CN114462159A - Multi-working-condition blade dehumidification optimal design method for marine wet steam turbine - Google Patents
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Abstract
The invention discloses a multi-working-condition blade dehumidification optimization design method of a marine wet steam turbine, which combines a blade parameterization reconstruction method, a Krigin approximate model and a multi-objective genetic optimization algorithm to form a wet steam non-equilibrium condensation flow characteristic result calculated by a three-dimensional flow field numerical simulation calculation method, takes the cascade outlet humidity of two operating working conditions of a minimized steam turbine as an optimization target, takes the stage efficiency of two working condition points which cannot be reduced and the flow of each working condition which keeps unchanged as a performance constraint condition and takes a parameterized leaf-type geometric variable as a design variable, and can realize the multi-working-condition multi-constraint dehumidification optimization design of the blades of the wet steam turbine.
Description
Technical Field
The invention belongs to the technical field of design of marine steam turbine parts, and particularly relates to a multi-working-condition blade dehumidification optimal design method for a marine wet steam turbine.
Background
The turbine blade is a core component for heat-work conversion of the marine turbine, and the performances of the turbine such as efficiency, power, safety, reliability, service life and the like are closely related to the blade profile. The development of the optimal design of the turbine blade has very important significance for ensuring the economy, reliability and safety of the turbine. Researchers have conducted extensive research on blade optimization design methods, but most of the research is directed to design conditions. The marine wet steam turbine has complex operation conditions and high maneuverability requirements, certain high-power single-cylinder turbine blades bear high-humidity steam and complex stress action, the overhigh steam humidity can not only reduce the output power and efficiency of the turbine, but also can cause the blades to be corroded for a long time, and the blades are extremely easy to damage or even break and lose efficacy, etc., so that the operation safety of the direct critical turbine is ensured, the performance under the multi-working-condition must be considered during the design, and the last-stage humidity is reduced as much as possible.
Disclosure of Invention
Aiming at the defects of the technology, the invention provides a multi-working-condition blade dehumidification optimal design method of a marine wet steam turbine, which can meet the performance requirements of a plurality of working condition points and improve the multi-working-condition operation reliability of the steam turbine.
In order to achieve the purpose, the multi-working-condition blade dehumidification optimal design method of the marine wet steam turbine is as follows:
the method comprises the following steps: parameterizing the blade profile of the blade based on a cubic Bezier curve, and determining design variables, objective functions and constraint conditions of the dehumidification optimization design of the blade profile of the steam turbine;
step two: taking the initial leaf profile parameters as central points, setting the value range of each design variable to meet the constraint conditions of the step two, and establishing a sample matrix X of the leaf profile design variables by adopting a Latin hypercube test design methodP×nSample matrix XP×nThe number of columns of (1) is n design variables, sample matrix XP×nThe number of rows of the sample matrix is P groups of samples, and each row of the sample matrix corresponds to one leaf type;
step three: determining a blade profile according to any set of design variables, establishing a blade cascade and a flow field model according to the blade profile, and calculating the flow characteristics of wet steam in the blade cascade formed by the blades by a three-dimensional flow field numerical simulation calculation method to obtain a target value sample matrix YP×2＝[Y1,Y2]The number of columns of the target value sample matrix Y is 2 and the number of rows is P;
step four: sample matrix X of design variablesP×nAnd a target value sample matrix YP×2As basic data, establishing a proxy model psi of blade design variables and a target function based on a Krigin approximate model;
step five: optionally, establishing a blade cascade model by using M groups of design variables meeting the constraint condition in the first step, and calculating M groups of objective function value matrixes of the flow characteristics of wet steam in the blade cascade by using a three-dimensional flow field numerical simulation calculation method;
setting up a leaf grid model by the M sets of design variables, bringing the leaf grid model into a proxy model psi in the fourth step to calculate an objective function value matrix, carrying out one-to-one correspondence comparison on the M sets of objective function value matrices for calculating the flow characteristics of wet steam in the leaf grid by a three-dimensional flow field numerical simulation calculation method and the M sets of objective function value matrices calculated by the proxy model psi, and turning to the sixth step if the proxy model meets the calculation precision requirement; otherwise, returning to the step two, and increasing the number of sample points until the agent model meets the calculation precision requirement;
step six: optimizing the constructed kriging proxy model psi through a multi-target non-dominated genetic algorithm, and obtaining an optimal objective function Y according to the constraint conditions in the step one1best,Y2bestAnd the corresponding optimum value of the design variable of the blade profile, Y1bestHumidity of cascade outlet at one time for optimum operating conditions, Y1bestAnd the humidity of the outlet of the blade cascade is the optimal working condition II.
Further, in the first step, the profile parameters include 12 parameters including 8 profile geometry parameters and 4 bessel curve shape control parametersThe geometric structural parameters of the 8 blade profiles are the width B of the blade, the installation angle gamma and the radius r of the arc of the front edge1Trailing edge arc radius r2Geometric steam inlet angle beta1Geometric steam outlet angle beta2Leading edge wedge
Trailing edge wedge
The 4 Bessel curve shape control parameters are h (1), h (2), h (3) and h (4), and each parameter corresponds to a design variable of a blade profile; n design variables are selected from 12 parameters, the rest 12-n parameters are constants, and n is more than or equal to 2 and less than or equal to 12.
Further, in the first step, the objective function is:
minY1(X1，X2，……，Xn)
minY2(X1，X2，……，Xn)
constraint conditions are as follows:
ld·X1≤X1≤X1·lu
ld·X2≤X2≤X2·lu
……
ld·Xn≤Xn≤Xn·lu
η01≤η1，η02≤η2
in the formula, X1，X2，……，XnRespectively 1 st, 2 nd, … … th and n th design variables; y is1Humidity eta of cascade outlet representing working condition at one time1Representing the isentropic efficiency of a working condition one; y is2Humidity eta of the cascade outlet when representing working condition two2Representing the isentropic efficiency under the working condition two; ldTaking 0.8-0.9; luTaking 1.1-1.2; eta01Equal entropy efficiency, eta, representing working condition time prototype blade grid02Prototype blade cascade for representing working condition twoIsentropic efficiency of (a).
Further, the isentropic efficiency is expressed as η ═ (h)in-hout)/(hin-hout,s)，hinFor the actual enthalpy value, h, of the cascade inletoutIs the actual enthalpy value of the cascade outlet hout,sIs the isentropic enthalpy of the outlet.
Further, in the second step, P is not less than 3 n.
Further, in the fourth step, the proxy model Ψ is:
Ψ＝f(xk)Tβ*+r(xk)Tγ*
β*＝(FTR-1F)-1FTR-1Y
γ*＝R-1(Y-Fβ*)
xkfor the parameters of the design variables, k is 1,2, … …, n;
in the formula, f (x)k) Parameter x as a design variablekFunction value f (x)k) F () is a first order polynomial function; r (x)k) Parameter x as a design variablekAnd the sample matrix XP×nA correlation function column vector between the samples; f matrix element is parameter x of design variablekFunction value f (x) corresponding to each samplei,k) I 1,2, … …, P, k 1,2, … … n; r represents a correlation function matrix, and the element expression in the matrix is as follows: r (X)i,Xj)＝Πk＝1exp(-θkdk 2)，i＝1,2,……,P，j＝1,2,……,P，k＝1,2,……,n，θkAs an anisotropy parameter, dkIs the distance between any two points in the sample.
Further, in the fifth step, M is more than or equal to 3 and less than or equal to P.
Further, in the fifth step, the calculation precision is 2% -3% of the relative error of the two calculated values.
Compared with the prior art, the invention has the following advantages: the design method fully considers the performance requirements of the steam turbine in the operation under multiple maneuvering conditions, takes the wet steam condensation flow thermodynamic parameters as an optimization target, and applies an optimization method based on an approximate model to carry out optimization design on a prototype blade by changing the profile parameters of the blade; the design method can control the condensation nucleation phenomenon, reduce the humidity of the through-flow part, give consideration to the performance requirements of a plurality of working condition points, and has important significance for improving the safety, reliability and economy of the multi-working-condition operation of the blade.
Drawings
FIG. 1 is a comparison graph before and after Dykas blade profile design optimization;
FIG. 2 is a cloud diagram of the humidity distribution of the initial blade profile under a rated working condition;
FIG. 3 is a cloud chart of optimized blade profile humidity distribution under rated conditions;
FIG. 4 is a cloud chart of initial leaf profile humidity distribution under a large flow condition;
FIG. 5 is a cloud chart of optimized leaf profile humidity distribution under a large flow working condition.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
The blade dehumidification optimal design method for the marine wet steam turbine under multiple working conditions specifically comprises the following steps:
the method comprises the following steps: representing the blade profile of the blade in a parameterized manner based on a cubic Bezier curve, wherein the blade profile parameters comprise 12 parameters including 8 blade profile geometric structure parameters and 4 Bezier curve shape control parameters, and the 8 blade profile geometric structure parameters comprise the width B of the blade, the installation angle gamma and the radius r of a front edge arc1Trailing edge arc radius r2Geometric steam inlet angle beta1Geometric steam outlet angle beta2Leading edge wedge
Trailing edge wedge
The 4 Bessel curve shape control parameters are h (1), h (2), h (3) and h (4), the 12 parameters can uniquely determine a blade profile, and each parameter corresponds to a design variable of the blade profile; optimized design for dehumidification of turbine blade profileWhen the method is used, n design variables are selected from 12 parameters, the rest 12-n parameters are constants, n satisfies n is more than or equal to 2 and less than or equal to 12, and two objective functions are determined as follows:
minY1(X1，X2，……，Xn)
minY2(X1，X2，……，Xn)
constraint conditions are as follows:
ld·X1≤X1≤X1·lu
ld·X2≤X2≤X2·lu
……
ld·Xn≤Xn≤Xn·lu
η01≤η1，η02≤η2
in the formula, X1，X2，……，XnRespectively 1 st, 2 nd, … … th and n th design variables; y is1Humidity eta of cascade outlet representing working condition at one time1Representing the isentropic efficiency of a working condition one; y is2Humidity eta of the cascade outlet when representing working condition two2Representing the isentropic efficiency under the working condition two; ldGenerally, 0.8-0.9 is selected; luTaking 1.1-1.2; eta01Equal entropy efficiency, eta, representing working condition time prototype blade grid02Expressing the isentropic efficiency of the prototype blade grid under the second working condition, and optimizing eta in design01And η02As a performance constraint. The isentropic efficiency is expressed as η ═ (h)in-hout)/(hin-hout,s)，hinFor the actual enthalpy value, h, of the cascade inletoutIs the actual enthalpy value of the cascade outlet hout,sIs the isentropic enthalpy of the outlet.
Step two: taking initial (before optimization) leaf profile parameters as central points, setting the value range of each design variable to meet the constraint condition of the step one, and establishing a sample matrix X of the leaf profile design variables by adopting a Latin hypercube test design methodP×nSample matrix XP×nThe number of columns is n design variablesSample matrix XP×nThe number of rows of the sample matrix is P groups of samples, P is not less than 3n, each row of the sample matrix corresponds to one leaf profile, namely P leaf profiles are total;
step three: determining a blade profile according to any set of design variables, establishing a blade cascade and a flow field model according to the blade profile, and calculating the flow characteristics of wet steam in the blade cascade formed by the blades by a three-dimensional flow field numerical simulation calculation method to obtain a target value sample matrix YP×2＝[Y1,Y2]The number of columns of the target value sample matrix Y is 2 and the number of rows is P;
step four: sample matrix X of design variablesP×nAnd a target value sample matrix YP×2As basic data, establishing a proxy model of blade design variables and an objective function based on a kriging approximate model, wherein the proxy model Ψ is as follows:
Ψ＝f(xk)Tβ*+r(xk)Tγ*
β*＝(FTR-1F)-1FTR-1Y
γ*＝R-1(Y-Fβ*)
xkfor the parameters of the design variables, k is 1,2, … …, n;
in the formula, f (x)k) Parameter x as a design variablekFunction value f (x)k) F () is a first order polynomial function; r (x)k) Parameter x as a design variablekAnd the sample matrix XP×nA correlation function column vector between the samples; f matrix element is parameter x of design variablekFunction value f (x) corresponding to each samplei,k) (i ═ 1,2, … …, P, k ═ 1,2, … … n); r represents a correlation function matrix, and the element expression in the matrix is as follows: r (X)i,Xj)＝Πk＝1exp(-θkdk 2)，i＝1,2,……,P，j＝1,2,……,P，k＝1,2,……,n，θkAs an anisotropy parameter, dkThe distance between any two points in the sample;
step five: optionally, establishing a cascade model by using M groups of design variables meeting the constraint condition in the first step, wherein M is more than or equal to 3 and is less than or equal to P; calculating M groups of objective function value matrixes of the flow characteristics of the wet steam in the blade cascade by a three-dimensional flow field numerical simulation calculation method;
simultaneously, establishing a blade grid model by the M sets of design variables, bringing the blade grid model into a proxy model psi in the fourth step to calculate an objective function value matrix, carrying out one-to-one correspondence comparison on the M sets of objective function value matrices of the flow characteristics of wet steam in the blade grid calculated by the three-dimensional flow field numerical simulation calculation method and the M sets of objective function value matrices calculated by the proxy model psi, and turning to the sixth step if the proxy model meets the calculation precision requirement (the calculated value has a relative error of 2-3%); otherwise, returning to the step two, and increasing the number of sample points until the agent model meets the calculation precision requirement;
step six: optimizing the constructed kriging proxy model psi by a multi-objective non-dominated genetic algorithm (NSGA-II) with the constraint conditions as the step one until an optimal objective function Y is obtained1best,Y2bestAnd the corresponding optimum value of the design variable of the blade profile, Y1bestHumidity of cascade outlet at one time for optimum operating conditions, Y1bestAnd the humidity of the outlet of the blade cascade is the optimal working condition II.
The invention combines a blade parameterization reconstruction method, a Kriging approximate model and a multi-objective genetic optimization algorithm to form a dehumidification optimization design system of the wet steam turbine, which takes the result of the wet steam unbalanced condensation flow characteristic calculated by a three-dimensional flow field numerical simulation calculation method as a basis, takes the blade cascade outlet humidity of two operating conditions of a minimized steam turbine as an optimization target, takes the stage efficiency of two operating conditions as a condition that the stage efficiency cannot be reduced and the flow of each operating condition is kept unchanged as a performance constraint condition and takes a parameterized blade type geometric variable as a design variable, can realize the multi-operating-condition multi-constraint dehumidification optimization design of the blades of the wet steam turbine, and provides powerful guidance for the intelligent optimization design and operation of the blades of the wet steam turbine.
According to the invention, the in-line blades and the twisted blades of the marine steam turbine can be optimally designed, and after the blade profiles at different positions along the blade height are respectively optimized, the three-dimensional solid blades with excellent performance can be constructed, and the multi-working-condition dehumidification optimal design of the moving and fixed blades of the steam turbine stage can be realized; the method can easily realize the optimization design of the comprehensive performance and the structural characteristics of the power, the efficiency, the humidity and the like of the steam turbine by changing the optimization target, the constraint condition and the design variable, has wide application prospect, not only can consider the performance requirements of a plurality of working condition points, improves the reliability of the multi-working condition operation of the steam turbine, but also can provide technical support for the intelligent optimization design of the variable-working-condition through-flow blades of the wet steam turbine.
Taking the example of a Dykas turbine blade, the unbalanced condensation flow of the wet steam affecting the loss of the moisture of the blade profile occurs mainly at the suction surface of the blade, and therefore 7 parameters (installation angle gamma, geometric steam inlet angle beta) are selected1Front edge wedge angle
Radius r of front and rear edge1And r2Bezier curve control variable h1And h2) As a design variable, i.e., n-7. Increasing a +/-10% floating value on the basis of an initial design variable to serve as a value range of the design variable (the variation of the performance of the blade cannot be reflected if the floating variable is too small and the blade is excessively deformed and has obvious difference with the actual blade profile of the steam turbine if the floating variable is too large obtained through a large amount of analysis), namely ld＝0.9，lu1.1. Meanwhile, in order to reduce the influence of the design variable unit on the result, the control variable h of the Bezier-removing curve is controlled1And h2All other variables are normalized by taking the initial leaf profile parameters as reference.
Adopting a sample space generated by a Latin hypercube test design method to obtain a design variable matrix of the blade, establishing a Dykas blade profile curve and a blade cascade flow field channel, adopting a three-dimensional flow field numerical simulation calculation method to carry out non-equilibrium condensation calculation, and obtaining a response value (Y) related to the blade profile under a rated working condition (working condition one) and a large-flow working condition (working condition two)1、η1、Y2、η2) (ii) a And establishing a proxy model of the blade design variables and the target function based on the Krigin approximate model according to the calculation result. 5 groups of geometric parameters in the optional sample are taken as input parameters to be brought into the constructed kriging agent model, the maximum value of the simulation calculation error between the model prediction value and the three-dimensional flow field numerical value is 1.7%, and the precision requirement is met; at the same time obtainThe degree of influence of each structural parameter on the humidity and efficiency of the objective function is shown in table 1.
TABLE 1 influence ratio of blade profile design variables on cascade efficiency and outlet humidity
The ratio of the optimization result and the initial result of the blade profile design parameters calculated by the method of the invention is shown in table 2. Relative to the initial blade cascade, the optimization blade profile reduces the geometric steam inlet angle and the control parameter h of the steam outlet edge of the Bezier curve of the suction surface2Therefore, the curvature from the throat part to the tail edge part of the suction edge of the blade profile is reduced, the profile of the suction surface of the blade near the throat part is more gentle, the steam flow expansion is more uniform, the local expansion rate and the steam flow turning are smaller, and a comparison graph before and after the blade profile optimization is shown in figure 1.
TABLE 2Dykas cascade design variable multi-condition dehumidification design optimization results
Table 3 shows the comparison between the Dykas cascade condensation characteristic optimization result calculated by the three-dimensional flow field numerical simulation calculation method and the initial result. Compared with the initial cascade, the outlet humidity is reduced by 6.1 percent, the entropy increase is reduced by 5.1 percent, the maximum droplet diameter is reduced by 11.4 percent, and the isentropic efficiency is improved by 0.6 percent after optimization under the rated working condition; under the working condition of large flow, the humidity of an outlet is reduced by 8.9 percent after optimization, the entropy increase is reduced by 15.2 percent, the maximum droplet diameter is reduced by 15.8 percent, and the isentropic efficiency is improved by 0.9 percent. As can be seen from comparison of the humidity distribution cloud charts before and after optimization of the working conditions in the figures 2 and 3, the optimized blade cascade can inhibit the non-equilibrium condensation flow process at two working condition points, and the steam humidity in the blade cascade channel is reduced.
TABLE 3Dykas cascade design variable multi-condition dehumidification design optimization results
Claims (8)
1. A multi-working-condition blade dehumidification optimal design method for a marine wet steam turbine is characterized by comprising the following steps of: the optimization design method comprises the following steps:
the method comprises the following steps: parameterizing the blade profile of the blade based on a cubic Bezier curve, and determining design variables, objective functions and constraint conditions of the dehumidification optimization design of the blade profile of the steam turbine;
step two: taking the initial leaf profile parameters as central points, setting the value range of each design variable to meet the constraint conditions of the step two, and establishing a sample matrix X of the leaf profile design variables by adopting a Latin hypercube test design methodP×nSample matrix XP×nThe number of columns of (1) is n design variables, sample matrix XP×nThe number of rows of the sample matrix is P groups of samples, and each row of the sample matrix corresponds to one leaf type;
step three: determining a blade profile according to any set of design variables, establishing a blade cascade and a flow field model according to the blade profile, and calculating the flow characteristics of wet steam in the blade cascade formed by the blades by a three-dimensional flow field numerical simulation calculation method to obtain a target value sample matrix YP×2＝[Y1,Y2]The number of columns of the target value sample matrix Y is 2 and the number of rows is P;
step four: sample matrix X of design variablesP×nAnd a target value sample matrix YP×2As basic data, establishing a proxy model psi of blade design variables and a target function based on a Krigin approximate model;
step five: optionally, establishing a blade cascade model by using M groups of design variables meeting the constraint condition in the first step, and calculating M groups of objective function value matrixes of the flow characteristics of wet steam in the blade cascade by using a three-dimensional flow field numerical simulation calculation method;
setting up a leaf grid model by the M sets of design variables, bringing the leaf grid model into a proxy model psi in the fourth step to calculate an objective function value matrix, carrying out one-to-one correspondence comparison on the M sets of objective function value matrices for calculating the flow characteristics of wet steam in the leaf grid by a three-dimensional flow field numerical simulation calculation method and the M sets of objective function value matrices calculated by the proxy model psi, and turning to the sixth step if the proxy model meets the calculation precision requirement; otherwise, returning to the step two, and increasing the number of sample points until the agent model meets the calculation precision requirement;
step six: optimizing the constructed kriging proxy model psi through a multi-target non-dominated genetic algorithm, and obtaining an optimal objective function Y according to the constraint conditions in the step one1best,Y2bestAnd the corresponding optimum value of the design variable of the blade profile, Y1bestHumidity of cascade outlet at one time for optimum operating conditions, Y1bestAnd the humidity of the outlet of the blade cascade is the optimal working condition II.
2. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 1, characterized in that: in the first step, the blade profile parameters comprise 12 parameters including 8 blade profile geometric structure parameters and 4 Bessel curve shape control parameters, and the 8 blade profile geometric structure parameters comprise the blade width B, the installation angle gamma and the front edge arc radius r1Trailing edge arc radius r2Geometric steam inlet angle beta1Geometric steam outlet angle beta2Leading edge wedge
Trailing edge wedge
The 4 Bessel curve shape control parameters are h (1), h (2), h (3) and h (4), and each parameter corresponds to a design variable of a blade profile; n design variables are selected from 12 parameters, the rest 12-n parameters are constants, and n is more than or equal to 2 and less than or equal to 12.
3. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 2, characterized in that: in the first step, the objective function is:
minY1(X1，X2，……，Xn)
minY2(X1，X2，……，Xn)
constraint conditions are as follows:
ld·X1≤X1≤X1·lu
ld·X2≤X2≤X2·lu
……
ld·Xn≤Xn≤Xn·lu
η01≤η1，η02≤η2
in the formula, X1，X2，……，XnRespectively 1 st, 2 nd, … … th and n th design variables; y is1Humidity eta of cascade outlet representing working condition at one time1Representing the isentropic efficiency of a working condition one; y is2Humidity eta of the cascade outlet when representing working condition two2Representing the isentropic efficiency under the working condition two; ldTaking 0.8-0.9; luTaking 1.1-1.2; eta01Equal entropy efficiency, eta, representing working condition time prototype blade grid02And expressing the isentropic efficiency of the prototype blade grid under the second working condition.
4. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 3, wherein: the isentropic efficiency is expressed as η ═ (h)in-hout)/(hin-hout,s)，hinIs the actual enthalpy value h of the inlet of the blade gridoutIs the actual enthalpy value of the cascade outlet hout,sIs the isentropic enthalpy of the outlet.
5. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 1, characterized in that: in the second step, P is not less than 3 n.
6. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 1, characterized in that: in the fourth step, the proxy model Ψ is:
Ψ＝f(xk)Tβ*+r(xk)Tγ*
β*＝(FTR-1F)-1FTR-1Y
γ*＝R-1(Y-Fβ*)
xkfor the parameters of the design variables, k is 1,2, … …, n;
in the formula, f (x)k) Parameter x as a design variablekFunction value f (x)k) F () is a first order polynomial function; r (x)k) Parameter x as a design variablekAnd the sample matrix XP×nA correlation function column vector between the samples; f matrix element is parameter x of design variablekFunction value f (x) corresponding to each samplei,k) I 1,2, … …, P, k 1,2, … … n; r represents a correlation function matrix, and the element expression in the matrix is as follows: r (X)i,Xj)＝Πk＝1exp(-θkdk 2)，i＝1,2,……,P，j＝1,2,……,P，k＝1,2,……,n，θkAs an anisotropy parameter, dkIs the distance between any two points in the sample.
7. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 1, characterized in that: in the fifth step, M is more than or equal to 3 and less than or equal to P.
8. The marine wet steam turbine multi-condition blade dehumidification optimal design method according to claim 1, characterized in that: in the fifth step, the calculation precision is 2% -3% of the relative error of the two calculated values.
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Citations (7)
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