Method for extracting flow loss value of large-intake-angle supersonic ultrathin cascade based on infinitesimal flow averaging

Abstract

The invention discloses a large-intake-angle supersonic ultrathin cascade flow loss value extraction method based on infinitesimal flow averaging, and belongs to the field of fluid dynamics. According to the method, on the basis of ultrasonic probe vibration data obtained in the real testing process, the maximum displacement of the probe in the testing direction and the incoming flow direction is determined in combination with testing position information, and therefore the infinitesimal size in flow loss analysis is further defined. On the basis, a numerical model for simulating the flow state of the working medium in the cascade is constructed according to the physical structure of the test bed, and is simplified into a single-channel model. In order to obtain an accurate simulation result, a plurality of turbulence models are selected, and the optimal turbulence model is selected by means of a plurality of evaluation indexes for subsequent analysis. Setting infinitesimal elements in the simulated flow field, wherein the size and the distribution of initial positions of the infinitesimal elements are defined according to position data in an actual test. According to the method, the flow loss characteristic of the supersonic cascade can be effectively evaluated, and the cascade design efficiency and reliability are improved.

Description

Technical Field

[0001] The invention relates to the field of fluid dynamics, in particular to the analysis of supersonic flow and flow loss, and to a numerical extraction method for flow loss of supersonic ultra-thin blade cascade with large air inlet angle based on a micro unit. Background Art

[0002] In the field of fluid dynamics, with the rapid development of high-tech fields such as aerospace, the study of supersonic flow has gradually become a hot topic in scientific and engineering research, especially in the fields of blade design, gas dynamics, and jet engines. In the process of studying this type of blade, the speed of the fluid exceeds its speed of sound, resulting in significant changes in the fluid properties, such as the appearance of shock waves, expansion waves and other flow phenomena. The characteristics of supersonic flow make the study of flow loss and optimization design complex and challenging. In the study of supersonic ultra-thin blades with large inlet angles, probe measurement technology is widely used. However, the complex flow environment and the effect of aerodynamic forces often lead to an offset in the measurement position, making it difficult to accurately extract the numerical value of flow loss. Summary of the invention

[0003] The purpose of the present invention is to take into account that the test position has certain fluctuations due to the influence of the incoming flow during the probe test, establish a microelement that conforms to the fluctuation range, and use the mass flow averaging data processing method to extract the energy loss generated during the flow process, thereby achieving the consistency between the numerical simulation results and the experimental results.

[0004] The technical solution adopted to achieve the purpose of the present invention is: A method for numerically extracting flow loss of supersonic ultra-thin blade cascade with large inlet angle based on micro-element flow averaging comprises the following steps: Step 1: Determination of supersonic ultra-thin blade cascade test micro-element: Step 1.1: Ultrasonic probe clamping position and clamping angle During the test of flow loss in supersonic ultra-thin blade cascade with large inlet angle, a four-degree-of-freedom displacement mechanism is used to clamp the supersonic U-shaped probe; the probe head is located at 50% blade height of the ultra-thin blade cascade with large inlet angle, and the cross-sectional distance from the probe head to the trailing edge of the blade cascade is L for:

[0005] k The value range of is 0.4~0.8; t The pitch of the ultra-thin blade cascade with large pitch angle; After the probe is clamped, the pressure of the flow field behind the grating is measured along the frontal line direction; The supersonic U-shaped probe is calibrated in a standard flow field with known pressure distribution before the test to establish an accurate calibration curve between the pressure value and the probe output signal; Step 1.2: Determine the actual test area of ​​the probe in the flow field A non-contact vibration measuring device is arranged above the probe head, and the measuring point is arranged in the wedge area of ​​the probe head; The vibration results in the direction perpendicular to the flow field are measured, and the maximum displacement of the probe in the test direction is obtained by processing. Y max , and derive the maximum displacement of the probe in the horizontal direction X max for:

[0006] in, β is the angle between the probe and the airflow; α is the probe tip angle; centered at the test point The formed rectangular area is the actual test area of ​​the probe; Step 2: Acquisition of aerodynamic performance data of supersonic ultra-thin blades Determine the aerodynamic test conditions and calculate the control Mach number according to the research requirements and the design parameters of the cascade:

[0007] in: Indicates the total incoming pressure, Indicates the static pressure behind the grid, k It represents the specific heat ratio; Record atmospheric pressure, atmospheric temperature, incoming flow temperature ; After reaching a stable flow, record the total pressure of the incoming flow , static pressure of incoming flow , static pressure behind the grid ;Use a supersonic U-shaped probe to measure the pressure value at the 50% blade height position of the cascade, and take points along the frontal line; Step 3: Calculate the energy loss quantified by the working fluid passing through the supersonic blade cascade based on the processed post-blade flow field information :

[0008] Where: i Indicates the collection point number. Indicates i The actual static pressure behind the grid at each collection point, Indicates i The ideal static pressure behind the grid at each collection point is: Indicates i The static pressure and total pressure of the incoming flow at each collection point,k It represents the specific heat ratio; Step 4: Numerical simulation model construction Step 4.1: Real flow field simulation The area is cut along the leading and trailing edges of the upper and lower blades to divide the calculation domain so that the flow field of the n cascade flow channel areas in the middle of the calculation domain can conform to the actual airflow law, and the inflow and outflow conditions are set; Step 4.3: Determination of the optimal turbulence model On the basis of the simplified model, the turbulence model is selected for simulating the real flow process; the simulation error is judged by comparing the pressure envelope of the simulation results with the test value. A single evaluation standard cannot fully reflect the applicability of the model, so a variety of evaluation indicators are introduced to evaluate each turbulence model and select the optimal turbulence model; after making each indicator dimensionless, the different error indicators of each model on the test data set are normalized, and the forward indicator and the reverse indicator are scored and calculated according to the following formulas; In the formula, It represents the scores of different indicators of each model after normalization. Represents the original scores of different indicators of each model, represents the maximum raw score, Represents the minimum original score; after normalizing each evaluation index, the normalized index is accumulated to obtain the comprehensive evaluation index of the model. The model with the highest score in each evaluation index is determined as the optimal turbulence model; Step 5: Extraction of flow loss Based on the simulation results of the optimal turbulence model in step 4, the subsequent loss extraction is carried out. First, the probe measurement position during the test is determined to be Lmm away from the trailing edge of the supersonic ultra-thin blade cascade. According to the calibration results of the probe vibration amplitude, the X max* Y max The analysis micro-element of mm size is used to determine the micro-element position information according to the probe displacement trajectory and the number of sampling points; the initial position of the micro-element is set as the placement position of the probe in the test. The probe placement position is the reference position for obtaining the test data, and the micro-element is segmented and analyzed with this position as the starting point; Step 6: Based on the mass flow rate, the total pressure value and the static pressure value of the divided micro-element are averaged and the energy loss of the blade cascade numerical analysis is calculated by the following formula; in, Indicates the mass flow rate before the grid; represents the micro-element mass flow rate after the grid; Indicates the total pressure behind the grid; Indicates the static pressure behind the grid; Indicates the static pressure of the incoming flow; Step 7: Compare the error between the loss result extracted by numerical simulation and the experimental measurement result, calculate the error, and determine whether it meets the set threshold. If the error is less than the set threshold, end the analysis; if the error does not meet the set threshold, update the position of the segmented microelement, and the update range is 0.4 times the grid pitch to 0.8 times the grid pitch; after the update is completed, return to step 6 to recalculate the loss.

[0009] The turbulence models in step 4.3 include Spalart Allmaras, Standard k-e, RNG k-e, Realizable k-e, Stand k-w, SST k-w, and Reynolds Stress.

[0010] The evaluation indicators in step 4.3 include the sample correlation coefficient r 2 , explained variance EVS, mean absolute error MAE, mean square error MSE, mean relative error MRE, maximum error ME, median absolute error MEAE.

[0011] The beneficial effects of the present invention are: The method of the present invention is used to accurately extract the flow loss of supersonic ultra-thin blades with large inlet angles. Compared with the prior art, the present invention uses the vibration data of the supersonic probe as the cornerstone, combines the test position details, and cleverly determines the maximum displacement of the probe in the test and incoming flow directions, thereby accurately defining the microelement size. The complexity of the wave system of the flow field behind the supersonic blade cascade and its influence on the probe pressure measurement position are fully considered, which greatly improves the accuracy and reliability of the flow loss analysis and solves the problem of difficulty in accurately extracting the loss value due to fluctuations in the measurement position caused by the complexity of the flow field.

[0012] This method is based on the supersonic probe vibration data obtained during the actual test process, and combines the test position information to determine the maximum displacement of the probe in the test direction and the incoming flow direction, thereby further defining the microelement size in the flow loss analysis. On this basis, a numerical model that can simulate the flow state of the working fluid in the blade grid is constructed for the physical structure of the test bench. Due to the complexity of the flow law, the model is simplified to a single-channel model for subsequent numerical simulation. In order to obtain accurate simulation results, a variety of turbulence models are selected, and the difference in blade surface static pressure distribution between the simulation results and the test values ​​is compared with multiple evaluation indicators, so as to select the best turbulence model for subsequent analysis. After determining the optimal turbulence model, a microelement is set in the simulated flow field, and its size and initial position distribution are defined according to the position data in the actual test test. Through this method, the present invention can effectively evaluate the flow loss characteristics of the supersonic blade grid, and provides a new idea and tool for improving the efficiency and reliability of blade grid design. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the method.

[0014] Figure 2 Schematic diagram of the position of the multi-degree-of-freedom U-shaped probe relative to the cascade test section.

[0015] Figure 3 Schematic diagram of microelement segmentation.

[0016] Figure 4 It is a schematic diagram of the test measurement section.

[0017] Figure 5 Comparison chart of evaluation indicators of turbulence models.

[0018] Figure 6 This is an illustration of the conversion of vibration along the flow direction.

[0019] Figure 7 Schematic diagram of the probe structure.

[0020] Figure 8 is the probe vibration curve. DETAILED DESCRIPTION Example

[0022] Figure 1 This is a flow chart of the energy loss extraction process of a supersonic blade cascade. The specific steps are as follows: Step 1: Determination of supersonic ultra-thin blade cascade test micro-element: Step 1.1: Ultrasonic probe clamping position and clamping angle During the test of flow loss of supersonic ultra-thin blade cascade at large inlet angle, in order to obtain the aerodynamic characteristic parameters behind the cascade, a four-degree-of-freedom displacement mechanism is used to clamp the supersonic U-shaped probe (its structural schematic diagram is shown in the figure). Figure 7 The probe is located at 50% blade height of the ultra-thin blade cascade with large air inlet angle. The cross-sectional distance from the probe to the trailing edge of the blade cascade is L ( Figure 2 ) is determined according to the following formula:

[0023] k The empirical value range is 0.4~0.8; t is the grating pitch of the ultra-thin blade cascade with large entrance angle. In addition, to ensure the accuracy of the outlet airflow angle obtained in the test, it is necessary to ensure that the probe clamping angle is consistent with the geometric angle of the supersonic ultra-thin blade cascade outlet. After the probe is clamped, the pressure of the flow field behind the cascade is measured along the frontal line direction. The supersonic U-type probe needs to be calibrated in a standard flow field with known pressure distribution before the test to establish an accurate calibration curve between the pressure value and the probe output signal.

[0024] Step 1.2: Determine the actual test area of ​​the probe in the flow field During the aerodynamic test of supersonic ultra-thin blade cascade with large inlet angle, the aerodynamic force behind the supersonic blade cascade causes the pressure measurement position of the probe probe to shift along the flow direction relative to the initial installation position. And the complex wave system in the flow field will cause different degrees of vibration of the probe probe. In order to determine the actual test area of ​​the probe under such circumstances, a non-contact vibration measurement device is set above the probe probe, and the measurement point is set in the probe wedge area. The structural dimensions of the wedge area can be expressed by the following parameters: wedge angle (12 degrees) and wedge size (5mm).

[0025] The angle between the airflow direction of the known flow field and the probe probe was gradually adjusted to observe the measurement results of the non-contact vibration test device at different Mach numbers. The acquisition frequency of the non-contact displacement measurement device was 5000HZ and the repeatability was 0.025. μm , the measurement accuracy is 0.02%FS.

[0026] After measuring the vibration results in the direction perpendicular to the flow field, the maximum displacement of the probe in the test direction under the influence of aerodynamic force and complex wave system behind the grid is obtained. Y max , the maximum displacement of the probe in the horizontal direction is derived according to the following formula X max .

[0027]

[0028] Angle between probe and airflowβ ; Probe tip angle α ;(like Figure 6 The maximum deflection of the probe along the test direction Y max ,; Centered on the test point The formed rectangular area is the actual test area of ​​the probe.

[0029] Step 2: Acquisition of aerodynamic performance data of supersonic ultra-thin blades Determine the aerodynamic test conditions, calculate the operating condition control Mach number according to the formula based on the research requirements and the design parameters of the cascade, where Indicates the total incoming pressure, Indicates the static pressure behind the grid. These are one of the key parameters to determine the test conditions. Record atmospheric pressure, atmospheric temperature, and incoming flow temperature These parameters will serve as the basic data for subsequent data processing and analysis. The wind tunnel inlet conditions are gradually adjusted until the required incoming flow Mach number ( Ma After reaching a steady flow, record the total pressure of the incoming flow. , static pressure of incoming flow , static pressure behind the grid Use the displacement mechanism to clamp the multi-degree-of-freedom U-shaped probe and measure the pressure value at the position of 50% blade height of the cascade. Take points along the frontal line.

[0030] Table 1 Test conditions data

[0031] Step 3: Calculate the energy loss quantified by the working fluid passing through the supersonic blade cascade according to the following formula based on the processed flow field information after the cascade: .

[0032]

[0033] Where: i Indicates the collection point number. Indicates i The actual static pressure behind the grid at each collection point, Indicates i The ideal static pressure behind the grid at each collection point is: Indicates i The static pressure and total pressure of the incoming flow at each collection point, k It represents the specific heat ratio; This formula is based on the principle of conservation of energy. By measuring the total pressure and static pressure of the flow field behind the cascade, it calculates the quantitative results of the energy loss caused by the working fluid passing through the supersonic cascade, which can intuitively reflect the influence of the cascade on the airflow energy.

[0034] Step 4: Numerical simulation model construction Step 4.1: Real flow field simulation In order to reflect the actual flow situation in the transonic flow field, the inlet and outlet airflow angle factors of the design condition are considered. First, the area is sheared along the leading and trailing edges of the upper and lower blades to divide the calculation domain so that the flow field of the n cascade flow channel areas in the middle of the calculation domain can conform to the actual airflow flow law. According to the actual test conditions, clear inflow and outflow conditions are set to enhance the authenticity and reliability of the model. The model is simplified and the channel is divided to make its upper and lower boundaries periodic.

[0035] Step 4.2: Determination of the optimal turbulence model On the basis of the simplified model, seven turbulence models including Spalart Allmaras, Standard k-e, RNG k-e, Realizable k-e, Stand k-w, SST k-w, and Reynolds Stress are selected to supplement the Reynolds stress equation for the simulation of the real flow process. In order to ensure the most realistic simulation of the flow loss characteristics of supersonic ultra-thin blades under extreme conditions, the above turbulence models are used for simulation respectively, and the simulation results are compared with the pressure envelope of the experimental values ​​to judge the simulation error, and the optimal turbulence model is selected. A single indicator evaluation cannot fully reflect the predictive ability of the model. In order to more comprehensively evaluate the performance of each loss model on this speed line, a variety of evaluation indicators are introduced, including the sample correlation coefficient (r 2 ), explained variance (EVS), mean absolute error (MAE), mean square error (MSE), mean relative error (MRE), maximum error (ME), median absolute error (MEAE). These indicators can measure the prediction accuracy and stability of the model from different angles. After making each indicator dimensionless, since different error indicators have different discrimination degrees for each model, the different error indicators of each model on the test data set are normalized, and the positive and negative indicators are scored and calculated according to the following formulas.

[0036] In the formula, It represents the scores of different indicators of each model after normalization. Represents the original scores of different indicators of each model, represents the maximum raw score, Indicates the minimum raw score.

[0037] After normalizing each evaluation index, these normalized indexes are accumulated to obtain the comprehensive evaluation index of the model. The model with the highest score in each evaluation index is determined as the optimal turbulence model; Step 5: Extraction of flow loss Based on the simulation results of the optimal turbulence model in step 4, the subsequent loss extraction is carried out. First, the probe measurement position during the test is determined to be Lmm away from the trailing edge of the supersonic ultra-thin blade cascade. According to the calibration results of the probe vibration amplitude, X max* Y max The analysis microelement of mm size is used to determine the microelement position information according to the probe displacement trajectory and the number of sampling points. The initial position of the microelement is set to the placement position of the probe in the test. This is because the probe placement position is the reference position for obtaining test data. The microelement is segmented and analyzed with this position as the starting point, which is convenient for comparing and verifying the numerical simulation results with the test measurement results.

[0038] Step 6: Calculate the total pressure and static pressure of the divided micro-element based on the mass flow rate. The calculation principle is the average value of the fluid mass passing through a specific cross section within a certain period of time. It can be calculated by the following formula and the calculation of the energy loss of the blade numerical analysis is completed according to the following formula.

[0039]

[0040] in, Indicates the mass flow rate before the grid; represents the micro-element mass flow rate after the grid; Indicates the total pressure behind the grid; Indicates the static pressure behind the grid; Indicates the static pressure of the incoming flow.

[0041] Table 2 Numerical simulation results

[0042] Step 7: Comparing the loss results extracted by numerical simulation with the experimental measurement results, the error is -1.41%, which is less than the set threshold and the analysis ends.

[0043] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the attached claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

[0044] The above contents are further detailed descriptions of the present invention in combination with specific preferred technical solutions, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A numerical extraction method for flow loss of supersonic ultra-thin blade cascade with large inlet angle based on micro-element flow averaging, characterized in that: The steps include: Step 1: Determination of supersonic ultra-thin blade cascade test micro-element: Step 1.1: Ultrasonic probe clamping position and clamping angle During the test of flow loss in supersonic ultra-thin blade cascade with large inlet angle, a four-degree-of-freedom displacement mechanism is used to clamp the supersonic U-shaped probe; the probe head is located at 50% blade height of the ultra-thin blade cascade with large inlet angle, and the cross-sectional distance from the probe head to the trailing edge of the blade cascade is L for: k The value range of is 0.4~0.8; t The pitch of the ultra-thin blade cascade with large pitch angle; After the probe is clamped, the pressure of the flow field behind the grating is measured along the frontal line direction; The supersonic U-shaped probe is calibrated in a standard flow field with known pressure distribution before the test to establish an accurate calibration curve between the pressure value and the probe output signal; Step 1.2: Determine the actual test area of ​​the probe in the flow field A non-contact vibration measuring device is arranged above the probe head, and the measuring point is arranged in the wedge area of ​​the probe head; The vibration results in the direction perpendicular to the flow field are measured, and the maximum displacement of the probe in the test direction is obtained by processing. Y max , and derive the maximum displacement of the probe in the horizontal direction X max for: ； in, β is the angle between the probe and the airflow; α is the probe tip angle; centered at the test point The formed rectangular area is the actual test area of ​​the probe; Step 2: Acquisition of aerodynamic performance data of supersonic ultra-thin blades Determine the aerodynamic test conditions and calculate the control Mach number according to the research requirements and the design parameters of the cascade: ； in: Indicates the total incoming pressure, Indicates the static pressure behind the grid, k It represents the specific heat ratio; Record atmospheric pressure, atmospheric temperature, incoming flow temperature ; After reaching a stable flow, record the total pressure of the incoming flow , static pressure of incoming flow , static pressure behind the grid ;Use a supersonic U-shaped probe to measure the pressure value at the 50% blade height position of the cascade, and take points along the frontal line; Step 3: Calculate the energy loss quantified by the working fluid passing through the supersonic blade cascade based on the processed post-blade flow field information : ； Where: i Indicates the collection point number. Indicates i The actual static pressure behind the grid at each collection point, Indicates i The ideal static pressure behind the grid at each collection point is: Indicates i The static pressure and total pressure of the incoming flow at each collection point; Step 4: Numerical simulation model construction Step 4.1: Real flow field simulation The area is cut along the leading and trailing edges of the upper and lower blades to divide the calculation domain so that the flow field of the n cascade flow channel areas in the middle of the calculation domain can conform to the actual airflow law, and the inflow and outflow conditions are set; Step 4.2: Determination of the optimal turbulence model On the basis of the simplified model, a turbulence model is selected for simulating the real flow process; the pressure envelope of the simulation results and the test values ​​is compared to judge the simulation error, and a variety of evaluation indicators are introduced to evaluate each turbulence model, and the optimal turbulence model is selected from them; after making each indicator dimensionless, the different error indicators of each model on the test data set are normalized, and the forward indicator and the reverse indicator are scored and calculated according to the following formulas; In the formula, It represents the scores of different indicators of each model after normalization. Represents the original scores of different indicators of each model, represents the maximum raw score, Indicates the minimum value of the original score; After normalizing each evaluation index, the normalized indexes are accumulated to obtain the comprehensive evaluation index of the model. The model with the highest score in each evaluation index is determined as the optimal turbulence model. Step 5: Extraction of flow loss Based on the simulation results of the optimal turbulence model in step 4, the subsequent loss extraction is carried out. First, the probe measurement position during the test is determined to be Lmm away from the trailing edge of the supersonic ultra-thin blade cascade. According to the calibration results of the probe vibration amplitude, the X max* Y max The analysis micro-element of mm size is used to determine the micro-element position information according to the probe displacement trajectory and the number of sampling points; the initial position of the micro-element is set as the placement position of the probe in the test. The probe placement position is the reference position for obtaining the test data, and the micro-element is segmented and analyzed with this position as the starting point; Step 6: Based on the mass flow rate, the total pressure value and the static pressure value of the divided micro-element are averaged and the energy loss of the blade cascade numerical analysis is calculated by the following formula; in, Indicates the mass flow rate before the grid; represents the micro-element mass flow rate after the grid; Indicates the total pressure behind the grid; Indicates the static pressure behind the grid; Indicates the static pressure of the incoming flow; Step 7: Compare the error between the loss result extracted by numerical simulation and the experimental measurement result, calculate the error, and determine whether it meets the set threshold. If the error is less than the set threshold, end the analysis; if the error does not meet the set threshold, update the position of the segmented microelement, and the update range is 0.4 times the grid pitch to 0.8 times the grid pitch; after the update is completed, return to step 6 to recalculate the loss.

2. The method for numerically extracting flow loss of supersonic ultra-thin blade cascade with large inlet angle based on micro-element flow averaging according to claim 1 is characterized by: The turbulence models in step 4.3 include Spalart Allmaras, Standard k-e, RNG k-e, Realizable k-e, Stand k-w, SST k-w, and Reynolds Stress.

3. The method for numerically extracting flow loss of supersonic ultra-thin blade cascade with large inlet angle based on micro-element flow averaging according to claim 1 is characterized by: The evaluation indicators in step 4.3 include the sample correlation coefficient r 2 , explained variance EVS, mean absolute error MAE, mean square error MSE, mean relative error MRE, maximum error ME, median absolute error MEAE.

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