CN107194118B - Pneumatic-thermal collaborative optimization method for turbine blade fan-shaped hole air film cooling structure - Google Patents

Pneumatic-thermal collaborative optimization method for turbine blade fan-shaped hole air film cooling structure Download PDF

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CN107194118B
CN107194118B CN201710464122.XA CN201710464122A CN107194118B CN 107194118 B CN107194118 B CN 107194118B CN 201710464122 A CN201710464122 A CN 201710464122A CN 107194118 B CN107194118 B CN 107194118B
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黄莺
张靖周
王春华
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a pneumatic-thermal collaborative optimization method for a turbine blade fan-shaped hole air film cooling structure. The method overcomes the characteristic that the traditional air film cooling structure optimization method needs to depend on a large number of samples, and has the advantages of nonlinear prediction capability, high prediction precision, strong memory capability and robustness, and good global approximation capability. And the weight of the aerodynamic performance and the thermal performance can be adjusted according to the actual requirement, and the optimal fan-shaped hole air film cooling structure with both the aerodynamic performance and the thermal performance is designed.

Description

Pneumatic-thermal collaborative optimization method for turbine blade fan-shaped hole air film cooling structure
Technical Field
The invention relates to a pneumatic-thermal cooperative optimization method for a turbine blade fan-shaped hole air film cooling structure, and belongs to the technical field of enhanced cooling.
Background
In the technical development process of an aircraft gas turbine engine, the pressure increase ratio of a compressor and the temperature of gas at the inlet of a turbine show a trend of increasing continuously. According to the future development trend of advanced aviation gas turbine engine technology, the thrust-weight ratio of a new generation engine reaches about 15, and the gas temperature at the inlet of the turbine reaches 2200K-2300K at the moment. The heat load of hot end parts such as turbine blades, a combustor flame tube, an exhaust nozzle and the like is greatly increased due to the increase of the temperature of the gas at the inlet of the turbine; at the same time, the improvement of the compression-air pressure ratio also leads to a reduction in the quality of the cooling air for the hot-end components. Hot-end component cooling technology is therefore a key technical issue in improving gas turbine engines.
Film cooling is widely applied to turbine blades of aircraft engines as an efficient cooling mode. The principle of the method is that secondary cooling air flow is introduced into a main flow from an air film hole of a high-temperature wall surface, the cooling air flow bends downstream under the action of pressure and friction force of the main flow and is attached to a certain area of the wall surface to form a cold air film with lower temperature to isolate the wall surface from high-temperature fuel gas and take away part of the high-temperature fuel gas, so that the wall surface is well cooled and protected. The development of maximum cooling efficiency with minimum cooling air volume and at the same time aerodynamic losses has been the focus of air film cooling research. Traditional optimization of the film hole cooling structure needs to rely on a large number of experiments and numerical simulation to summarize the law, so that not only a large amount of time needs to be consumed, but also the cost is relatively high.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the prior art, the pneumatic-thermal collaborative optimization method for the turbine blade fan-shaped hole air film cooling structure is provided, the turbine blade fan-shaped hole air film cooling structure is used for carrying out nonlinear mapping on an air film cooling pneumatic parameter and a thermal parameter, and the method has the advantages of high prediction precision, high efficiency and good global approximation capability.
The technical scheme is as follows: a pneumatic-thermal collaborative optimization method for a turbine blade fan-shaped hole air film cooling structure comprises the following steps:
step 1, determining a to-be-optimized design variable of an air film cooling structure and a range of the to-be-optimized design variable;
step 2, designing a data sample of the radial basis function neural network agent model;
step 3, establishing a CFD model for the data sample, and calculating an objective function value Fobj,cal；
Step 4, training and testing the radial basis function neural network by utilizing the training sample and the testing sample;
step 5, outputting a radial basis function neural network prediction objective function value Fobj,preAnd the test sample objective function value Fobj.testExpansion speed at minimum error;
step 6, searching an optimal design point by utilizing a particle swarm algorithm coupled with a radial basis function neural network;
step 7, CFD evaluation is carried out on the optimization design point, and if the radial basis function value F is predicted by the radial basis function neural networkobj,preAnd CFD calculates the objective function value Fobj,calIf the error is more than 5%, the optimization design point is expanded to a training sample database, and iteration is started from the step 4 again until the radial basis function value F is predicted by the radial basis function neural networkobj,preAnd CFD calculates the objective function value Fobj,calAnd (5) stopping iteration when the error is within a preset range to obtain a global optimal design point.
Further, the design variables to be optimized in step 1 include the following parameters: the corresponding variation ranges of the inclination angle alpha of the fan-shaped hole of the turbine blade, the lateral spread angle beta of the fan-shaped hole and the forward spread angle gamma of the fan-shaped hole are respectively 25-55 degrees, 10-20 degrees and 3-15 degrees.
Further, the step of designing the data sample in step 2 includes:
step 2.1, designing 25 groups of data as training samples by adopting a Latin hypercube design method, wherein the parameters to be optimized are the inclination angle alpha of a fan-shaped hole of the turbine blade, the lateral spread angle beta of the fan-shaped hole and the forward spread angle gamma of the fan-shaped hole;
2.2, randomly combining the inclination angle alpha of a fan-shaped hole, the lateral expansion angle beta of the fan-shaped hole and the forward expansion angle gamma of the fan-shaped hole of the turbine blade to be optimized, and designing 8 groups of data to be used as a test sample;
step 2.3, normalization processing is carried out on the parameters to be optimized, and the method comprises the following steps:
Figure BDA0001325516650000021
in the formula:
Figure BDA0001325516650000022
for the normalized data, x is the actual value of the parameter to be optimized, xmaxFor the maximum value of the parameter to be optimized, xminIs the minimum value of the parameter to be optimized.
Further, the objective function in step 3 is expressed as:
F(α,β,γ)＝λ1ηad,av+λ2Cd
in the formula: lambda [ alpha ]1η is the average cooling efficiency weight ratio of the turbine blade facead,avIs a vortexAverage cooling efficiency of the blade faces of the wheel; lambda [ alpha ]2The weight ratio of the flow coefficient of the fan-shaped hole is used; cdIs the flow coefficient of the fan-shaped hole.
Further, the radial basis function neural network in step 4 is expressed as follows:
the radial basis function neural network is divided into three layers: an input layer, a hidden layer, an output layer,
the input value of the ith neuron node center of the hidden layer is expressed as:
Hi＝||X-Ci||
in the formula: x ═ X1，x2，…，xk) For the network input vector, k denotes the number of network inputs, xjRepresents the jth network input, j ═ 1,2,3.. k; ci＝(c1i，c2i，…，cki) Is the center of the i-th neuron node, cjiA center of an ith neuron node representing a jth network input; | | represents the euclidean norm;
the output value of the jth neuron node of the hidden layer is expressed as:
Figure BDA0001325516650000031
in the formula: representing the expansion speed of the radial basis function neural network;
the output values for the output layer neurons are expressed as:
Figure BDA0001325516650000032
in the formula: w ═ w (w)1，w2，…，wn) N represents the number of hidden layers for the weight connecting the hidden layers and the output layers.
Further, the radial basis function neural network of step 5 predicts an objective function value Fobj,preAnd test specimen Fobj.testThe error is expressed as:
Figure BDA0001325516650000033
obtaining a radial basis function value F predicted by a radial basis function neural network based on a large-range expansion speed by applying a trial-and-error methodobj,preAnd a test sample Fobj.testThe minimum error.
Further, the particle group algorithm optimization problem in step 6 is expressed as:
max F(α,β,γ)＝λ1ηad,av+λ2Cd
Figure BDA0001325516650000034
wherein F (α, gamma) is fitness function, αmin、αmaxThe parameter α corresponds to the maximum value and the minimum value of the variation range βmin、βmaxThe parameter β corresponds to the maximum and minimum values of the variation range, gammamin、γmaxThe parameter gamma corresponds to the maximum value and the minimum value of the variation range;
step 6.1, setting maximum iteration times, particle swarm size, inertia weight and learning factors, and initializing particles and particle speed;
step 6.2, detecting the particle fitness;
6.3, searching individual extremum and group extremum;
step 6.4, updating speed and position;
step 6.5, calculating the particle fitness;
6.6, updating the individual extremum and the group extremum;
and 6.7, judging whether the termination condition is met, and if not, returning to the step 6.4.
Further, the inertial weight in step 6.1 adopts a dynamic change method, and the formula is as follows:
w(k)＝wstart-(wstart-wend)(k/Nmax)2
in the formula: k is the current iteration algebra, and w (k) is the inertial weight of the current iteration; w is astartIs an initial inertial weight, wstart＝0.9；wendFor the inertial weight at the maximum number of iterations,wend＝0.4；Nmaxis the maximum iteration algebra.
Further, the radial basis function neural network of step 7 predicts an objective function value Fobj,preAnd CFD calculates the objective function value Fobj,calThe error is expressed as:
Figure BDA0001325516650000041
has the advantages that: according to the method, a CFD model verified through experiments is utilized, a training sample and a test sample are utilized to perform function approximation based on a Radial Basis Function Neural Network (RBFNN), and an optimal design point is obtained by coupling particle swarm algorithm global search; the optimization algorithm is based on a particle swarm algorithm, and in order to solve the problem that the local minimum value is possibly trapped, the inertia weight adopts a dynamic change method; the invention can expand the database, and can search out the accurate optimal design point globally by a small amount of training samples and testing samples; according to the invention, the weight of the aerodynamic performance and the thermal performance can be adjusted according to the actual requirement, and an air film cooling structure of the optimal fan-shaped hole with both the aerodynamic performance and the thermal performance is designed; the invention has high efficiency and less resource consumption, and can greatly reduce the time and economic cost.
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FIG. 1 is a flow chart of a method for the aerodynamic-thermal collaborative optimization of a turbine blade fan-shaped hole film cooling structure;
FIG. 2 is a geometric model of a turbine blade fan hole film cooling;
FIG. 3 is a partial enlarged view of the sector holes;
FIG. 4 is a front view of the fan-shaped hole;
FIG. 5 is a top view of the scallops;
FIG. 6 is a radial basis function neural network structure;
number designation in the figures: 1. the main flow inlet, 2 main flow and secondary flow outlets, 3 turbine blade suction surfaces, 4 turbine blade pressure surfaces, 5 cold air cavities, 6 fan-shaped holes, 7 fan-shaped holes, 8 fan-shaped hole cold air inlets and 9 fan-shaped hole cold air outlets.
Detailed Description
The invention is further explained below with reference to the drawings.
FIG. 1 is a flow chart of a method for the aerodynamic-thermal collaborative optimization of a turbine blade fan hole film cooling structure according to the invention, and the method will be described with reference to FIG. 1.
Step 1, based on the turbine blade fan-shaped hole air film cooling geometric model of FIG. 2, the speed of a main flow inlet is 140m/s, the temperature of the main flow inlet is 540K, the speed of a fan-shaped air film hole cold air inlet is 80.4m/s, and the temperature of the air film hole cold air inlet is 310K.
The pitch P of the fan-shaped holes is set to be 4.5D, the height h of the fan-shaped holes is set to be 2.5D, and the forward expansion length l of the fan-shaped holes1D, the lateral expansion length l of the fan-shaped hole2Length l of cylindrical part of sector hole for 2D3Selecting an inclination angle α of a fan-shaped hole of the turbine blade for (h/sin α -3D), wherein the lateral spread angle β of the fan-shaped hole and the forward spread angle gamma of the fan-shaped hole are design variables to be optimized, and the change ranges are respectively 25-55 degrees, 10-20 degrees and 3-15 degrees, and the structure diagram is shown in FIG. 3.
Step 2, designing 25 groups of data as training samples by adopting a Latin hypercube design method, wherein the parameters to be optimized are the inclination angle alpha of a fan-shaped hole of the turbine blade, the lateral expansion angle beta of the fan-shaped hole and the forward expansion angle gamma of the fan-shaped hole; randomly combining the inclination angle alpha of the fan-shaped hole, the lateral expansion angle beta of the fan-shaped hole and the forward expansion angle gamma of the fan-shaped hole of the turbine blade to be optimized, and designing 8 groups of data to be used as a test sample. The structural parameters of the training and test samples are shown in table 1.
TABLE 1
Figure BDA0001325516650000051
Figure BDA0001325516650000061
Normalization processing is carried out on the parameters to be optimized, and the normalization processing method comprises the following steps:
Figure BDA0001325516650000062
in the formula:
Figure BDA0001325516650000063
for the normalized data, x is the actual value of the parameter to be optimized, xmaxFor the maximum value of the parameter to be optimized, xminIs the minimum value of the parameter to be optimized.
Step 3, establishing a CFD model for the data sample, and calculating an objective function value Fobj，cal. The objective function is expressed as:
F(α,β,γ)＝λ1ηad,av+λ2Cd
in the formula: lambda [ alpha ]1η is the average cooling efficiency weight ratio of the turbine blade facead,avAverage cooling efficiency for turbine blade faces; lambda [ alpha ]2The weight ratio of the flow coefficient of the fan-shaped hole is used; cdIs the flow coefficient of the fan-shaped hole.
Turbine blade face average cooling efficiency ηad,avThe expression is as follows:
Figure BDA0001325516650000071
wherein D is the circular diameter of the inlet of the fan-shaped hole, ηad,avxThe line average adiabatic film cooling efficiency is given. Coefficient of flow CdThe expression is as follows:
Figure BDA0001325516650000072
in the formula: m is the actual flow through the gas film channel; a is the cross-sectional area of the cold air channel at the outlet of the air film hole; rhooutDensity, P, of gas at the outlet of the gas film holein *Is the total pressure of the gas at the inlet of the gas film hole, PoutStatic pressure of the gas at the exit of the gas film hole.
And 4, training and testing the RBFNN by using the training sample and the testing sample. The radial basis function neural network structure is shown in fig. 4 and comprises three layers: input layer, hidden layer, output layer.
The input value of the ith neuron node center of the hidden layer is expressed as:
Hi＝||X-Ci||
in the formula: x ═ X1，x2，…，xk) For the network input vector, k denotes the number of network inputs, xjRepresents the jth network input, j ═ 1,2,3.. k; ci＝(c1i，c2i，…，cki) Is the center of the i-th neuron node, cjiA center of an ith neuron node representing a jth network input; | | | represents the euclidean norm.
The output value of the jth neuron node of the hidden layer is expressed as:
Figure BDA0001325516650000073
in the formula: indicating the RBFNN expansion speed.
The output values for the output layer neurons are expressed as:
Figure BDA0001325516650000074
in the formula: w ═ w (w)1，w2，…，wn) Is the weight value connecting the hidden layer and the output layer.
Step 5, outputting RBFNN predicted objective function value Fobj,preAnd the test sample objective function value Fobj.testSpeed of expansion with minimal error. RBFNN predicted objective function value Fobj,preAnd test specimen Fobj.testThe error is expressed as:
Figure BDA0001325516650000075
RBFNN prediction objective function value F is obtained based on large-range expansion speed by applying trial and error methodobj,preAnd test specimen Fobj.testThe minimum error.
And 6, searching an optimal design point by utilizing a Particle Swarm Optimization (PSO) coupled RBFNN.
The particle swarm algorithm fitness function is expressed as:
max F(α,β,γ)＝λ1ηad,av+λ2Cd
Figure BDA0001325516650000081
in the formula, F (α, gamma) is a fitness function αmin、αmaxThe parameter α corresponds to the maximum value and the minimum value of the variation range βmin、βmaxThe parameter β corresponds to the maximum and minimum values of the variation range, gammamin、γmaxThe parameter gamma corresponds to the maximum and minimum values of the variation range.
Step 6.1, setting maximum iteration times, particle swarm size, inertia weight and learning factors, and initializing particles and particle speed;
the inertia weight adopts a dynamic change method, and the formula is as follows:
w(k)＝wstart-(wstart-wend)(k/Nmax)2
in the formula: k is the current iteration algebra, and w (k) is the inertial weight of the current iteration; w is astartIs an initial inertial weight, wstart＝0.9；wendIs the inertial weight at the time of iteration to the maximum number, wend＝0.4；NmaxIs the maximum iteration algebra.
Step 6.2, detecting the particle fitness;
6.3, searching individual extremum and group extremum;
step 6.4, updating speed and position;
step 6.5, calculating the particle fitness;
6.6, updating the individual extremum and the group extremum;
and 6.7, judging whether the termination condition is met, and if not, returning to the step 6.4.
Step 7, CFD evaluation is carried out on the optimization design point, and if RBFNN predicts the objective function value Fobj,preComputing an objective function with CFDValue Fobj,calIf the error is more than 5%, expanding the training sample database by the optimization design point, and iterating from the step 4 again until the RBFNN forecast FobjAnd CFD FobjAnd (5) the error meets the requirement, and iteration is terminated to obtain a global optimal design point. Wherein RBFNN predicts objective function value Fobj,preAnd CFD calculates the objective function value Fobj,calThe error is expressed as:
Figure BDA0001325516650000091
the foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (3)

1. A pneumatic-thermal collaborative optimization method for a turbine blade fan-shaped hole air film cooling structure is characterized by comprising the following steps: the method comprises the following steps:
step 1, determining a to-be-optimized design variable of an air film cooling structure and a range of the to-be-optimized design variable; the design variables to be optimized comprise the following parameters: the inclination angle alpha of a fan-shaped hole of the turbine blade, the lateral spread angle beta of the fan-shaped hole and the forward spread angle gamma of the fan-shaped hole are respectively 25-55 degrees, 10-20 degrees and 3-15 degrees;
step 2, designing a data sample of the radial basis function neural network agent model; the step of designing the data sample comprises:
step 2.1, designing 25 groups of data as training samples by adopting a Latin hypercube design method, wherein the parameters to be optimized are the inclination angle alpha of a fan-shaped hole of the turbine blade, the lateral spread angle beta of the fan-shaped hole and the forward spread angle gamma of the fan-shaped hole;
2.2, randomly combining the inclination angle alpha of a fan-shaped hole, the lateral expansion angle beta of the fan-shaped hole and the forward expansion angle gamma of the fan-shaped hole of the turbine blade to be optimized, and designing 8 groups of data to be used as a test sample;
step 2.3, normalization processing is carried out on the parameters to be optimized, and the method comprises the following steps:
Figure FDA0002527947480000011
in the formula:
Figure FDA0002527947480000012
for the normalized data, x is the actual value of the parameter to be optimized, xmaxFor the maximum value of the parameter to be optimized, xminIs the minimum value of the parameter to be optimized;
step 3, establishing a CFD model for the data sample, and calculating an objective function value Fobj,cal(ii) a The objective function is expressed as:
F(α,β,γ)＝λ1ηad,av+λ2Cd
in the formula: lambda [ alpha ]1η is the average cooling efficiency weight ratio of the turbine blade facead,avAverage cooling efficiency for turbine blade faces; lambda [ alpha ]2The weight ratio of the flow coefficient of the fan-shaped hole is used; cdIs a fan-shaped hole flow coefficient;
step 4, training and testing the radial basis function neural network by utilizing the training sample and the testing sample;
step 5, outputting a radial basis function neural network prediction objective function value Fobj,preAnd the test sample objective function value Fobj.testExpansion speed at minimum error;
step 6, searching an optimal design point by utilizing a particle swarm algorithm coupled with a radial basis function neural network;
step 7, CFD evaluation is carried out on the optimization design point, and if the radial basis function value F is predicted by the radial basis function neural networkobj,preAnd CFD calculates the objective function value Fobj,calIf the error is more than 5%, the optimization design point is expanded to a training sample database, and iteration is started from the step 4 again until the radial basis function value F is predicted by the radial basis function neural networkobj,preAnd CFD calculates the objective function value Fobj,calThe iteration is terminated when the error is within a preset range, and a global optimal design point is obtained;
step 5, predicting the target function by the radial basis function neural networkValue Fobj,preAnd test specimen Fobj.testThe error is expressed as:
Figure FDA0002527947480000021
obtaining a radial basis function value F predicted by a radial basis function neural network based on a large-range expansion speed by applying a trial-and-error methodobj,preAnd test specimen Fobj.testThe minimum error;
the particle group algorithm optimization problem in step 6 is expressed as:
maxF(α,β,γ)＝λ1ηad,av+λ2Cd
s.t.
Figure FDA0002527947480000022
wherein F (α, gamma) is fitness function, αmin、αmaxThe parameter α corresponds to the maximum value and the minimum value of the variation range βmin、βmaxThe parameter β corresponds to the maximum and minimum values of the variation range, gammamin、γmaxThe parameter gamma corresponds to the maximum value and the minimum value of the variation range;
step 6.1, setting maximum iteration times, particle swarm size, inertia weight and learning factors, and initializing particles and particle speed;
step 6.2, detecting the particle fitness;
6.3, searching individual extremum and group extremum;
step 6.4, updating speed and position;
step 6.5, calculating the particle fitness;
6.6, updating the individual extremum and the group extremum;
step 6.7, judging whether the termination condition is met, if not, returning to the step 6.4;
in step 6.1, the inertia weight adopts a dynamic change method, and the formula is as follows:
w(k)＝wstart-(wstart-wend)(k/Nmax)2
in the formula: k is the current iteration algebra, and w (k) is the inertial weight of the current iteration; w is astartIs an initial inertial weight, wstart＝0.9；wendIs the inertial weight at the time of iteration to the maximum number, wend＝0.4；NmaxIs the maximum iteration algebra.
2. The method for the aerodynamic-thermal collaborative optimization of the turbine blade fan hole film cooling structure according to claim 1, wherein the method comprises the following steps: step 4, the radial basis function neural network is expressed as follows:
the radial basis function neural network is divided into three layers: an input layer, a hidden layer, an output layer,
the input value of the ith neuron node center of the hidden layer is expressed as:
Hi＝||X-Ci||
in the formula: x ═ X1，x2，…，xk) For the network input vector, k denotes the number of network inputs, xjRepresents the jth network input, j ═ 1,2,3.. k; ci＝(c1i，c2i，…，cki) Is the center of the i-th neuron node, cjiA center of an ith neuron node representing a jth network input; | | represents the euclidean norm;
the output value of the jth neuron node of the hidden layer is expressed as:
Figure FDA0002527947480000031
in the formula: representing the expansion speed of the radial basis function neural network;
the output values for the output layer neurons are expressed as:
Figure FDA0002527947480000032
in the formula: w is aj＝(w1，w2，…，wn) N represents the number of hidden layers for the weight connecting the hidden layers and the output layers.
3. The method for the aerodynamic-thermal collaborative optimization of the turbine blade fan hole film cooling structure according to claim 1, wherein the method comprises the following steps: step 1, predicting an objective function value F by using a radial basis function neural networkobj,preAnd CFD calculates the objective function value Fobj,calThe error is expressed as:
Figure FDA0002527947480000033
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