CN112446097B - Multi-objective optimization method for volume and load of steam generator - Google Patents

Multi-objective optimization method for volume and load of steam generator Download PDF

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CN112446097B
CN112446097B CN202011410167.7A CN202011410167A CN112446097B CN 112446097 B CN112446097 B CN 112446097B CN 202011410167 A CN202011410167 A CN 202011410167A CN 112446097 B CN112446097 B CN 112446097B
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刘政
王成
方园
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Wuhan No 2 Ship Design Institute No 719 Research Institute of China Shipbuilding Industry Corp
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Abstract

The invention relates to a multi-objective optimization method for the volume and the load of a steam generator, which comprises the following steps of setting objective functions of multi-objective optimization design of the steam generator: miny (Miny) SG ＝F SG (x)＝(f V_SG (x),f Q_SG (x) In the formula, f V_SG (x) As a function of SG volume with respect to decision variables; f (f) Q_SG (x) As a function of SG thermal power with respect to decision variables, f Q_SG (x) Is Q SG Taking the value obtained by the inverse, namely: f (f) Q_SG (x)＝‑Q SG (x)；Q SG (x) As a function of thermal power with respect to decision variables. The method of the invention realizes that a larger load is borne by a smaller steam generator volume, thereby gradually realizing the miniaturization of the nuclear power device.

Description

Multi-objective optimization method for volume and load of steam generator
Technical Field
The invention relates to multi-objective optimization of a steam generator, in particular to a multi-objective optimization design method for the volume and the load of a natural circulation type steam generator.
Background
The miniaturization of the nuclear power plant is one direction of the development of the current ship nuclear power plant, the volume and the power level of the nuclear power plant are important factors influencing the performance of the nuclear power ship, the volume of the nuclear power plant needs to be reduced as much as possible on the premise of meeting the safety, and the output power level of the device needs to be ensured not to be reduced. The nuclear power plant is a complex system consisting of various nuclear power equipment, the optimization of the nuclear power equipment in the plant is the basis for realizing the system optimization of the nuclear power plant, and the optimization design of the nuclear power equipment can provide reference and guidance for realizing the system-level optimization of the nuclear power plant.
Steam generators are critical devices in nuclear power plants, and a typical design goal is to carry a large load with a small steam generator volume. The traditional multi-objective optimization method mostly adopts a weighting method, namely, each objective is assigned with a weight and then is converted into a single objective problem, but the method can seriously depend on weighting factors selected by designers, different weighting factors usually correspond to different optimization results, the setting of the weights of each objective is subjective because the weights of the objectives cannot be quantized, and in order to avoid the introduction of artificial subjectivity during multi-objective optimization of the steam generator, a method capable of objectively optimizing the volume and the load of the steam generator is necessary to be studied.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a multi-objective optimization method for the volume and the load of a steam generator, which realizes that the volume of the steam generator is smaller to bear larger load, and further gradually realizes the miniaturization of a nuclear power plant.
The technical scheme adopted for achieving the aim of the invention is a multi-objective optimization method for the volume and the load of a steam generator, which comprises the following steps:
setting an objective function of multi-objective optimization design of the steam generator:
Miny SG ＝F SG (x)＝(f V_SG (x),f Q_SG (x))
wherein f V_SG (x) As a function of SG volume with respect to decision variables; f (f) Q_SG (x) As a function of SG thermal power with respect to decision variables, f Q_SG (x) Is Q SG Taking the value obtained by the inverse, namely: f (f) Q_SG (x)＝-Q SG (x)；Q SG (x) As a function of thermal power with respect to decision variables;
the decision vector functions are:
x＝[P,T in ,T out ,G,P sg ,v,d tube_out ,R pitch ]
wherein P is the operating pressure of the reactor, T in T is the inlet temperature of the reactor out For the exit temperature of the reactivity, G is the mass flow rate of the reactor primary loop coolant, P sg Is the secondary side pressure of the steam generatorForce v is the flow rate of the coolant in the steam generator heat transfer tube, d tube0out For the outer diameter of the heat-transfer tube, R pitch Is the pitch diameter ratio of the heat transfer tube.
In the above technical solution, the multi-objective optimization method for the volume and the load of the steam generator further includes constraint conditions, where the constraint conditions include a value range of the decision variable and upper and lower limits of the constraint variable.
In the technical scheme, the NSGA-II algorithm is utilized to solve y SG Minimum value of (2), min y SG 。
Further, according to the solved Min y SG The Pareto optimal solution set of the volume and the load of the steam generator is obtained, and a proper solution is selected from the solution set according to actual requirements.
In the above technical solution, the f V_SG (x) And f Q_SG (x) Calculated by modeling the steam generator.
Further, key parameters of the mother type equipment are collected and compared with calculation results of the mathematical model, reliability of evaluation programs of mathematics and development of the equipment is verified, accuracy of calculation results of the equipment programs is verified, and key parameters of the mother type equipment, namely, the diameter of a bent pipe section, the number of heat transfer pipes, the total heat transfer area, the height of a steam generator, the height of a straight pipe section, the wall thickness of the heat transfer pipes, the inner diameter of an upper cylinder, the wall thickness of the upper cylinder and the wall thickness of a lower cylinder are collected.
The traditional multi-objective optimization method mostly adopts a weighting method, namely, each objective is assigned with a weight and then is converted into a single objective problem, but the method can seriously depend on weighting factors selected by designers, different weighting factors usually correspond to different optimization results, and the setting of the weights of the objectives is subjective because the weights of the objectives cannot be quantized. It can be seen that the conventional optimization method has large workload and strong subjectivity, the quality of the final scheme depends on the past design experience to a great extent, and the optimal design scheme can only be determined from a plurality of candidate schemes. The invention adopts a non-dominant idea, provides a method for objectively optimizing the volume and the load of a steam generator by combining a mathematical model of the steam generator by using an NSGA-II algorithm and setting the volume and the load as optimization targets, and can obtain a Pareto optimal solution set of the volume and the load of the steam generator, so that a designer can select an optimal solution according to actual needs, and finally, the aim of bearing a larger load by a smaller volume of the steam generator is realized, and further, the miniaturization of a nuclear power device is gradually realized.
Drawings
FIG. 1 is a flow chart of a steam generator volume and load multi-objective optimization method of the present invention.
FIG. 2 is a flow chart of modeling steam generators in the optimization method of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
As shown in fig. 1, the multi-objective optimization method for the volume and the load of the steam generator of the present invention comprises:
s1, establishing a mathematical model of the steam generator, as shown in figure 2.
S1.1, a mathematical model of the steam generator is mainly designed in an analysis way from the aspects of heat transfer, flow, structure and the like. The basic structural form and thermal parameters of the steam generator are required in the thermodynamic calculation in order to calculate the heat transfer area of the heat transfer tube for structural design and hydraulic calculation.
S1.1.1, calculating a heat transfer temperature difference between a primary side and a secondary side according to a formula (2-1), namely:
wherein: Δt (delta t) max And delta t min The maximum temperature difference and the minimum temperature difference at the two ends of the heat exchange area are respectively at the temperature of DEG C.
S1.1.2 calculating the primary side flow G according to the formula (2-2) sg ：
In the middle of：h li Enthalpy J/kg for the steam generator heat transfer tube inlet; h is a lo Enthalpy J/kg for the steam generator heat transfer tube outlet; η (eta) sg The heat transfer efficiency of the primary side and the secondary side is achieved; q (Q) sg Is the thermal power of the steam generator, W.
S1.1.3 calculating the forced convection heat transfer coefficient alpha of the primary side coolant in the heat transfer pipe to the pipe wall by combining the formula (2-2) 1 :
Wherein: lambda (lambda) 1 W/(m.K) is the heat conductivity coefficient of the coolant; d, d i The inner diameter of the heat transfer tube is m; re (Re) f For Reynolds number of coolant, pr f Is the planchet number of the coolant. Re is a dimensionless number of a heat transfer standard, G is calculated according to the prior art by using the formula (2-2) sg Re can be calculated.
S1.1.4, calculating the boiling heat exchange coefficient of the heat exchange type of the secondary side according to the formula (2-4).
α 2 ＝5P sg 0.2 q 0.7 (2-4)
Wherein: p (P) sg The operating pressure of the secondary side, pa; q is the heat flux density of the heat transfer tube, W/m 2 。
S1.1.5 calculating the thermal resistance R of the pipe wall according to the formula (2-5) ω The heat transfer tube material used in this example was Incoloy-800, and the heat transfer coefficient was calculated according to the formula recommended by KWU:
λ＝11.628+1.57*10 -2 t w (2-5)
wherein: t is t w Is the temperature of the pipe wall and the temperature of the pipe wall.
S1.1.6 calculating the primary and secondary heat transfer coefficients k by combining the formulas (2-3), (2-4), (2-5):
wherein: d, d o And d i Respectively the outer diameter and the inner diameter of the heat transfer tube, m; r is R ω Is the thermal resistance of the pipe wall, (m) 2 ·℃)/W；R s For heat resistance of fouling of heat transfer tube wall, (m) 2 ·℃)/W。
S1.1.7, calculating the heat transfer area of the heat transfer pipe by combining the formulas (2-1) and (2-6):
wherein: the reserve factor c=1.1 taken in this example; q (Q) sg Is the heat exchange quantity, W; delta t is the temperature difference of heat transfer of the secondary side and DEG C; k is the heat transfer coefficient of the secondary side, W/(m) 2 ·℃)。
S1.2, carrying out detailed calculation of an internal structure after the heat transfer area of the heat transfer pipe is obtained through thermal calculation, wherein the structural calculation aims to obtain parameters such as the number of the heat transfer pipes, the diameter of a pipe bundle, the height of a straight pipe section and the like, and the parameters are used for the next hydraulic calculation.
S1.2.1, calculating the number of heat transfer area heat transfer pipes of the heat transfer pipes according to a formula (2-8):
wherein: d, d i Is the inner diameter of the heat transfer tube, m; u (u) l The flow velocity of working medium in the heat transfer pipe is m/s; ρ l To the density of working medium in the heat transfer tube, kg/m 3 ；G sg The flow rate is kg/s at the primary side.
S1.2.2, in combination with formulas (2-8), calculate the tube bundle diameter:
wherein: when the heat transfer tubes are arranged in a square shape, b takes a value of 1.19; b takes a value of 1.1 when arranged in a triangle; n is the number of pull rods; s is the pitch of the heat transfer tube, m; b' = (1 to 1.5) d 0 。
S1.2.3, calculating the height of the straight section of the heat transfer tube bundle of the steam generator by combining the formula (2-8):
wherein: l (L) total The total length of the U-shaped pipe is m;the average diameter of the heat transfer pipe in the bent pipe area is m.
S1.3, after the thermodynamic calculation and the structural design calculation of the steam generator are completed, hydraulic calculation can be performed, and the purpose is to determine the circulation multiplying power and the circulation speed of the secondary side. The hydraulic calculation of the steam generator comprises calculation of the flow resistance of a primary side, calculation of the motion pressure head of a secondary side and calculation of the circulation resistance, wherein the purpose of the calculation of the primary side is to provide a reference basis for the design of a primary circulation pump of a loop, and the circulation multiplying power is required to be set during the hydraulic calculation of the secondary side so that the motion pressure head and the flow resistance of the circulation loop reach balance. The hydraulic calculation of the secondary side needs to be solved in a joint iteration way with the design processes of heating power, structure and the like until convergence; the calculation of the resistance on the primary side needs to be calculated after the design of the steam generator is determined;
(1) Primary side resistance calculation
S1.3.1 on the primary side of the steam generator, the resistance includes frictional resistance and local resistance in the heat transfer tube, taking into account the reserve factor, which is 1.1 times the total calculated resistance.
Calculating the friction resistance in the heat transfer tube according to the formula (2-11):
wherein: ρ is the density of the coolant, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the u is the flow velocity of the coolant in the heat transfer tube, m/s; l (L) avg And m is the average length of the heat transfer tube.
S1.3.2, the local resistance calculated according to formulas (2-12):
wherein: zeta type toy i Is a local drag coefficient.
(2) Secondary side hydraulic calculation
The motion pressure head is produced by different densities of working media in a descending space and an ascending space in the steam generator, water in the descending space is single-phase supercooled water, and the supercooling degree is generally smaller, so that the density difference between the supercooled water and saturated water is usually ignored in actual calculation, and the calculation is uniformly carried out according to the saturated water density; in the secondary side rising section, the single-phase water absorbs heat to become saturated water until boiling, and the density is reduced.
S1.3.3 calculating the motion head of the secondary side of the steam generator according to the formula (2-13):
P m ＝(ρ s -ρ m )gH r (2-13)
wherein: ρ s Density of saturated water, kg/m 3 ；ρ m To average density of the steam-water mixture, kg/m 3 ；H r Is the height of the steam-containing section, m.
S1.3.4, by combining the formulas (2-11), (2-12) and (2-13), the circulation resistance is adjusted so that the circulation movement pressure head and the flow resistance of the secondary side of the steam generator are equal:
P m ＝ΔP r +ΔP s +ΔP d (2-14)
wherein: ΔP d 、ΔP r And DeltaP s The resistances of the secondary side descending section, the ascending section and the steam-water separator are respectively.
S1.4, the flow, heat transfer and structure are not independent, the calculation is repeatedly and alternately carried out until the calculation result is converged, and in the invention, the balance between the flow resistance of the secondary side and the circulating pressure head is taken as a convergence condition, so that the circulating multiplying power is required to be continuously adjusted.
S1.5, the inside of the steam generator is in a high-pressure state, and the design of bearing capacity is needed to ensure the operation safety of the steam generator. The intensity calculation can be performed after the internal detailed structure of the steam generator is determined, and the thicknesses of the cylinder and the sealing head are determined, so that the external structural parameters of the steam generator are determined. The wall thickness was calculated using ASME design specifications.
S2, after the mathematical model of the steam generator is established according to the step S1, in order to verify the reliability of the equipment mathematics and the developed evaluation program, the accuracy of the calculation result of the equipment program can be checked, and the calculation result of the program and the key parameters of the master equipment are compared. The parameters of the diameter of the bent pipe section, the number of the heat transfer pipes, the total heat transfer area, the height of the steam generator, the height of the straight pipe section, the wall thickness of the heat transfer pipe, the inner diameter of the upper cylinder, the wall thickness of the lower cylinder and the like can be specifically adopted.
S3, establishing a multi-objective optimization algorithm
And compiling an NSGA-II algorithm, and reserving variable interfaces such as decision variables, target variables, constraint variables, solving algebra, population number and the like.
S4, steam generator optimization model
S4.1, objective function
Setting an objective function of the multi-objective optimization design of the steam generator as follows:
Min y SG ＝F SG (x)＝(f V_SG (x),f Q_SG (x)) (2-15)
wherein: f (f) V_SG (x) As a function of SG volume with respect to decision variables; f (f) Q_SG (x) As a function of SG thermal power with respect to decision variables, f Q_SG (x) Is Q SG Taking the value obtained by the inverse, namely: f (f) Q_SG (x)＝-Q SG (x)；Q SG (x) As a function of thermal power with respect to decision variables.
S4.2 decision variables
Design parameters, including both thermal and structural aspects, that affect the objective function are determined from the design process of the steam generator. The thermal parameters are the operating pressure P of the reactor, the inlet temperature T of the reactor in And outlet temperature T out Mass flow rate G of primary loop coolant of reactor, secondary side pressure P of steam generator sg The flow velocity v of the coolant in the steam generator heat transfer tubes; the structural parameters mainly comprise the outer diameter do of the heat transfer tubePitch diameter ratio R of heat transfer tube pitch Etc., the decision vector is specifically:
x＝[P,T in ,T out ,G,P sg ,v,d tube_out ,R pitch ] (2-16)
s4.3, setting constraint conditions
In order to enable the steam generator to meet the requirements of actual engineering, constraint conditions are required to be added, wherein the constraint conditions specifically comprise a value range of a decision variable and upper and lower limits of the constraint variable, the value range of the decision variable is determined according to the specific steam generator, the value range is generally set to be a value nearby a primary value, and the larger the set range is, the wider the design requirements of the steam generator are met; the range of constraint variables is not specifically limited depending on the specific steam generator and designer's requirements.
S5, setting a solving model
The variable interface reserved in the NSGA-II algorithm is utilized to assign a value to the variable in the algorithm, specifically to a decision variable x and a target variable f in the steam generator optimization model V_SG Constraint variable C, solving algebra T, population number N, etc.
After the solution is completed, a Pareto optimal solution set of the volume and the load of the steam generator is obtained, a plurality of groups of optimization schemes are provided, and a proper solution is selected from the solution set according to actual requirements.

Claims (2)

1. A method for multi-objective optimization of steam generator volume and load, characterized by: setting an objective function of multi-objective optimization design of the steam generator:
Miny SG ＝F SG (x)＝(f V_SG (x),f Q_SG (x))
wherein f V_SG (x) As a function of SG volume with respect to decision variables; f (f) Q_SG (x) As a function of SG thermal power with respect to decision variables, f Q_SG (x) Is Q SG (x) Taking the value obtained by inverting, Q SG (x) As a function of thermal power with respect to decision variables;
the decision variables are:
x＝[P,T in ,T out ,G,P sg ,v,d tube_out ,R pitch ]
wherein P is the operating pressure of the reactor, T in T is the inlet temperature of the reactor out G is the mass flow of the reactor primary loop coolant, P, for the outlet temperature of the reactor sg V is the flow rate of the coolant in the steam generator heat transfer tube, d is the steam generator secondary side pressure tube_out For the outer diameter of the heat-transfer tube, R pitch The pitch diameter ratio of the heat transfer pipe;
the objective function further comprises constraint conditions, wherein the constraint conditions comprise a value range of a decision variable and upper and lower limits of the constraint variable; solving y using NSGA-II algorithm SG Minimum value of (2), min y SG The method comprises the steps of carrying out a first treatment on the surface of the From the solved Min y SG Obtaining a Pareto optimal solution set of the volume and the load of the steam generator, and selecting a proper solution from the solution set according to actual requirements;
said f V_SG (x) And f Q_SG (x) Calculation by establishing a mathematical model of a steam generator, comprising:
the heat transfer temperature difference of the primary side and the secondary side is calculated according to the formula (2-1), namely:
wherein: Δt (delta t) max And delta t min The maximum temperature difference and the minimum temperature difference at the two ends of the heat exchange area are respectively;
calculating the primary side flow G according to the formula (2-2) sg ：
Wherein: h is a li Enthalpy of inlet of heat transfer tube of steam generator, h lo Enthalpy, eta, of outlet of heat transfer tube of steam generator sg For the heat transfer efficiency of the primary side and the secondary side, Q SG Thermal power for the steam generator;
calculating the forcing of the primary side coolant in the heat transfer tube to the tube wall according to the formula (2-2)Coefficient of convective heat transfer alpha 1 ：
Wherein: lambda (lambda) 1 D is the heat conductivity of the coolant i Re is the inner diameter of the heat transfer tube f For Reynolds number of coolant, pr f Is the planchet number of the coolant;
calculating the boiling heat exchange coefficient of the heat exchange type of the secondary side according to the formula (2-4):
α 2 ＝5P sg 0.2 q 0.7 (2-4)
wherein: p (P) sg The operation pressure of the secondary side is represented by q, and the heat flux density of the heat transfer tube is represented by q;
when the thermal resistance of the pipe wall is calculated according to the formula (2-5), the thermal conductivity coefficient formula is calculated:
λ＝11.628+1.57*10 -2 t w (2-5)
wherein: t is t w Is the temperature of the pipe wall;
the primary and secondary heat transfer coefficients k are calculated in combination with equations (2-3), (2-4), (2-5):
wherein: d, d o And d i Respectively the outer diameter and the inner diameter of the heat transfer tube, R ω R is the thermal resistance of the pipe wall s Heat resistance for fouling of heat transfer tube walls;
the heat transfer area of the heat transfer pipe is calculated in combination with the formulas (2-1), (2-6):
wherein: c is a reserve coefficient, Q sg For heat exchange quantity, Δt is a secondary side heat transfer temperature difference, and k is a secondary side heat transfer coefficient;
calculating the number of heat transfer area heat transfer tubes of the heat transfer tubes according to the formula (2-8):
wherein: d, d i For the inner diameter of the heat-transfer tube, u l For the flow velocity of the working medium in the heat transfer tube, ρ l G is the density of the working medium in the heat transfer tube sg Is the primary side flow;
the tube bundle diameter was calculated in conjunction with formulas (2-8):
wherein: b takes a value of 1.19 when the heat transfer tubes are arranged in a square shape, and takes a value of 1.1 when the heat transfer tubes are arranged in a triangle shape; n is the number of pull rods; s is the heat transfer tube pitch, b' = (1-1.5) d 0 ；
Calculating the height of the straight section of the heat transfer tube bundle of the steam generator according to the formula (2-10):
wherein: l (L) total For the total length of the U-shaped tube,the average diameter of the heat transfer pipe in the bent pipe area;
calculating the friction resistance in the heat transfer tube according to the formula (2-11):
wherein: ρ is the coolant density, u is the coolant flow rate in the heat transfer tube, l avg Is the average length of the heat transfer tube;
local resistance calculated according to equation (2-12):
wherein: zeta type toy i Is a local resistance coefficient;
calculating the motion head of the secondary side of the steam generator according to the formula (2-13):
P m ＝(ρ s -ρ m )gH r (2-13)
wherein: ρ s Density of saturated water ρ m To average density of the steam-water mixture, H r Is the height of the steam-containing section;
the circulation resistance is adjusted by combining formulas (2-11), (2-12) and (2-13) so that the circulation movement pressure head and the flow resistance of the secondary side of the steam generator are equal:
P m ＝ΔP r +ΔP s +ΔP d (2-14)
wherein: ΔP d 、ΔP r And DeltaP s The resistances of the secondary side descending section, the ascending section and the steam-water separator are respectively.
2. The method of multi-objective optimization of steam generator volume and load according to claim 1, wherein: and (3) collecting key parameters of the female equipment, comparing the key parameters with calculation results of the mathematical model, verifying the reliability of an evaluation program for equipment mathematics and development, and verifying the accuracy of calculation results of equipment programs, wherein the key parameters of the female equipment comprise the diameter of a bent pipe section, the number of heat transfer pipes, the total heat transfer area, the height of a steam generator, the height of a straight pipe section, the wall thickness of the heat transfer pipes, the inner diameter of an upper cylinder, the wall thickness of the upper cylinder and the wall thickness of a lower cylinder.
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