道，

其中：h_h，in为热侧通道入口比焓，h_h，in为热侧通道出口比焓，

为热侧通道质量流量，N_ch为PCHE热侧或冷侧的换热通道数目，W为PCHE芯体宽度，H为高度，P为PCHE通道间距，t_p为板厚。Step 4.2: After obtaining the heat exchange amount of the heat exchanger according to the efficiency, take the width W, height H, channel diameter D, channel spacing P, and plate thickness t _p of the PCHE as input to obtain the number of heat exchanger channels N _ch and The heat exchange Q _ch of a single channel. PCHE uses a design with the same number of heat exchange channels on both sides of the cold and hot sides, then the number of heat exchanger channels on one side

The total heat exchange of the heat exchanger, evenly distributed to each channel,

Where: h _{h, in} is the specific enthalpy of the hot side channel inlet, h _{h, in} is the specific enthalpy of the hot side channel outlet,

is the mass flow rate of the hot side channel, _Nch is the number of heat exchange channels on the hot side or cold side of the PCHE, W is the PCHE core width, H is the height, P is the PCHE channel spacing, and t _p is the plate thickness.

Step 4.3: Since the temperature of the fluid in the heat exchanger varies greatly, in order to make the size of the heat exchanger obtained by the design calculation of the heat exchanger more accurate, divide N sub-heat exchangers along the length of the heat exchanger, and use the efficiency-heat transfer unit. The effectiveness-NTU method was used to calculate the UA value of the heat exchanger design.

其中：U_i为第i个传热单元的总换热系数，k_i为芯体材料的导热率，t＝1.15D/2.0为等效导热厚度；h_h，i为热侧的对流换热系数，h_c，i为冷侧的对流换热系数，针对不同的工质可使用不同的经验关系式计算获得，例如，Taylor经验关系式、Ginielinski经验关系式。Step 4.4: The total heat transfer coefficient of the i-th sub-heat exchanger satisfies

Where: U _i is the total heat transfer coefficient of the _i -th heat transfer unit, ki is the thermal conductivity of the core material, t=1.15D/2.0 is the equivalent thermal conductivity thickness; h _{h, i} is the convective heat transfer on the hot side The coefficient, h _{c, i} is the convective heat transfer coefficient of the cold side, which can be calculated and obtained by using different empirical relational expressions for different working fluids, for example, Taylor empirical relational expression and Ginielinski empirical relational expression.

其中：uA_i为第i个传热单元的热导率，U_i为总换热系数，D为通道直径。根据子换热器的长度计算更新冷热两侧的压降

其中：D_h为通道的水力半径，ρ_i为第i个子换热内流体的密度，u_i为流体速度；f为摩擦系数，针对不同的工质可使用不同的经验公式，例如Taylor经验关系式、Cole-Brook经验关系式。Step 4.5: Length of Heat Exchanger Core

Where: uA _i is the thermal conductivity of the ith heat transfer unit, U _i is the total heat transfer coefficient, and D is the diameter of the channel. Update the pressure drop on the hot and cold sides based on the length of the sub-heat exchanger

Where: D _h is the hydraulic radius of the channel, ρ _i is the density of the fluid in the ith sub-heat exchange, _ui is the fluid velocity; f is the friction coefficient, different empirical formulas can be used for different working fluids, such as Taylor's empirical relationship formula, Cole-Brook empirical relational formula.

Step 4.6: Compare the calculated pressure drop with the assumed initial pressure drop. If it is less than the specified error, it is considered that the heat exchanger design calculation is converged, the heat exchanger mass is calculated according to the geometric design, and the pressure drop ΔP ₅₆ =ΔP _c,new , ΔP ₂₃ =ΔP _h,new and quality information of the heat exchanger are returned; Otherwise, go back to step 4.1, update the pressure drop of the heat exchanger, and repeat the above calculation.

Step 5: As shown in Figure 3, combined with the precooler hot side inlet temperature T3 calculated and determined in step ₄ , according to the input precooler efficiency, the design calculation of the heat exchanger is performed, and the outlet parameters and quality information of the heat exchanger are calculated, After the calculation converges, the pressure drop on the cold side of the precooler ΔP ₇₈ =ΔP _c,new , the pressure drop on the hot side ΔP ₃₄ =ΔP _h,new , the outlet temperature T _4,new and the quality information are obtained, including:

Step 5.1: According to the definition of the efficiency of the regenerator, calculate the outlet temperatures T ₈ and T ₄ on both cold and hot sides of the regenerator. At this time, the pressure at the outlet of the heat exchanger is obtained by the pressure drop ΔP.

换热器的总换热量，平均分配给每个通道，

其中：h_h，in为热侧通道入口比焓，h_h，in为热侧通道出口比焓，

为热侧通道质量流量，N_ch为PCHE热侧或冷侧的换热通道数目，W为PCHE芯体宽度，H为高度，P为PCHE通道间距，t_p为板厚。Step 5.2: After obtaining the heat exchange amount of the heat exchanger according to the efficiency, using the width W, height H, channel diameter D, channel spacing P, and plate thickness t _p of the PCHE as inputs, obtain the number of heat exchanger channels N _ch and The heat exchange Q _ch of a single channel. PCHE uses a design with the same number of heat exchange channels on both sides of the cold and hot sides, then the number of heat exchanger channels on one side

The total heat exchange of the heat exchanger, evenly distributed to each channel,

Where: h _{h, in} is the specific enthalpy of the hot side channel inlet, h _{h, in} is the specific enthalpy of the hot side channel outlet,

is the mass flow rate of the hot side channel, _Nch is the number of heat exchange channels on the hot side or cold side of the PCHE, W is the PCHE core width, H is the height, P is the PCHE channel spacing, and t _p is the plate thickness.

Step 5.3: Since the temperature of the fluid in the heat exchanger varies greatly, in order to make the size of the heat exchanger obtained by the design calculation of the heat exchanger more accurate, divide N sub-heat exchangers along the length of the heat exchanger, and use the efficiency-heat transfer unit. The effectiveness-NTU method was used to calculate the UA value of the heat exchanger design.

其中：U_i为第i个传热单元的总换热系数，k_i为芯体材料的导热率，t＝1.15D/2.0为等效导热厚度；h_h，i为热侧的对流换热系数，h_c，i为冷侧的对流换热系数，针对不同的工质可使用不同的经验关系式计算获得，例如，Taylor经验关系式、Ginielinski经验关系式。Step 5.4: The total heat transfer coefficient of the i-th sub-heat exchanger satisfies

Where: U _i is the total heat transfer coefficient of the _i -th heat transfer unit, ki is the thermal conductivity of the core material, t=1.15D/2.0 is the equivalent thermal conductivity thickness; h _{h, i} is the convective heat transfer on the hot side The coefficient, h _{c, i} is the convective heat transfer coefficient of the cold side, which can be calculated and obtained by using different empirical relational expressions for different working fluids, for example, Taylor empirical relational expression and Ginielinski empirical relational expression.

其中：UA_i为第i个传热单元的热导率，U_i为总换热系数，D为通道直径。根据子换热器的长度计算更新冷热两侧的压降

其中：D_h为通道的水力半径，ρ_i为第i个子换热内流体的密度，u_i为流体速度；f为摩擦系数，针对不同的工质可使用不同的经验公式，例如Taylor经验关系式、Cole-Brook经验关系式。Step 5.5: Length of Heat Exchanger Core

Among them: UA _i is the thermal conductivity of the ith heat transfer unit, U _i is the total heat transfer coefficient, and D is the diameter of the channel. Update the pressure drop on the hot and cold sides based on the length of the sub-heat exchanger

Where: D _h is the hydraulic radius of the channel, ρ _i is the density of the fluid in the ith sub-heat exchange, _ui is the fluid velocity; f is the friction coefficient, different empirical formulas can be used for different working fluids, such as Taylor's empirical relationship formula, Cole-Brook empirical relational formula.

Step 5.6: Compare the calculated pressure drop with the assumed initial pressure drop. If it is less than the specified error, the heat exchanger design calculation is considered to be converged, and the heat exchanger mass is calculated according to the geometric design, and the pressure drop ΔP ₇₈ =ΔP _c,new , ΔP ₃₄ =ΔP _h,new and quality information of the heat exchanger are returned; Otherwise, go back to step 5.1, update the pressure drop of the heat exchanger, and repeat the above calculation.

Step ₆ : It is judged that when the error between the newly calculated compressor inlet temperature T4 _,new and the assumed temperature T4 is less than the specified value, proceed to the next step; otherwise, go back to Step 3 to update the compressor inlet temperature to T4 _{,new and} repeat the above calculation.

其中：h_out为堆芯冷却剂出口比焓，h_in为堆芯入口比焓，

为堆芯冷却剂质量流量，N_assbl为堆芯内组件数量，F_qr为堆芯径向功率峰因子。Step 7: Calculate the thermal power of the reactor and the temperature of different materials according to the core inlet temperature T ₆ and the input core outlet temperature T ₁ , specifically: for a single channel in the assembly, the same node division as the heat exchanger is also used , the geometric size of the fixed fuel assembly, according to the core radius R, the number of fuel assemblies in the core N _assbl can be calculated, then the heat exchange of a single coolant channel in the hottest assembly of the reactor is h _out =H(T _out , P _out ), h _in =H(T _in , P _in ),

Where: h _out is the specific enthalpy of the core coolant outlet, h _in is the specific enthalpy of the core inlet,

is the core coolant mass flow, N _assbl is the number of components in the core, and F _qr is the core radial power peak factor.

其中：T_i为冷却剂主流温度；T_clad,i为包壳内表面温度；T_matrix,i为包壳外表面温度；T_fuel,i为燃料表面温度；T_c,i为燃料中心温度；

为单个通道内冷却剂的质量流量，h_i为冷却剂在第i个几点处的比焓，h_in为冷却剂入口比焓，Q_ch为单个通道的热功率，H为堆芯高度，z_i为第i节点的轴向坐标，h_i为第i个节点处的对流换热系数，D_coolant为冷却剂通道直径，D_clad为包壳的直径，D_matrix为按面积等效的直径，D_fuel燃料元件直径，κ_clad，i、κ_matrix，i、κ_fuel，i分别为包壳材料、基体材料、燃料元件的导热系数。在堆芯计算中，堆芯的尺寸参数应保证不同材料的温度值分布应小于其对应的安全限值即T<T_max。根据各节点的冷却剂主流温度，更新堆芯冷却剂通道内压降

由于工质的物性和压降相互影响，需要进行迭代计算直至压降收敛，其中，f_i为摩擦系数，ρ_i为冷却剂密度，u_i冷却剂速度，l_i第i个节点单元的长度。When the axial power of the core has a cosine distribution, according to the energy conservation, Newton's cooling theorem, the cylinder wall and the cylinder thermal conductivity formula, the temperature of each structural material at the i-th node is calculated in turn,

Where: T _i is the mainstream temperature of the coolant; T _clad,i is the inner surface temperature of the cladding; T _matrix,i is the outer surface temperature of the cladding; T _fuel,i is the fuel surface temperature; T _c,i is the fuel center temperature;

is the mass flow rate of the coolant in a single channel, hi is the specific enthalpy of the coolant at the _ith point, h _in is the specific enthalpy of the coolant inlet, _Qch is the thermal power of a single channel, H is the core height, _zi is the axial coordinate of the _ith node, hi is the convective heat transfer coefficient at the ith node, D _coolant is the diameter of the coolant channel, D _clad is the diameter of the cladding, and D _matrix is the equivalent diameter by area , D _fuel fuel element diameter, κ _{clad, i} , κ _{matrix, i} , κ _{fuel, i} are the thermal conductivity of cladding material, matrix material, and fuel element, respectively. In the core calculation, the size parameters of the core should ensure that the temperature distribution of different materials should be less than the corresponding safety limit, namely T<T _max . Update the pressure drop in the core coolant channel according to the coolant mainstream temperature at each node

Since the physical properties of the working fluid and the pressure drop affect each other, iterative calculation is required until the pressure drop converges, where f _i is the friction coefficient, ρ _i is the coolant density, u _i is the coolant velocity, and l _i is the length of the i-th node element .

Step 8: Update the circuit pressure according to the newly calculated component pressure drop, and judge that when the newly calculated pressure drop ΔP _c,new , ΔP _h,new and the initial assumed values ΔP _c , ΔP _h meet the error requirements, then Brayton is considered The loop calculation converges; otherwise, return to step 1 to update the assumed value of the pressure drop.

The system quality and efficiency analysis refers to: based on the Brayton cycle thermodynamic calculation, carry out parametric analysis and optimization analysis for the system quality and loop efficiency indicators, and obtain the optimal system quality design that satisfies the design constraints. The analysis process is shown in Figure 1. For the core, the radius of the core has a more significant impact on the quality of the core. Therefore, during the analysis process, the height of the core is fixed, and according to the temperature limit of the core material, the approximate search allows The minimum core radius of , including:

Step 1: Keep other parameters unchanged, adjust a certain input parameter, and carry out parametric analysis. According to the system thermodynamic calculation, the loop mass efficiency information is obtained.

Step ②: Approach the minimum core mass according to the design constraints, that is, when the temperature of the core material is less than the upper temperature limit T<T _max , further reduce the core radius and return to step ① for cyclic thermodynamic calculation; otherwise, it is considered that the specified design has been searched Minimum core radius under constraints.

Step ③: When it is judged that the current power reaches the target power value, if it is, it is considered to find the Brayton cycle design parameters that meet the target power requirements and include the minimum core radius; otherwise, according to the target power, after adjusting the loop mass flow, return to step ① .

Step ④: According to the calculation results, analyze the system quality and efficiency. Quantitatively analyze the dependence of system quality and efficiency on different input parameters, grasp the system quality distribution, reduce the number of analysis variables for system optimization analysis, and determine the upper and lower limits of the optimized input parameters based on the system quality results.

The use of the NSGA-II optimization algorithm for further optimization analysis means: for the input variables that have a greater impact on the quality of the system, the multi-objective genetic algorithm NSGA-II is used, and the quality and efficiency calculated by the Brayton thermodynamic cycle are used as objective functions. , to obtain the optimal solution set regarding quality and efficiency of system design. The specific steps include:

Step a: From the cycle parameters and the equipment parameters, determine the input parameters to be investigated and set the upper and lower limit values of their variation ranges; at the same time, initialize other input parameters to a certain fixed value.

Step b: Take the Brayton thermodynamic cycle calculation flow that returns the mass of the system as the objective function.

Step c: Use the geatpy library in Python to call the multi-objective genetic algorithm NSGA-II for multi-objective optimization analysis.

As shown in Figure 7, after a specific actual experiment, in the Windows 10 environment, the above method is run with the basic input parameters in Table 1, and the turbine inlet temperature T ₁ is changed to obtain its influence on the system quality. In addition to the simple regenerative cycle (single compression cycle), a double compression cycle incorporating a recompression process was also calculated on this basis. For both cycle configurations, increasing the turbine inlet temperature can reduce the quality of the system and increase the efficiency. And this relationship is nonlinear. When the turbine inlet temperature is low, the cycle efficiency increases and the system quality decreases faster. Although the double compression cycle can bring higher cycle efficiency, it is obvious that its overall quality Also bigger. On the other hand, from the point of view of the mass source of the system, most of the mass of the system is occupied by the core and the heat exchanger, reflecting that the design parameters of the heat exchanger are an important factor affecting the quality of the system. Through the investigation of different input variables, the input variables and upper and lower limits for optimization analysis are finally determined, as shown in Table 2.

Table 1 Basic operating parameters

Table 2 Input variables and upper and lower limits of NSGA-II optimization analysis

Turbine inlet temperature TKT[K] Regenerator efficiency Average molar mass of helium and xenon upper limit 923.15 40% 16.7g/mol lower limit 1140.58 95% 67.6g/mol

As shown in Figure 8, in order to use the NSGA-II algorithm to obtain the optimal solution set with the minimum system quality as the optimization objective under different turbine inlet temperatures, although increasing the turbine inlet temperature can reduce the minimum system quality, it will increase the The requirements for turbine material strength and other aspects are shown in Table 3, and the key parameter information of the two selected optimal design points is listed.

Table 3 The key design parameters for selecting the optimal point

Compared with the prior art, the method optimizes the quality of the Brayton cycle system coupled with the small nuclear reactor, analyzes and evaluates the influence of the cycle parameters and equipment parameters on the dimensional quality of the small nuclear reactor device, and reduces the quality improvement of the device system under the specified constraints. its maneuverability.

The above-mentioned specific implementation can be partially adjusted by those skilled in the art in different ways without departing from the principle and purpose of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above-mentioned specific implementation. Each implementation within the scope is bound by the present invention.

Claims (9)

1. a Brayton cycle system design optimization method matching mobile solid nuclear reactor, it is characterized in that, carry out Brayton cycle thermodynamic calculation according to design constraint initialization input parameter, carry out system quality and efficiency analysis according to the result obtained by calculation, obtain according to analysis The important parameters affecting the quality of the system are further optimized and analyzed by the improved non-dominated sorting genetic algorithm to realize the optimization of the Brayton cycle system; The important parameters that affect the quality of the system include: turbine inlet temperature, heat exchanger efficiency, and average molar mass of ammonia mixed working medium. 2. The Brayton cycle system design optimization method of matching mobile solid nuclear reactor according to claim 1, is characterized in that, described Brayton cycle thermodynamic calculation refers to: obtain loop efficiency, power and quality information by calculation; calculate The whole is based on the energy conservation and steady-state thermodynamic equations of each component, combined with cycle parameters, and uses empirical relational or geometric design methods for different components to obtain mass estimation results. 3. The Brayton cycle system design optimization method of matching mobile solid nuclear reactor according to claim 1 or 2, wherein the Brayton cycle thermodynamic calculation comprises the following steps: Step 1: Initialize the cycle parameters and the geometric parameters of the heat exchanger according to the input, and assume that the pressure drop of the high-pressure side and the low-pressure side of the circuit is both 0.1MPa, so as to obtain the inlet pressure P ₁ and outlet pressure P ₂ of the turbine; Step 2: Calculation of the turbine thermodynamic process; according to the inlet temperature T ₁ pressure P ₁ , the inlet entropy value is obtained by looking up the physical property table, and the outlet entropy value is equal to the inlet according to the isentropic process, and the outlet enthalpy value is obtained, S ₁ =S(T ₁ , P ₁ ), h _2s =H(S ₁ , P ₂ ), further combined with the definition of isentropic efficiency, the actual turbine outlet enthalpy and temperature can be calculated, h ₂ =h ₁ -η _t ×(h ₁ -h _2s ), T ₂ =T(h ₂ , P ₂ ), where: the subscript 1 represents the turbine inlet parameter, the subscript 2 represents the turbine outlet parameter, and the subscript 2s is the outlet parameter of the isentropic process; S is the The entropy of the working fluid, T is the temperature, P is the pressure, h is the specific enthalpy, and η _t is the entropy efficiency of the turbine; Step 3: The calculation of the thermodynamic process of the compressor is similar to that of the turbine; the outlet enthalpy value h _5s under the isentropic process is obtained first, and the actual outlet enthalpy value h ₅ and temperature T ₅ are calculated in combination with the definition of isentropic efficiency; , generator and compressor together form the Brayton rotating unit in the system, the mass of which is calculated using the empirical relation,

Where: π is the compressor pressure ratio, N _total is the number of Brayton rotating units, α _BRU is the system specific mass coefficient, which is related to the turbine inlet temperature T ₁ , specifically

P _e is the output power of a single Brayton rotating unit; Step 4: Combine the inlet temperatures T ₅ and T ₂ of the hot and cold sides of the regenerator calculated and determined in Step 3 and Step 2, according to the input regenerator efficiency, carry out the design calculation of the heat exchanger, and calculate the outlet parameters and quality of the heat exchanger information, including: Step 4.1: According to the definition of the efficiency of the regenerator, calculate the outlet temperatures T ₃ and T ₆ on both cold and hot sides of the regenerator. At this time, the pressure at the outlet of the heat exchanger is obtained by the assumed pressure drop ΔP; Step 4.2: After obtaining the heat exchange amount of the heat exchanger according to the efficiency, take the width W, height H, channel diameter D, channel spacing P, and plate thickness t _p of the PCHE as input to obtain the number of heat exchanger channels N _ch and The heat exchange amount Q _ch of a single channel; PCHE uses a design with the same number of heat exchange channels on both sides of the cold and hot sides, then the number of heat exchanger channels on one side is

The total heat exchange of the heat exchanger, evenly distributed to each channel,

Where: h _{h, in} is the specific enthalpy of the hot side channel inlet, h _{h, in} is the specific enthalpy of the hot side channel outlet,

is the mass flow rate of the hot side channel, _Nch is the number of heat exchange channels on the hot side or cold side of the PCHE, W is the width of the PCHE core, H is the height, P is the PCHE channel spacing, and t _p is the plate thickness; Step 4.3: Since the temperature of the fluid in the heat exchanger varies greatly, in order to make the size of the heat exchanger obtained by the design calculation of the heat exchanger more accurate, divide N sub-heat exchangers along the length of the heat exchanger, and use the efficiency-heat transfer unit. Calculate the UA value of the heat exchanger design by the effectiveness-NTU method; Step 4.4: The total heat transfer coefficient of the i-th sub-heat exchanger satisfies

Where: U _i is the total heat transfer coefficient of the _i -th heat transfer unit, ki is the thermal conductivity of the core material, t=1.15D/2.0 is the equivalent thermal conductivity thickness; h _{h, i} is the convective heat transfer on the hot side Coefficient, h _{c, i} is the convective heat transfer coefficient of the cold side, which can be calculated and obtained by using different empirical relations for different working fluids, such as Taylor's empirical relation and Ginielinski's empirical relation; Step 4.5: Length of Heat Exchanger Core

Among them: UA _i is the thermal conductivity of the ith heat transfer unit, U _i is the total heat transfer coefficient, D is the diameter of the channel; calculate and update the pressure drop on both sides of the hot and cold sides according to the length of the sub-heat exchanger

Where: D _h is the hydraulic radius of the channel, ρ _i is the density of the fluid in the ith sub-heat exchange, _ui is the fluid velocity; f is the friction coefficient, different empirical formulas can be used for different working fluids, such as Taylor's empirical relationship formula, Cole-Brook empirical relational formula; Step 4.6: Compare the calculated pressure drop with the assumed initial pressure drop; if it is less than the specified error, the heat exchanger design calculation is considered to be converged, the heat exchanger mass is calculated according to the geometric design, and the pressure drop ΔP of the heat exchanger is returned ₅₆ =ΔP _c,new , ΔP ₂₃ =ΔP _h,new and quality information; otherwise, go back to step 4.1, update the pressure drop of the heat exchanger, and repeat the above calculation; Step 5: In combination with the precooler hot side inlet temperature T ₃ calculated and determined in step 4, according to the input precooler efficiency, the design calculation of the heat exchanger is performed, and the outlet parameters and quality information of the heat exchanger are calculated. After the calculation converges, the precooler is obtained. Cooler cold side pressure drop ΔP ₇₈ =ΔP _c,new , hot side pressure drop ΔP ₃₄ =ΔP _h,new , outlet temperature T _4,new and quality information; Step ₆ : judge that when the error between the newly calculated compressor inlet temperature T4 _,new and the assumed temperature T4 is less than the specified value, proceed to the next step; otherwise, return to step 3 to update the compressor inlet temperature to be T4 _{,new and} repeat the above calculation; Step 7: Calculate the thermal power of the reactor and the temperature of different materials according to the core inlet temperature T ₆ calculated above and the input core outlet temperature T ₁ ; similarly, for a single channel in the assembly, a heat exchanger similar to The number of fuel assemblies in the core N assbl is calculated according to the core radius R, and the number of fuel assemblies in the core N _assbl is calculated, then the heat exchange of a single coolant channel in the hottest assembly of the reactor is h _out =H(T _out , P _out ), h _in =H(T _in , P _in ),

Where: h _out is the specific enthalpy of the core coolant outlet, h _in is the specific enthalpy of the core inlet,

is the core coolant mass flow, N _assbl is the number of components in the core, and F _qr is the core radial power peak factor; When the axial power of the core has a cosine distribution, according to the energy conservation, Newton's cooling theorem, the cylinder wall and the cylinder thermal conductivity formula, the temperature of each structural material at the i-th node is calculated in turn,

Where: T _i is the mainstream temperature of the coolant; T _clad,i is the inner surface temperature of the cladding; T _matrix,i is the outer surface temperature of the cladding; T _fuel,i is the fuel surface temperature; T _c,i is the fuel center temperature;

is the mass flow rate of the coolant in a single channel, hi is the specific enthalpy of the coolant at the _ith point, h _in is the specific enthalpy of the coolant inlet, _Qch is the thermal power of a single channel, H is the core height, _zi is the axial coordinate of the _ith node, hi is the convective heat transfer coefficient at the ith node, D _coolant is the diameter of the coolant channel, D _clad is the diameter of the cladding, and D _matrix is the equivalent diameter by area , D _fuel fuel element diameter, κ _{clad, i} , κ _{matrix, i} , κ _{fuel, i} are the thermal conductivity of cladding material, matrix material, and fuel element, respectively; in the calculation of the core, the size parameters of the core should be guaranteed to be different The temperature value distribution of the material should be less than its corresponding safety limit, namely T<T _max ; update the pressure drop in the core coolant channel according to the coolant mainstream temperature at each node

Since the physical properties of the working fluid and the pressure drop affect each other, iterative calculation is required until the pressure drop converges, where f _i is the friction coefficient, ρ _i is the coolant density, u _i is the coolant velocity, and l _i is the length of the i-th node element ; Step 8: Update the circuit pressure according to the newly calculated component pressure drop, and judge that when the newly calculated pressure drop ΔP _c,new , ΔP _h,new and the initial assumed values ΔP _c , ΔP _h meet the error requirements, then Brayton is considered The loop calculation converges; otherwise, return to step 1 to update the assumed value of the pressure drop. 4. The Brayton cycle system design optimization method of matching mobile solid nuclear reactor according to claim 3, is characterized in that, described step 5, specifically comprises: Step 5.1: According to the definition of the efficiency of the regenerator, calculate the outlet temperatures T ₈ and T ₄ on both cold and hot sides of the regenerator. At this time, the pressure at the outlet of the heat exchanger is obtained by the pressure drop ΔP; Step 5.2: After obtaining the heat exchange amount of the heat exchanger according to the efficiency, using the width W, height H, channel diameter D, channel spacing P, and plate thickness t _p of the PCHE as inputs, obtain the number of heat exchanger channels N _ch and The heat exchange amount Q _ch of a single channel; PCHE uses a design with the same number of heat exchange channels on both sides of the cold and hot sides, then the number of heat exchanger channels on one side is

The total heat exchange of the heat exchanger, evenly distributed to each channel,

Where: h _{h, in} is the specific enthalpy of the hot side channel inlet, h _{h, in} is the specific enthalpy of the hot side channel outlet,

is the mass flow rate of the hot side channel, _Nch is the number of heat exchange channels on the hot side or cold side of the PCHE, W is the width of the PCHE core, H is the height, P is the PCHE channel spacing, and t _p is the plate thickness; Step 5.3: Since the temperature of the fluid in the heat exchanger varies greatly, in order to make the size of the heat exchanger obtained by the design calculation of the heat exchanger more accurate, divide N sub-heat exchangers along the length of the heat exchanger, and use the efficiency-heat transfer unit. Calculate the UA value of the heat exchanger design by the effectiveness-NTU method; Step 5.4: The total heat transfer coefficient of the i-th sub-heat exchanger satisfies

Where: U _i is the total heat transfer coefficient of the _i -th heat transfer unit, ki is the thermal conductivity of the core material, t=1.15D/2.0 is the equivalent thermal conductivity thickness; h _{h, i} is the convective heat transfer on the hot side Coefficient, h _{c, i} is the convective heat transfer coefficient of the cold side, which can be calculated and obtained by using different empirical relations for different working fluids, such as Taylor's empirical relation and Ginielinski's empirical relation; Step 5.5: Length of Heat Exchanger Core

Among them: UA _i is the thermal conductivity of the ith heat transfer unit, U _i is the total heat transfer coefficient, D is the diameter of the channel; calculate and update the pressure drop on both sides of the hot and cold sides according to the length of the sub-heat exchanger

Where: D _h is the hydraulic radius of the channel, ρ _i is the density of the fluid in the ith sub-heat exchange, _ui is the fluid velocity; f is the friction coefficient, different empirical formulas can be used for different working fluids, such as Taylor's empirical relationship formula, Cole-Brook empirical relational formula; Step 5.6: Compare the calculated pressure drop with the assumed initial pressure drop; if it is less than the specified error, the heat exchanger design calculation is considered to be converged, the heat exchanger mass is calculated according to the geometric design, and the pressure drop ΔP of the heat exchanger is returned ₇₈ =ΔP _c,new , ΔP ₃₄ =ΔP _h,new and quality information; otherwise, go back to step 5.1, update the pressure drop of the heat exchanger, and repeat the above calculation. 5. The Brayton cycle system design optimization method of matching mobile solid nuclear reactor according to claim 1, is characterized in that, described system quality and efficiency analysis refer to: thermodynamic calculation based on Brayton cycle, for system quality and Loop efficiency index, carry out parametric analysis and optimization analysis, and obtain the optimal design of system quality that satisfies the design constraints. For the core, since the radius of the core has a more significant impact on the quality of the core, in the analysis process, the fixed reactor The height of the core, according to the temperature constraints on the core material, approximates the minimum core radius allowed by the search. 6. The Brayton cycle system design optimization method for matching mobile solid nuclear reactors according to claim 1 or 5, wherein the system quality and efficiency analysis specifically includes: Step 1: Fix other parameters unchanged, adjust a certain input parameter, and carry out parametric analysis; obtain the loop quality efficiency information according to the system thermodynamic calculation; Step ②: Approach the minimum core mass according to the design constraints, that is, when the temperature of the core material is less than the upper temperature limit T<T _max , further reduce the core radius and return to step ① for cyclic thermodynamic calculation; otherwise, it is considered that the specified design has been searched Minimum core radius under constraints; Step ③: When it is judged that the current power reaches the target power value, if it is, it is considered to find the Brayton cycle design parameters that meet the target power requirements and include the minimum core radius; otherwise, according to the target power, after adjusting the loop mass flow, return to step ① ; Step 4: According to the calculation results, carry out system quality and efficiency analysis; quantitatively analyze the dependence of system quality and efficiency on different input parameters, grasp the system quality distribution, reduce the number of analysis variables for system optimization analysis, and combine the system quality results Determine the upper and lower bounds of the optimized input parameters. 7. The Brayton cycle system design optimization method for matching mobile solid nuclear reactors according to claim 1, wherein the further optimization analysis of the improved non-dominated sorting genetic algorithm refers to: for a larger impact on the quality of the system The input variables of , using the multi-objective genetic algorithm NSGA-II, take the quality and efficiency calculated by the Brayton thermodynamic cycle as the objective function, and obtain the optimal solution set of the system design regarding the quality and efficiency. 8. The Brayton cycle system design optimization method for matching mobile solid nuclear reactors according to claim 1 or 7, wherein the improved non-dominated sorting genetic algorithm is further optimized and analyzed, and the specific steps include: Step a: from the cycle parameters and the equipment parameters, determine the input parameters to be investigated and set the upper and lower limit values of their variation ranges; at the same time, initialize other input parameters to a certain fixed value; Step b: take the Brayton thermodynamic cycle calculation process returning the system mass as the objective function; Step c: Use the geatpy library in Python to call the multi-objective genetic algorithm NSGA-II for multi-objective optimization analysis. 9. A system for implementing the Brayton cycle system design optimization method for matching mobile solid nuclear reactors according to any one of claims 1 to 8, characterized in that it comprises: a Brayton cycle thermodynamic calculation unit, a parametric analysis unit and a maximum The optimization analysis unit, in which: the Brayton cycle thermodynamic calculation unit performs the system loop thermodynamic calculation according to the input parameters of the cycle, obtains the loop temperature and pressure distribution, and completes the component design calculation at the same time to obtain the system quality information, and the parameterization analysis unit changes for different input parameters. value, call the Brayton cycle thermodynamic calculation unit to obtain system efficiency and quality information under different design parameters. Obtain the optimal design solution set for the system.

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