CN115114750B - Multi-working-point optimization method for wide-working-condition power turbine - Google Patents
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Abstract
The invention discloses a multi-working-point optimization method of a wide working-condition power turbine, which utilizes a constrained combined differential evolution algorithm to design and calculate the inverse problem optimization of each single working point of the wide working-condition power turbine and solve a mathematical model required by the optimization design of the turbine to obtain an optimal solution at each designed rotating speed value, wherein the optimal solution comprises the following steps: optimum flow channel geometry; according to the design parameters of the multiple working points of the wide working condition power turbine, carrying out positive problem calculation on the wide working condition power turbine corresponding to the optimal solution under each design rotating speed value to obtain the wide working condition power turbine efficiency of different working points; and constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine, and calculating to obtain a comprehensive performance evaluation index value of the wide-working-condition power turbine, so as to obtain an optimal performance value of the wide-working-condition power turbine.
Description
Technical Field
The invention belongs to the field of turbines, and particularly relates to a multi-working-point optimization method for a wide-working-condition power turbine.
Background
Conventional turboshaft or turboprop power turbines often operate at substantially constant rotational speeds near the design point, and their aerodynamic efficiency can only be ensured over a narrow range of operating conditions. The task characteristics of the high-speed helicopter provide higher requirements on the performance and working condition range of the turboshaft engine power turbine, the power turbine is required to work for a long time under a plurality of working conditions with larger difference in rotating speed, the power turbine is essentially different from the conventional power turbine, new challenges are provided for the power turbine design technology, key improvements and innovations are required for the power turbine design technology, and a special wide working condition power turbine design technology is developed and formed.
The method mainly solves the problem that when the wide-working-condition power turbine is designed in one-dimensional through flow, one-dimensional parameters of the turbine with the best comprehensive performance are obtained according to the working condition range provided by the turbine.
Disclosure of Invention
The invention aims to solve the technical problems in the background technology and provides a multi-working-point optimization method for a wide-working-condition power turbine.
In order to solve the technical problems, the technical scheme of the invention is as follows:
setting design parameters of multiple working points of the wide-working-condition power turbine;
inputting a preset optimized rotating speed range and corresponding rotating speed quantity, and preprocessing to obtain a plurality of preprocessed design rotating speed values, namely obtaining the design rotating speed value of each single working point; establishing a mathematical model required by the optimal design of the turbine;
And carrying out inverse problem optimization design calculation on each single working point of the wide working condition power turbine by using a constrained combined differential evolution algorithm for the design rotating speed value of each single working point, and solving a mathematical model required by the turbine optimization design to obtain an optimal solution under each design rotating speed value, wherein the optimal solution comprises: optimum flow channel geometry;
According to the design parameters of the multiple working points of the wide working condition power turbine, carrying out positive problem calculation on the wide working condition power turbine corresponding to the optimal solution under each design rotating speed value to obtain the wide working condition power turbine efficiency of different working points;
And constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine, and calculating to obtain a comprehensive performance evaluation index value of the wide-working-condition power turbine, so as to obtain an optimal performance value of the wide-working-condition power turbine.
Further, the turbine multi-operating point includes: take-off operating point, cruise operating point, and high speed flight operating point.
Further, the parameters of the multiple working points of the turbine include: rotational speed parameters, fuel consumption parameters, shaft power parameters, and operating time parameters.
Further, the optimal performance value of the wide-working-condition power turbine corresponds to the wide-working-condition power turbine designed at the design rotating speed, and the wide-working-condition power turbine with the optimal comprehensive performance is obtained.
Further, inputting a preset optimized rotating speed range and corresponding rotating speed quantity, and carrying out equally dividing treatment to obtain a plurality of equally divided design rotating speed values, namely obtaining the design rotating speed value of each single working point.
Further, according to the rotating speed parameter and the shaft power parameter in the design parameters of the multiple working points of the wide working condition power turbine, carrying out one-dimensional positive problem calculation processing on the wide working condition power turbine corresponding to the optimal solution under each designed rotating speed value, and obtaining the wide working condition power turbine efficiency of different working points.
Further, the construction of the wide-working-condition power turbine comprehensive performance evaluation index model specifically comprises the following steps:
And constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine according to the wide-working-condition power turbine efficiency of different working points and design parameters of multiple working points of the wide-working-condition power turbine.
Further, the design parameters of the wide-working-condition power turbine efficiency and the multiple working-condition power turbine working points of different working points are input into a wide-working-condition power turbine comprehensive performance evaluation index model, and the wide-working-condition power turbine comprehensive performance evaluation index value is obtained through calculation.
Further, the wide-working-condition power turbine with the best comprehensive performance is as follows: the power turbine can work relatively efficiently and stably in a wide rotating speed range.
Compared with the prior art, the invention has the advantages that: a low-dimensional optimization design method of a turbine working in a very wide rotating speed range is provided, and the flow channel geometry with optimal overall performance of the turbine in the whole flight task of an aircraft can be designed.
Drawings
FIG. 1 is a main flow chart of a wide-operating-range power turbine multi-operating-point optimization method of the invention;
FIG. 2 is a graph of the overall performance of the wide-operating-range power turbine multi-operating-point optimization method of the present invention.
Detailed Description
The following describes specific embodiments of the present invention with reference to examples:
it should be noted that the structures, proportions, sizes and the like illustrated in the present specification are used for being understood and read by those skilled in the art in combination with the disclosure of the present invention, and are not intended to limit the applicable limitations of the present invention, and any structural modifications, proportional changes or size adjustments should still fall within the scope of the disclosure of the present invention without affecting the efficacy and achievement of the present invention.
Also, the terms such as "upper," "lower," "left," "right," "middle," and "a" and the like recited in the present specification are merely for descriptive purposes and are not intended to limit the scope of the invention, but are intended to provide relative positional changes or modifications without materially altering the technical context in which the invention may be practiced.
Example 1:
The multi-stage turbine meridian flow passage optimization design is a constraint optimization problem, the one-dimensional optimization design of the multi-stage low-pressure turbine which is free from flow passage limitation is of no practical significance, the development trend of the meridian flow passage molded line of the turbine part of the current efficient engine is used for referencing the quantitative treatment of the multi-stage turbine meridian flow passage limitation condition, and the multi-stage turbine meridian flow passage optimization design method is developed by combining a combined differential evolution algorithm. Specifically, the turbine outlet maximum outer diameter dimension, the trough and the casing profile are included. In addition, the absolute turbine outlet airflow angle and the outlet Mach number should be limited to a certain range.
The mathematical model required for establishing the turbine optimization design is specifically as follows:
In engineering applications, the premise that the multi-stage low-pressure turbine meridian flow passage form is acceptable is that the turbine valley and casing profile development is continuous, and the first derivative is slowly transiting. For this purpose, the divergence angle of each turbine stage wheel Gu Xingxian and the casing profile is defined It should be noted that, "expansion" refers to an angle formed by a wheel load or a casing line between an inlet and an outlet of a rotor or a stator, so that a flow passage characteristic of each stage of turbine is represented by four expansion angles: stator casing molded line expansion angleStator hub molded line angle of divergenceRotor casing molded line expansion angleAnd rotor hub molded line angle of divergence. The range of the expansion angle of the first-stage guide vane runner is given, and the increment of the expansion angle of the next-blade row of the turbine and the molded line of the case is controlled to be in a certain range at the same time, so that the purpose of controlling the development of the runner is achieved. With reference to the current turbine runner form, its casing profile is always distended and raised up to a maximum outer diameter. The given optimization constraints mainly have the following points:
(1) The absolute air flow angle and Ma number limit of the final outlet of the turbine;
(2) The maximum outer diameter limit of the turbine final stage outlet casing;
(3) The turbine first stage guide vane wheel load and the casing type line expansion angle limit;
(4) And the increment of the difference value of the flow passage divergence angles between the adjacent blade rows is limited.
(5) Turbine stageIs limited by (a);
The total efficiency of the turbine is adopted to measure the advantages and disadvantages of one-dimensional optimization design results of the turbine, and an objective function of a differential evolution algorithm is the total efficiency of the multistage low-pressure turbine predicted by a loss model :
All angles and their increments in the DE optimization constraints are limited to a range except for the maximum outer diameter of the outlet, so each constraint is equivalent to two inequality constraints. Such as the angle of divergence of the flow pathThe inequality constraint is:
；
in practice, the constraint optimization problem described in this embodiment includes three equality constraints, namely, the sum of the work distribution coefficients of each turbine stage, the turbine axial length, and the maximum outer diameter of the turbine last stage blade row.
；
Converting the constraint optimization problem into an unconstrained optimization problem by using a penalty function method, and constructing the following penalty function according to conditions:
Then, the mathematical model for solving the multi-stage turbine meridian runner optimization design problem by using the differential evolution algorithm provided by the embodiment is as follows:
(0.2)
penalty factor in Is a very large number (e.g. 1e 7).
The number of inequality constraints varies from turbine stage to turbine stage. The single-stage turbine speed triangle is determined by five parameters, namely a load coefficient, a flow coefficient, an inverse force, an axial speed ratio coefficient and a movable vane inlet-outlet pitch diameter ratio, and meanwhile, the parameters are related to efficiency, and the multistage is required to consider the work distribution coefficients of each stage; in addition, parameters such as the aspect ratio, the relative grid distance and the relative maximum thickness of each blade row are related by adopting a AMDCKO loss model, and the aspect ratio and the relative grid distance of the blades determine the expansion angle of the flow channel and the distribution of the blades, so that the aspect ratio and the relative grid distance are taken as decision variables of an optimization problem, and other parameters play an important role in two-dimensional design, but for one-dimensional design, the influence of the parameters on efficiency depends on the loss model, so that the relationship of the parameters on efficiency is difficult to predict with better precision in the conventional loss model, and the variables excessively influence the calculation of the optimization speed, so that the parameters are temporarily not considered. Thus, the turbine efficiency per stage is determined by 10 parameters, and the aspect ratio is defined using the blade height at each blade discharge opening. The work distribution coefficient of the final stage turbine becomes a known quantity due to the corresponding processing of the work distribution coefficient, and a decision variable can be reduced. Therefore, for the M-stage low-pressure turbine, the meridional flow channel optimization design is commonAnd decision variables.
If a certain secondary power turbine is optimized, there are 19 optimization variables from the above expression. The parameters required by the inverse problem design give the range of values for all optimization variables (taking table 1 as an example):
TABLE 1
While for turbine constraints, starting from the turbine stage first, it can be seen from the above analysis that to represent the continuity of the turbine flow path, table 2 below is an inequality constraint on the turbine stage geometry flow path.
TABLE 2
For the constraint of a full stage turbine, consider the combustor outlet conditions and the requirements after turbine outlet to constrain it, for example, table 3:
TABLE 3 Table 3
Example 2:
And (3) carrying out inverse problem optimization design calculation on each single working point of the wide working condition power turbine by utilizing a constrained combined differential evolution algorithm according to the design rotating speed value of each single working point, wherein the calculation flow is as follows:
1. Parameter initialization processing:
Optimized variable load factor required for turbine Flow coefficientForce of opposite directionsAxial speed ratio coefficientRatio of inlet to outlet of movable vaneCoefficient of work distributionAspect ratio of guide vaneAspect ratio of movable bladeRelative pitch of guide vaneRelative pitch of movable vanesWhere the superscript i denotes the number of turbine stages, so that the i-stage turbines have a total of 10i-1 variables.
Since each variable needs to provide an optimization scope, each variable performs an initialization process:
； (0.3)
Wherein X is represented as an optimization variable, and subscripts Max and Min represent maximum values and minimum values which can be obtained by the optimization variable.
Setting a population NP, a control parameter set and a strategy set, wherein the control parameter set comprises three groups of scaling factors F and cross probabilities Cr:
； (0.4)
The policy set includes three variant policies:
rand/1/bin:
； (0.5)
rand/2/bin:
； (0.6)
Current-to-best/1:
； (0.7)
wherein r1, r2, r3, r4 and r5 are In the optimization method, best is the subscript of the corresponding parameter of the current optimal value, G represents the current population evolution iteration number, U represents the variable vector after mutation, j represents the position of the optimization vector, if 10 optimization variables exist, the value range of j is between 1 and 10 directly, if the first optimization variable is processed, j=1,It means that an optimization variable position is randomized before the first variable is processed, and if the random value satisfies the position of the optimization variable pair, it is executed as formula (0.5).
2. Performing turbine one-dimensional inverse problem calculation on the initial population to obtain all objective functions and penalty functions, calculating parameter information of the recorded optimal value through a mathematical model, and setting evolution iteration number G=0;
The turbine geometric flow channel and each section parameter value can be obtained by utilizing the turbine overall parameters and the optimization variables initialized before through inverse problem calculation, the efficiency value (objective function value) is obtained, the geometric parameters and the pneumatic parameters of each flow channel parameter are recorded, constraint processing is carried out on the flow channel parameters, a penalty function is carried out, and a new objective function is obtained by combining the penalty function and the objective function and is used as a new optimized objective function.
3. Randomly selecting a group of control parameters from the control parameter set for each individual parameter, and calling three new individual generation strategies in the individual parameter generation strategy set to generate new vectors;
It can be known from the formula (0.4) that three sets of control set parameters are total, before data updating is performed, each optimization variable needs to randomly take any one set of values in the three sets of data, and the values are respectively brought into (0.5) (0.6) (0.7) to obtain updated values of three different strategies.
4. Calculating the objective function values and penalty function values (through inverse problems) of the three new vectors, and obtaining an optimal value (new objective function) corresponding to the individual through a mathematical model as an attempt vector U;
and as the initial population is given, obtaining an objective function value corresponding to the population, and finding the optimal objective function value, wherein the optimal variable parameter corresponding to the value is a vector U.
5. And comparing the target vector X with the optimal value corresponding to the newly generated vector U, and if U is better than X. Then replace X with U to enter next generation population
6. Judging whether all individuals in the population are executed completely, if not, executing the step 3, otherwise, executing the step 7
7. Finding out the optimal individual of the next generation population, and updating the information of the optimal individual, wherein G=G+1;
8. And (3) judging whether a termination condition is met, outputting the best individual information and the corresponding objective function value if the termination condition is met, terminating the algorithm, and otherwise executing the step (3).
Example 3:
And constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine, and calculating to obtain a comprehensive performance evaluation index value of the wide-working-condition power turbine, so as to obtain an optimal performance value of the wide-working-condition power turbine.
The comprehensive performance evaluation index model of the wide-working-condition power turbine is as follows:
； (0.8)
Wherein, The working time of different state points is represented by T, the total working time is represented by T,The fuel consumption for the different status points,For the fuel consumption rate of the design point,For the shaft power at the different state points,For the shaft power of the design point,Is the efficiency of the different status points.
Example 4:
for the multi-working-point optimal design method, the states of the aircraft, such as take-off, flat flight, high-speed flight and the like, under different working states are considered, and the states correspond to the engine rotating speed N and the fuel consumption The shaft power P, the operating time period T are different, so that the following steps can be performed on them by means of these parameters:
Setting design parameters of multiple working points of the wide-working-condition power turbine; obtaining the rotation speed Fuel consumptionShaft powerDuration of workWherein the subscript E represents the number of status points; as shown in table 4:
TABLE 4 Table 4
Wherein the working time length satisfies:
； (0.9)
inputting a preset optimized rotating speed range and corresponding rotating speed quantity, and preprocessing to obtain a plurality of preprocessed design rotating speed values;
And carrying out inverse problem optimization calculation on the wide-working-condition power turbine by utilizing a constrained combined differential evolution algorithm on a plurality of preprocessed design rotating speed values to obtain an optimal solution under each design rotating speed value, wherein the optimal solution comprises: optimum flow channel geometry;
According to the design parameters of the multiple working points of the wide working condition power turbine, carrying out positive problem calculation processing on the wide working condition power turbine corresponding to the optimal solution under each design rotation speed value to obtain the wide working condition power turbine efficiency of different working points;
And constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine, and calculating to obtain a comprehensive performance evaluation index value of the wide-working-condition power turbine, so as to obtain an optimal performance value of the wide-working-condition power turbine.
It can be understood that: construction functionAnd (3) as an evaluation standard for evaluating the comprehensive performance of the turbine, calculating an F value according to the efficiency obtained at different design rotating speeds, wherein the optimal value is used as the optimal performance value of the turbine under the wide working condition.
By the method, a one-dimensional design of a certain two-stage power turbine under a wide working condition is performed, and according to the calculation result of fig. 2, the geometric flow passage with the best comprehensive performance can be obtained by designing at the rotating speed of 17200 RPM.
While the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the above embodiments, and various changes may be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Many other changes and modifications may be made without departing from the spirit and scope of the invention. It is to be understood that the invention is not to be limited to the specific embodiments, but only by the scope of the appended claims.
Claims (6)
1. The multi-operating-point optimization method for the wide-operating-condition power turbine is characterized by comprising the following steps of:
setting design parameters of multiple working points of the wide-working-condition power turbine;
Inputting a preset optimized rotating speed range and corresponding rotating speed quantity, and preprocessing to obtain a plurality of preprocessed design rotating speed values, namely obtaining the design rotating speed value of each single working point;
establishing a mathematical model required by the optimal design of the turbine;
And carrying out inverse problem optimization design calculation on each single working point of the wide working condition power turbine by using a constrained combined differential evolution algorithm for the design rotating speed value of each single working point, and solving a mathematical model required by the turbine optimization design to obtain an optimal solution under each design rotating speed value, wherein the optimal solution comprises: optimum flow channel geometry;
According to the design parameters of the multiple working points, positive problem calculation is carried out on the wide working condition power turbine corresponding to the optimal solution under each design rotating speed value, so that the wide working condition power turbine efficiency of different working points is obtained;
Constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine, and calculating to obtain a comprehensive performance evaluation index value of the wide-working-condition power turbine, namely obtaining an optimal performance value of the wide-working-condition power turbine;
the turbine multi-operating point includes: a take-off operating point, a cruise operating point, and a high-speed flight operating point;
The parameters of the multiple working points of the turbine comprise: a rotational speed parameter, a fuel consumption parameter, a shaft power parameter and a working time parameter;
Inputting a preset optimized rotating speed range and corresponding rotating speed quantity, and carrying out equally dividing treatment to obtain a plurality of equally divided design rotating speed values, namely obtaining the design rotating speed value of each single working point.
2. The multi-operating-point optimization method of the wide-operating-condition power turbine according to claim 1, wherein the optimal performance value of the wide-operating-condition power turbine corresponds to the wide-operating-condition power turbine designed at the designed rotating speed, and the wide-operating-condition power turbine is the wide-operating-condition power turbine with the optimal comprehensive performance.
3. The method for optimizing the multiple working points of the wide-working-condition power turbine according to claim 1, wherein the wide-working-condition power turbine corresponding to the optimal solution under each designed rotating speed value is subjected to one-dimensional positive problem calculation processing according to the rotating speed parameter and the shaft power parameter in the design parameters of the multiple working points of the wide-working-condition power turbine, so that the wide-working-condition power turbine efficiency of different working points is obtained.
4. The method for optimizing multiple operating points of a wide-operating-condition power turbine according to claim 1, wherein the construction of the wide-operating-condition power turbine comprehensive performance evaluation index model is specifically as follows:
And constructing a comprehensive performance evaluation index model of the wide-working-condition power turbine according to the wide-working-condition power turbine efficiency of different working points and design parameters of multiple working points of the wide-working-condition power turbine.
5. The method for optimizing the multiple working points of the wide-working-condition power turbine according to claim 1, wherein design parameters of the wide-working-condition power turbine efficiency and the multiple working points of the wide-working-condition power turbine at different working points are input into a wide-working-condition power turbine comprehensive performance evaluation index model, and the wide-working-condition power turbine comprehensive performance evaluation index value is calculated.
6. The wide-operating-condition power turbine multi-operating-point optimization method according to claim 2, wherein the wide-operating-condition power turbine with the best comprehensive performance is: the power turbine can work relatively efficiently and stably in a wide rotating speed range.
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