Special-shaped gas film cooling effect prediction method based on Gaussian superposition under physical constraint

Abstract

The invention discloses a special-shaped gas film cooling effect prediction method based on Gaussian superposition under physical constraints, and belongs to the field of aero-engine turbine blade cooling. In the area of each vortex pair, the air film cooling effect is fitted through Gaussian function superposition; selecting a plurality of groups of parameter combinations in a selected design variable range to carry out calculation model construction and simulation calculation; training by using a neural network to obtain a cold efficiency distribution proxy model; and performing air film cooling effect prediction by using the cooling effect distribution agent model. According to the method, the Gaussian function and the physical constraint are combined, the air film cooling effect distribution corresponding to the special-shaped air film hole vortex pair can be precisely fitted, the prediction precision is greatly improved, the fitting precision reaches 98% or above, the training time is shortened by 40-60 times, and the relative average prediction error is reduced by 3-4%. According to the method, a high-precision prediction result can be obtained in a short time without re-modeling simulation calculation. The method is higher in adaptability and can be widely applied to cold efficiency prediction of various special-shaped air film holes.

Description

Technical Field

[0001] The present invention belongs to the technical field of aero-engine turbine blade cooling, and particularly relates to a method for predicting the cooling effectiveness of a special-shaped film hole based on Gaussian superposition under physical constraints. Background Art

[0002] With the continuous development of aero-gas turbine engine technology, the temperature before the turbine continues to increase, making the hot-end components such as blades bear more severe gas-thermal loads, which puts forward higher requirements for efficient film cooling design. The existing methods for calculating film cooling effectiveness mainly include empirical formulas, CFD (Computational Fluid Dynamics) numerical simulations, and prediction models based on machine learning, but all have certain limitations. First, the applicable range of traditional empirical formulas is relatively limited. They are mainly established based on experimental data under specific working conditions and simple hole shapes, and it is difficult to accurately apply to the film cooling design of different special-shaped holes (such as fan-shaped holes, convergent slot-shaped holes, double jet holes) and different curvature conditions. Second, although CFD numerical simulations can provide high-precision flow and heat transfer information, the calculation process is complex and time-consuming, and it is difficult to meet the high-efficiency requirements of the optimization design of blade cooling structures. Finally, in recent years, prediction methods based on machine learning have been gradually applied to this field. Although certain progress has been made in the prediction of single-hole cooling effectiveness and the prediction of the cooling effectiveness distribution of the entire blade, the existing models mainly rely on pure data-driven and lack physical constraints, resulting in insufficient accuracy in the prediction of two-dimensional cooling effectiveness distribution under the characteristics of special-shaped holes, which limits the reliability of engineering applications.

[0003] Therefore, for the prediction of the cooling effectiveness distribution of special-shaped film holes under different conditions, it is urgent to propose a method with wide applicability, high calculation efficiency, and high prediction accuracy to improve the efficiency and reliability of turbine blade cooling design. Summary of the Invention

[0004] The present invention provides a method for predicting the cooling effectiveness of a special-shaped film hole based on Gaussian superposition under physical constraints, and its main purpose is: for the special-shaped film hole structure, use Gaussian superposition to represent physical constraints to achieve accurate and efficient prediction of the film cooling effectiveness distribution.

[0005] The present invention simultaneously considers the working condition parameters and geometric design parameters, and can complete Gaussian distribution and superposition according to the distribution of kidney-shaped vortices under physical conditions, so as to accurately match the distribution characteristics of the film holes, and train through a neural network to finally achieve efficient prediction of the cooling effectiveness distribution.

[0006] The technical solution adopted by the present invention to solve the technical problems is as follows:

[0007] A method for predicting the cooling effectiveness of a special-shaped film hole based on Gaussian superposition under physical constraints provided by the present invention includes the following steps:

[0008] Step S1: Conduct identification of the film jet vortex pair to determine the vortex pair structure after the film hole jet;

[0009] Step S2: For each region of the vortex pair, fit the film cooling effectiveness by superposing Gaussian functions;

[0010] Step S3: Select multiple groups of parameter combinations within the selected design variable range to construct a calculation model and perform simulation calculations;

[0011] Step S4: Use neural network training to obtain a surrogate model for the cooling effectiveness distribution;

[0012] Step S5: Use the surrogate model of the cooling effectiveness distribution to predict the film cooling effectiveness.

[0013] Further, in Step S1, the Q-criterion vortex identification method and streamline analysis method are used to determine the number of vortex pair structures after the film hole jet.

[0014] Further, on the same flow direction cross-section, if there are n vortex structures, then n - 1 vortex pair structures can be formed.

[0015] Further, in Step S2, the mathematical expression of the Gaussian function is:

[0016]

[0017] where y0 is the baseline value; A is the amplitude; x c is the mean value, that is, the spanwise direction coordinate of the vertex center; w is the standard deviation, representing the expansion range of the vortex pair; x is the spanwise coordinate of the reference axis.

[0018] Further, take y0, x c , w, A in formula (1) as unknown parameters, and use the least squares method to fit the film cooling effectiveness. When the fitting accuracy of the superposed Gaussian function is higher than 98%, it is considered that the fitting result meets the accuracy requirements.

[0019] Further, take y0, x c , w, A in formula (1) as unknown parameters, and use the symmetry characteristics of the vortex pair to set the Gaussian function parameters of the symmetric points to be the same, so as to reduce the number of unknown parameters of the Gaussian function and improve the superposition fitting efficiency.

[0020] Further, in Step S2, the mathematical expression of the film cooling effectiveness is:

[0021]

[0022] where T g , T c are the inlet temperatures of the mainstream and cooling gas respectively, and T aw is the adiabatic wall temperature.

[0023] Further, in step S3, multiple groups of parameter combinations are selected within the selected design variable range to construct a calculation model; after simulation calculation, film cooling effectiveness data at a certain flow direction interval are extracted downstream of the film holes, and the film cooling effectiveness data points at each flow direction interval are respectively subjected to Gaussian function superposition fitting according to step S2 to obtain the corresponding unknown parameters of the Gaussian function, which are used as the output parameters for neural network training.

[0024] Further, in step S4, the inputs of the neural network are operating condition parameters, geometric design parameters, and flow direction interval; the output of the neural network is the unknown parameters of the Gaussian function, and when the training error is lower than 5%, the training is considered completed, and a film cooling effectiveness distribution surrogate model is obtained.

[0025] Further, in step S5, the operating condition parameters, geometric design parameters, and flow direction interval to be predicted are input, and the unknown parameters of the Gaussian function are predicted using the film cooling effectiveness distribution surrogate model to obtain a two-dimensional matrix of the film cooling effectiveness distribution, and a two-dimensional contour map or other forms of visualization charts of the film cooling effectiveness are output.

[0026] The beneficial effects of the present invention are as follows:

[0027] 1. By combining the Gaussian function with physical constraints, the present invention can accurately fit the film cooling effectiveness distribution corresponding to the vortex pair structure of the shaped film holes, greatly improving the prediction accuracy, and the fitting accuracy can reach more than 98%.

[0028] 2. Compared with the direct prediction without constraints, the training time of the present invention is shortened by 40 to 60 times, and the relative average prediction error is reduced by 3% - 4%.

[0029] 3. By combining the neural network, the present invention greatly reduces the human and material resources, and can obtain high-precision prediction results in a short time without reconstructing the model and performing simulation calculations again.

[0030] 4. In addition, the present invention considers the comprehensive effects of different operating conditions and geometric design parameters, has stronger adaptability, and can be widely applied to the film cooling effectiveness prediction of various shaped film holes, and has strong generality.

[0031] Therefore, the present invention is superior to the prior art in terms of prediction accuracy, calculation efficiency, and applicability, and provides an innovative and efficient method for predicting the film cooling effectiveness of shaped film holes and optimizing the design. Description of the Drawings

[0032] Figure 1 It is a schematic diagram of the vortex pair structure of a flat plate converging slot hole.

[0033] Figure 2 It is a schematic diagram of the jet vortex pair structure of a flat plate converging slot hole.

[0034] Figure 3 It is a comparison between the result of Gaussian function superposition and the spanwise distribution of the converging slot holes on the flat plate.

[0035] Figure 4 It is a schematic diagram of the symmetric geometric structure of the converging slot holes on the flat plate.

[0036] Figure 5 It is a comparison between the numerical calculation of film cooling effectiveness and the prediction result of neural network under different blowing ratios. In the figure, (a) is the numerical calculation result; (b) is the prediction result of neural network. Specific implementation manners

[0037] A method for predicting the film cooling effectiveness of special-shaped holes based on Gaussian superposition under physical constraints provided by the present invention has the following specific implementation process:

[0038] Step S1: Identification of film jet vortex pairs;

[0039] Through the identification of film jet vortex pairs, the number of vortex pair structures after the jet of film holes can be confirmed.

[0040] In the present invention, the Q-criterion vortex identification method and streamline analysis method are specifically used to confirm the vortex structure after the jet of film holes. On the same flow direction cross-section, if there are n vortex structures, then n - 1 vortex pair structures can be formed.

[0041] Step S2: Gaussian function superposition fitting;

[0042] Specifically, within the region of each vortex pair, a Gaussian function is used to fit the film cooling effectiveness.

[0043] Among them, the mathematical expression of the Gaussian function is shown in formula (1):

[0044]

[0045] Among them, y0 is the baseline value; A is the amplitude; x c is the mean value, that is, the spanwise direction coordinate of the vertex center; w is the standard deviation, representing the expansion range of the vortex pair; x is the spanwise coordinate of the reference axis.

[0046] In order to better fit the characteristics of the vortex pair, y0, x c , w, and A in formula (1) are used as unknown parameters and are fitted by the least squares method or other optimization algorithms. When the fitting accuracy of the superposed Gaussian function is higher than 98%, it can be considered that the fitting result meets the accuracy requirements. Since the vortex pair has a certain symmetry in most cases, this characteristic can be used to simplify the fitting process of the Gaussian function. Specifically, if the vortex pair has obvious symmetry, the Gaussian function parameters at the symmetric points can be set to be the same or approximately the same, so as to reduce the number of unknown parameters of the Gaussian function and improve the efficiency of Gaussian function superposition fitting.

[0047] Among them, the definition of the film cooling effectiveness is shown in Equation 2:

[0048]

[0049] Among them, T g and T c are the inlet temperatures of the mainstream and cooling gas respectively, and T aw is the adiabatic wall temperature.

[0050] Step S3: Dataset construction;

[0051] By constructing the dataset, sufficient and reliable data can be provided for neural network training.

[0052] Specifically, multiple groups of parameter combinations are selected within the selected design variable range to construct corresponding calculation models. After the calculations are completed through simulation software, the film cooling effectiveness data at appropriate flow direction intervals are extracted downstream of the film holes. The film cooling effectiveness data points at each flow direction interval are respectively fitted by Gaussian function superposition according to Step S2, so as to obtain the unknown parameters of the corresponding Gaussian function, which are used as the output parameters for neural network training.

[0053] Step S4: Neural network training;

[0054] Through neural network training, a surrogate model of the cooling effectiveness distribution can be obtained.

[0055] The inputs of the neural network are operating condition parameters (such as blowing ratio, density ratio), geometric design parameters, and flow direction intervals, and the outputs are the unknown parameters of each Gaussian function. When the training error is lower than 5%, the training is considered completed, and thus a trained surrogate model of the cooling effectiveness distribution is obtained.

[0056] Step S5: Film cooling effectiveness prediction;

[0057] Through the film cooling effectiveness prediction step, accurate prediction of the film cooling effectiveness under different operating conditions and geometric design parameters can be achieved. By combining the Gaussian function with the machine learning model, fast and high-precision film cooling effectiveness prediction results can be provided in a complex film cooling environment.

[0058] Specifically, by inputting the operating condition parameters, geometric design parameters, and flow direction intervals to be predicted, and using the obtained surrogate model of the cooling effectiveness distribution, the unknown parameters of the Gaussian function are predicted to obtain a two-dimensional matrix of the film cooling effectiveness distribution, and a two-dimensional contour map or other forms of visualization charts of the film cooling effectiveness are output.

[0059] Next, in combination with the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0060] Taking a method for predicting the film cooling effectiveness of a flat converging slot-shaped hole based on Gaussian superposition under physical constraints as an example for introduction.

[0061] (1) Identification of film jet vortex pairs of flat converging slot-shaped holes;

[0062] According to the present invention, when using the Q-criterion vortex identification method and streamline analysis method to confirm the vortex structure after the film hole jet, on the same flow direction cross-section, if there are n vortex structures, then n - 1 vortex pair structures can be formed.

[0063] In this embodiment, the vortex pair structure of the flat converging slot-shaped hole is as Figure 1 shown. After confirmation by the Q-criterion vortex identification method and streamline analysis method, it can be obtained that after the film jet flows through the flat converging slot-shaped hole, two main vortex structures A and two secondary vortex structures B are formed under the shearing action on both sides of the flat converging slot-shaped hole; as the flat converging slot-shaped hole develops downstream, the two main vortex structures A gradually expand under the mixing action of the mainstream, while the two secondary vortex structures B are gradually dissipated in the far downstream region. As Figure 2 shown ( Figure 2 in which, X and x have the same meaning and both represent the spanwise coordinate of the reference axis), four vortices will be formed at the outlet of the flat converging slot-shaped hole, and these four vortex structures form three vortex pairs, including a main anti-kidney-shaped vortex pair, the center of the main anti-kidney-shaped vortex pair corresponding to the position "2" in Figure 2 , plus two left and right kidney-shaped vortex pairs, the centers of the kidney-shaped vortex pairs corresponding to the positions "1, 3" in Figure 2 respectively.

[0064] (2) Fitting the film cooling effectiveness by Gaussian function superposition;

[0065] According to the present invention, within the region of each vortex pair, a Gaussian function is used to fit the film cooling effectiveness. In this embodiment, specifically, the centers of the three vortex pairs are respectively used as the peak points of the Gaussian functions. After superimposing and fitting with the three Gaussian functions respectively, it is found that the superimposed result can better reproduce the spanwise distribution characteristics of the flat converging slot-shaped hole, as Figure 3As shown (Figure A shows the comparison of the fitting results of three Gaussian functions with the film cooling effectiveness distribution of the converging slot hole along the spanwise direction when X / D = 2; Figure B shows the comparison of the fitting results of three Gaussian functions with the film cooling effectiveness distribution of the converging slot hole along the spanwise direction when X / D = 12; Figure C shows the comparison of the fitting results of three Gaussian functions with the film cooling effectiveness distribution of the converging slot hole along the spanwise direction when X / D = 22; D represents the diameter of the inlet of the flat converging slot hole), and the fitting accuracy is higher than 98%, indicating that the fitting results are highly reliable. The symmetric geometric structure of the flat converging slot hole makes the downstream film show a symmetric distribution in the spanwise direction, and the film cooling effectiveness is almost 0 outside the film coverage area. Therefore, the total 12 parameters contained in the three Gaussian functions can be simplified to 5 parameters, and the specific corresponding parameters are shown in Table 1.

[0066] Table 1 Simplified parameters of Gaussian function

[0067]

[0068]

[0069] (3) Dataset construction;

[0070] The symmetric geometric structure of the flat converging slot hole is as Figure 4 shown. The selected variables are blowing ratio M (0.5 - 1.5), density ratio DR (1.5 - 2.5), incident angle α (30° - 45°), aspect ratio L / D (2.8 - 3.6), and exit slot length ratio l / w (3 - 9). The diameter D of the inlet of the flat converging slot hole is taken as 0.4 mm. The definitions of the blowing ratio and the density ratio are as follows:

[0071]

[0072] Among them, ρ c and u c are the density and velocity of the cooling gas at the inlet of the flat converging slot hole respectively, and ρ g and u g are the density and velocity of the mainstream inlet respectively. Multiple parameter combinations are selected within the selected design variable range. In this embodiment, a total of 46 parameter combinations are selected for model construction and simulation calculation. After the calculation is completed through the simulation software, the film cooling effectiveness data is extracted at a flow direction interval of 0.04 mm downstream of the flat converging slot hole. After extraction, the film cooling effectiveness data points at each flow direction interval are respectively subjected to Gaussian function superposition fitting according to step (2) to obtain the corresponding fitting parameters.

[0073] (4) BP neural network training;

[0074] In the BP neural network, the input parameters are the blowing ratio, density ratio, incident angle, aspect ratio, outlet slot length ratio, and flow direction interval, and the output parameters are the parameters of the superposition fitting of three Gaussian functions. In this embodiment, the number of hidden layers of the selected BP neural network is 2, and the number of neurons is 10. The data set is divided into a training set (80%) and a test set (20%). The neuron activation function selects the ReLU function, and the training structure error is lower than 2%, meeting the accuracy requirements. Through BP neural network training, a cold effect distribution proxy model can be obtained.

[0075] (5) Prediction of film cooling effectiveness;

[0076] Predictions are made for the design structures with three blowing ratios, a density ratio DR = 2, an incident angle α = 37.5°, an aspect ratio L / D = 3.2, and an outlet slot length ratio l / w = 6. The results are as Figure 5 shown. The results obtained by the constrained neural network prediction basically capture the distribution characteristics of the film cooling effectiveness at different blowing ratios, and better restore the numerical calculation results. Table 2 shows the relative errors of the surface-averaged film cooling effectiveness prediction. The overall relative error of the constrained prediction is within 5%, indicating that the prediction accuracy of the present invention is relatively high.

[0077] Table 2 Relative errors of surface-averaged film cooling effectiveness prediction

[0078] Numerical calculation results Constrained neural network prediction results Relative error M＝0.5 0.119 0.122 2.52％ M＝1.0 0.216 0.222 2.78％ M＝1.5 0.265 0.279 5.28％

[0079] A method for predicting the film cooling effectiveness of special-shaped films based on Gaussian superposition under physical constraints according to the present invention can achieve accurate prediction of the film cooling effectiveness under different working conditions and geometric design parameters. By combining Gaussian functions with machine learning models, it can provide fast and high-precision film cooling effectiveness prediction results in complex film cooling environments.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features, but these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the cooling effect of a special-shaped air film based on Gaussian superposition under physical constraints, characterized in that, It includes the following steps: Step S1: Conduct air film jet vortex pair identification to determine the vortex pair structure after the air film hole jet; Step S2: Within the region of each vortex pair, fit the air film cooling effect by superposing Gaussian functions; Step S3: Select multiple groups of parameter combinations within the selected design variable range to construct a calculation model and perform simulation calculations; Step S4: Use neural network training to obtain a cooling effect distribution surrogate model; Step S5: Use the cooling effect distribution surrogate model to predict the air film cooling effect.

2. The method for predicting the cooling effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 1, wherein In Step S1, the Q-criterion vortex identification method and streamline analysis method are used to determine the number of vortex pair structures after the air film hole jet.

3. A method for predicting the cold effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 2, characterized in that On the same flow direction cross-section, if there are n vortex structures, then n - 1 vortex pair structures can be formed.

4. A method for predicting the cooling effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 1, characterized in that In Step S2, the mathematical expression of the Gaussian function is: Among them, y0 is the baseline value; A is the amplitude; x c is the mean value, that is, the spanwise coordinate of the vertex center; w is the standard deviation, representing the expansion range of the vortex pair; x is the spanwise coordinate of the reference axis.

5. A method for predicting the cold effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 4, characterized in that Regarding y0, x in formula (1) c , w, and A as unknown parameters, the least squares method is used to fit the film cooling effectiveness. When the fitting accuracy of the superimposed Gaussian function is higher than 98%, the fitting result is considered to meet the accuracy requirements.

6. A method for predicting the cold effect of a special-shaped air film based on Gaussian superposition under physical constraints, as described in claim 4, wherein Taking y0, x c , w, and A in formula (1) as unknown parameters, and using the symmetry characteristics of the vortex pair, the Gaussian function parameters of the symmetric points are set to be the same to reduce the number of unknown parameters of the Gaussian function and improve the superposition fitting efficiency.

7. A method for predicting the cooling effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 1, characterized in that In Step S2, the mathematical expression of the air film cooling effect is: Among them, T g , T c are the inlet temperatures of the mainstream and cooling gas respectively, and T aw is the adiabatic wall temperature.

8. A method for predicting the cooling effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 1, characterized in that, In Step S3, select multiple groups of parameter combinations within the selected design variable range to construct a calculation model; after simulation calculations, extract the air film cooling effect data at a certain flow direction interval downstream of the air film hole, and perform Gaussian function superposition fitting on the air film cooling effect data points of each flow direction interval according to Step S2 to obtain the corresponding unknown parameters of the Gaussian function, which are used as the output parameters for neural network training.

9. A method for predicting the cooling effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 1, characterized in that, In Step S4, the inputs of the neural network are operating condition parameters, geometric design parameters, and flow direction interval; the output of the neural network is the unknown parameters of the Gaussian function. When the training error is lower than 5%, the training is considered completed, and a cooling effect distribution surrogate model is obtained.

10. A method for predicting the cold effect of a special-shaped air film based on Gaussian superposition under physical constraints according to claim 1, characterized in that, In Step S5, input the operating condition parameters, geometric design parameters, and flow direction interval to be predicted, use the cooling effect distribution surrogate model to predict the unknown parameters of the Gaussian function, obtain a two-dimensional matrix of the air film cooling effect distribution, and output a two-dimensional contour map of the air film cooling effect or other forms of visualization charts.

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