A method for determining the influence of the Reynolds number on the engine performance under the whole machine condition

Abstract

The application belongs to the field of aero-engine design and is a calculation method for determining the influence of Reynolds number on engine performance under the condition of the whole machine. By selecting steady-state performance test data to be processed, performing comparative analysis on parameter sensitivity, correlation and condition number, first, performance parameter test data meeting the identification calculation requirements are found, performance correction factors of each component are obtained through identification calculation, then the influence degree change relationship of Reynolds number and the performance correction factors of each component is quantitatively obtained through statistical analysis, and finally the baseline steady-state performance model is corrected according to the change relationship, so that the whole machine performance and the performance of each component under different working conditions can be accurately calculated, the calculation precision of the steady-state performance model in the working envelope is improved, the test cost of each component is significantly reduced, and the development cycle is shortened.

Description

Technical Field

[0001] This application belongs to the field of aero-engine design, and specifically relates to a calculation method for determining the impact of Reynolds number on engine performance under whole-engine conditions. Background Technology

[0002] The Reynolds number (Re) is one of the important criteria for measuring the impact of fluid viscosity on the performance of various components of an aero-engine. The influence of the Reynolds number must be considered in high-altitude performance analysis, aerodynamic stability design, and control law design. During ground-based bench tests, the Reynolds number is in its self-mode region, and its impact on the engine fan, compressor, and turbine is negligible. However, as the engine's operating range expands, especially under high-altitude, low-Mach number flight conditions, the Reynolds number falls into the non-self-mode region. The flow field characteristics deviate from the design state, and the performance of compressor and turbine components deteriorates, significantly affecting engine performance. Therefore, it is necessary to calculate and analyze the impact of the Reynolds number on the performance of various engine components.

[0003] Existing technical solutions include the following: calculating the impact of Reynolds number on component performance based on ground-based component test results and combining empirical formulas from aviation standards, and then correcting the performance of each component. It also includes obtaining the component performance of the compressor and turbine through testing under different inlet pressure and temperature conditions. The main problems with these solutions are as follows: because different flow channels and airfoil designs have different critical Reynolds numbers, the degree of influence of the Reynolds number effect on the performance of different components also varies, and the calculation formulas for the Reynolds number effect from aviation standards are not entirely applicable; component performance tests are usually conducted on ground-based test benches, and due to limitations in testing equipment capabilities, funding costs, and development cycles, it is difficult to obtain the performance of each component under different inlet pressure and temperature conditions.

[0004] Therefore, accurately calculating the impact of Reynolds number on engine performance under different flow channels and airfoils is a problem that needs to be solved. Summary of the Invention

[0005] The purpose of this application is to provide a calculation method for determining the impact of Reynolds number on engine performance under whole-machine conditions, so as to solve the problem in the prior art that it is difficult to quantitatively assess the degree of impact of Reynolds number on the performance of various components under different intake pressure and temperature conditions.

[0006] The technical solution of this application is: a calculation method for determining the influence of Reynolds number on engine performance under whole-machine conditions, comprising: selecting typical test points on the ground and at high altitude within the engine's operating envelope to obtain the steady-state performance test data to be processed; establishing an influence coefficient matrix, performing comparative analysis of sensitivity, correlation, and condition number, and selecting the optimal measurement parameters for gas path identification and calculation analysis; based on the test data, baseline steady-state performance model, and selected measurement parameters, using a nonlinear gas path analysis algorithm to identify and calculate the performance correction factors of each component under the same engine conversion speed state; statistically analyzing the relationship between the Reynolds number and the performance correction factors of each component to obtain the degree of influence of the Reynolds number on the performance of each component; correcting the baseline steady-state performance model through the relationship between the Reynolds number and the performance correction factors of each component; statistically comparing the calculation accuracy of the corrected baseline steady-state performance model to verify the effectiveness of the calculation results; and finally using the corrected baseline steady-state performance model to calculate the whole-machine performance and the performance of each component under different operating conditions.

[0007] Preferably, the typical test points include the boundary points of the working envelope and typical operating conditions of the aircraft during takeoff, continuous operation, climb, and cruise; the steady-state performance test data includes operating parameters, overall performance parameters, cross-sectional parameters of each component, and control parameters; the performance changes of the engine before and after the high-altitude test should remain basically unchanged, without bleed air and power extraction, and the selected steady-state performance test data can ensure the validity and accuracy of the subsequent calculation and analysis of the influence of Reynolds number on engine performance.

[0008] Preferably, the formula for calculating the parameter sensitivity is:

[0009]

[0010] In the formula, This represents the baseline model calculation result for the i-th measurement parameter. and These represent the calculated result of the i-th parameter and the relative deviation after the offset of the performance correction factor of the j-th component is implanted, respectively;

[0011] The formula for calculating the correlation of the parameters is:

[0012]

[0013] In the formula, P and Q represent vectors composed of performance correction factors for each component corresponding to the changes in the measured parameters in the influence coefficient matrix;

[0014] The formula for calculating the parameter condition number is:

[0015]

[0016] In formula (3), H represents the influence coefficient matrix and λ represents the condition number.

[0017] Preferably, the calculation formula for the nonlinear gas path analysis is:

[0018] Z = h(X) (4)

[0019] If the component performance parameter X changes, then δ represents the degree of change in the component performance parameter. Performing a first-order Taylor series expansion of h(x) at a given operating point yields:

[0020] h(X+δX)=h(X)+H·δX +HOT (5)

[0021] The influence coefficient matrix H is obtained, and its mathematical expression is:

[0022]

[0023] Ignoring the influence of higher-order terms in the influence coefficient matrix H, we obtain:

[0024]

[0025] The following was obtained through matrix transformation:

[0026] δX=(H T H) -1 H T δZ (8)

[0027] Preferably, the Reynolds number is defined as:

[0028]

[0029] The Reynolds number is characterized by the Reynolds number exponent RNI, and we obtain:

[0030]

[0031] In formula (10), P represents the total pressure measured at the component inlet, T represents the total temperature measured at the component inlet, μ represents the dynamic viscosity coefficient, R represents the gas constant, and P ref =101.325 kPa, T ref =288.15K, R ref =287J(kg*K).

[0032] Preferably, the method for calculating the validity of the calculation result is as follows:

[0033] Set a threshold for relative deviation, and use the test results of engine intake total pressure P2, intake total temperature T2, ambient pressure Pamb and low-pressure rotor converted speed N1r as the calculation input conditions of the steady-state performance model. Simulate and calculate each measured parameter using the baseline steady-state performance model and the modified steady-state performance model respectively. Statistically compare the relative deviation between the test results and the calculation results of each test point parameter. The specific algorithm is shown in formula (11). Determine whether the relative deviation is within the set threshold range. If so, it proves that the calculation result is valid.

[0034]

[0035] In formula (11), Y mea Y is represented by the measured value of the steady-state performance parameter. exp Y represents the calculated value of the corrected steady-state performance model parameters, and Y represents the relative deviation of the performance parameter calculation.

[0036] e

[0037] This application discloses a calculation method for determining the impact of Reynolds number on engine performance under whole-machine conditions. By selecting the steady-state performance test data to be processed, and conducting comparative analyses of parameter sensitivity, correlation, and condition number, the method first identifies performance parameter test data that meet the requirements for identification calculation. Then, it obtains the performance correction factors for each component through identification calculation. Next, it quantitatively obtains the relationship between the influence degree of Reynolds number and the performance correction factors of each component through statistical analysis. Finally, it corrects the baseline steady-state performance model based on the obtained relationship, thereby accurately calculating the whole-machine performance and the performance of each component under different operating conditions. This improves the calculation accuracy of the steady-state performance model within the working envelope, significantly reduces component testing costs, and shortens the development cycle. Attached Figure Description

[0038] To more clearly illustrate the technical solution provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some examples of this application.

[0039] Figure 1 This is a schematic diagram of the overall process of this application;

[0040] Figure 2 This is a schematic diagram showing the distribution of test points for the engine's high-altitude steady-state performance in this application;

[0041] Figure 3 This application shows the relationship between the turbocharger stage performance correction factor and the turbocharger stage inlet Reynolds number index.

[0042] Figure 4 This application shows the relationship between the performance correction factor of the high-pressure compressor and the inlet Reynolds number index of the high-pressure compressor.

[0043] Figure 5 This is a schematic diagram showing the calculated relative deviation of the physical speed of the high-voltage rotor in this application;

[0044] Figure 6 This is a schematic diagram showing the relative deviation results of the calculated total temperature at the outlet of the high-pressure turbine in this application. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0046] A calculation method for determining the impact of Reynolds number on engine performance under whole-machine conditions, such as... Figure 1 As shown, it includes the following steps:

[0047] Step S100: Select typical test points on the ground and at high altitude within the engine's operating envelope to obtain the steady-state performance test data that needs to be processed;

[0048] The test data for the whole machine include ambient pressure, total intake pressure, total intake temperature, low-pressure rotor speed, high-pressure rotor speed, thrust, air flow, fuel flow, total pressure and temperature at the fan outlet, total pressure and temperature at the inlet and outlet of the high-pressure compressor, total pressure and temperature at the outlet of the high-pressure turbine, and total pressure and temperature at the outlet of the low-pressure turbine.

[0049] Typical test points include the boundary points of the working envelope and typical operating conditions of the aircraft during takeoff, continuous operation, climb, and cruise; steady-state performance test data include operating parameters, overall performance parameters, cross-sectional parameters of each component, and control parameters.

[0050] The performance changes of the engine before and after the high-altitude test should remain basically unchanged. No aircraft bleed air and power extraction were performed. The selected steady-state performance test data can ensure the validity and accuracy of the subsequent calculation and analysis of the impact of Reynolds number on engine performance.

[0051] The selected steady-state performance test points are as follows: Figure 2 As shown, Figure 2 The linear structure in the diagram represents the engine's operating envelope, while the point structure represents the steady-state performance test points.

[0052] Step S200: Select measurement parameters for engine air path performance analysis, establish an influence coefficient matrix, conduct comparative analysis of parameter sensitivity, correlation and condition number, and select the optimal measurement parameters for air path identification calculation analysis to improve the effectiveness of identification calculation results.

[0053] The formula for calculating the parameter sensitivity is:

[0054]

[0055] In formula (1), This represents the baseline model calculation result for the i-th measurement parameter. and These represent the calculated result of the i-th parameter and the relative deviation after the offset of the performance correction factor of the j-th component is implanted, respectively;

[0056] The formula for calculating the correlation of the parameters is:

[0057]

[0058] In formula (2), P and Q represent vectors composed of performance correction factors of each component corresponding to the change in the measured parameters in the influence coefficient matrix;

[0059] The formula for calculating the parameter condition number is:

[0060]

[0061] In formula (3), H represents the influence coefficient matrix and λ represents the condition number.

[0062] According to formulas (1) to (3), among the selected measurement parameters, sensitivity analysis is first performed to find the most sensitive measurement parameter. Then, correlation analysis is performed to exclude similar data in the test parameters to avoid repeated calculations. Finally, condition number comparison analysis is performed to find the set of measurement parameters with the lowest condition number as the set of measurement parameters required for this application. Based on the selected set of measurement parameters, steady-state performance model and test data, an engine steady-state performance identification model is constructed.

[0063] In one specific implementation, the condition number comparisons for different combinations of measurement parameters are shown in Table 1:

[0064] Table 1. Calculation results of condition numbers for different combinations of measurement parameters.

[0065] Measurement parameter combination condition number Wfm,P44,P13,T44,T5,N2,P3,P25,T25 30.1 Wfm,P44,P13,T44,T5,N2,P3,P25,T25 121.5 Wfm,P44,P13,T44,T5,N2,P3,P25,T25 149.7 Wfm,P44,P13,T44,T5,N2,P3,P25,T25 615.7

[0066] Where Wfm is the fuel flow rate, P44 is the total pressure at the high-pressure turbine outlet, P13 is the total pressure at the fan outlet, T44 is the total temperature at the high-pressure turbine outlet, T5 is the total temperature at the low-pressure turbine outlet, N2 is the high-pressure rotor speed, P3 is the total pressure at the high-pressure compressor outlet, P25 is the total pressure at the high-pressure compressor inlet, and T25 is the total temperature at the total pressure compressor inlet. As can be seen from Table 1, the combination of measurement parameters in the first row has the smallest condition number. Therefore, the combination of measurement parameters in the first row is selected as the required measurement parameters.

[0067] Step S300: Based on the experimental data, baseline steady-state performance model and selected measurement parameters, the nonlinear gas path analysis algorithm is used to identify and calculate the performance correction factors of each component under the same converted speed state.

[0068] Since the performance parameters of components cannot be directly measured, it is necessary to calculate and analyze the changes in the performance of each component by measuring the changes in these parameters. The calculation formula for nonlinear gas path analysis at a given engine operating point is as follows:

[0069] Z = h(X) (4)

[0070] Where h represents the functional relationship between the measurement parameters and the component performance correction factors (expressed using a steady-state performance model), Z represents the measurement parameter vector, and X represents the performance correction factor vector of each component.

[0071] The measurement parameter vector Z is formed by the measurement parameters calculated in step S200.

[0072] If the performance of a component changes, δ represents the degree of parameter change. A first-order Taylor series expansion of h(x) at a given operating point yields:

[0073] h(X+δX)=h(X)+H·δX +HOT (5)

[0074] The influence parameter matrix H is obtained, and its mathematical expression is:

[0075]

[0076] Ignoring the influence of higher-order terms in the parameter matrix H, we obtain:

[0077] h(X+δX)=h(X)+H·δX (7)

[0078] The following was obtained through matrix transformation:

[0079] δX=(H T H) -1 H T δZ (8)

[0080] Based on the parameter relationships in formula (8), the nonlinear equations are solved using the Newton-Rapson algorithm to obtain the calculated values ​​of the performance correction factors for each component that meet the accuracy requirements of the objective function measurement parameters. Engine components include the fan, booster stage, high-pressure compressor, high-pressure turbine, and low-pressure turbine.

[0081] Through steps S100 to S300, the performance correction factors of each component corresponding to different test points can be calculated. By comparing them with the corresponding component inlet Reynolds number, the correspondence between the Reynolds number and the performance correction factors of each component can be obtained.

[0082] Step S400: Statistically analyze the relationship between the Reynolds number and the performance correction factor of each component to obtain the degree of influence of the Reynolds number on the performance of each component.

[0083] The Reynolds number is defined as:

[0084]

[0085] In formula (9), ρ represents the airflow density, L represents the chord length of the impeller blade, V represents the relative velocity of the inlet airflow, and μ represents the dynamic viscosity coefficient.

[0086] The Reynolds number is characterized by the Reynolds number exponent RNI, and we obtain:

[0087]

[0088] In formula (10), P represents the total pressure measured at the component inlet, T represents the total temperature measured at the component inlet, μ represents the dynamic viscosity coefficient, R represents the gas constant, and P ref =101.325 kPa, T ref =288.15K, R ref =287J(kg*K), engine inlet RNI at reference point =1.

[0089] The relationship between the Reynolds number and the performance (efficiency and converted flow rate) of the booster stage and high-pressure compressor components is as follows: Figure 3 and Figure 4 As shown, where Figure 3 The horizontal axis represents the Reynolds number index RNI at the inlet of the booster stage, and the vertical axis represents the performance correction factor for the booster stage components. f_IPC_Eff is the booster stage efficiency correction factor, and f_IPC_WRstd is the booster stage converted flow rate correction factor. Figure 4 The horizontal axis represents the Reynolds number index RNI at the high-pressure compressor inlet, and the vertical axis represents the performance correction factor for high-pressure compressor components. f_HPC_Eff is the high-pressure compressor efficiency correction factor, and f_HPC_WRstd is the high-pressure compressor converted flow rate correction factor.

[0090] Step S500: Substitute the relationship between the Reynolds number and the performance correction factor of each component into the baseline steady-state performance model to form the corrected steady-state performance model;

[0091] Step S600: Statistically compare the calculation accuracy of the corrected steady-state performance model to verify the validity of the calculation results;

[0092] Preferably, the method for calculating the validity of the calculation results is as follows:

[0093] A threshold for the relative deviation of the performance parameter calculation results is set. The test results of engine intake total pressure P2, intake total temperature T2, ambient pressure Pamb, and low-pressure rotor converted speed N1r are used as the calculation input conditions of the steady-state performance model. Simulation calculations are performed using the baseline steady-state performance model and the modified steady-state performance model respectively. The relative deviations between the test results and the calculation results of each test point are statistically compared to determine whether the relative deviation is within the set threshold range. If so, the calculation results are considered valid.

[0094] In one specific implementation, the relative deviation in the calculation of the physical speed N2 of the high-voltage rotor is as follows: Figure 5 As shown, the calculated relative deviation of the total outlet temperature T44 of the high-pressure turbine is as follows: Figure 6 As shown. The deviation in performance parameter calculation is given by formula (11):

[0095]

[0096] In formula (11), Y mea Y is represented by the measured value of the steady-state performance parameter. exp Y represents the calculated value of the corrected steady-state performance model parameters, and Y represents the relative deviation of the performance parameter calculation.

[0097] e

[0098] Step S700: Use the modified steady-state performance model to calculate the overall performance and the performance of each component under different operating conditions.

[0099] This application selects the steady-state performance test data to be processed and conducts comparative analysis of parameter sensitivity, correlation, and condition number. First, it selects the test data of measurement parameters that meet the requirements of identification calculation, and obtains the performance correction factors of each component through identification calculation. Then, it obtains the influence relationship between Reynolds number and performance correction factors of each component through statistical analysis. Finally, it corrects the baseline steady-state performance model based on this relationship, thereby accurately calculating the overall performance and the performance of each component under different operating conditions, improving the calculation accuracy of the steady-state performance model within the working envelope, significantly reducing component test costs, and shortening the development cycle.

[0100] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A calculation method for determining the effect of Reynolds number on engine performance under overall machine conditions, characterized by, The method comprises the following steps: Selecting typical test points on the ground and at high altitudes in the engine operating envelope to obtain steady-state performance test data for processing; By establishing an influence coefficient matrix, the sensitivity, correlation and condition number of the performance parameters are compared and analyzed, and the optimal measurement parameters for gas path performance identification and calculation analysis are selected; Based on the test data, the baseline steady-state performance model and the selected measurement parameters, the performance correction factors of each component of the engine at the same converted speed are calculated and identified using a nonlinear gas path analysis algorithm; The relationship between the Reynolds number and the performance correction factors of each component is statistically analyzed to determine the influence of the Reynolds number on the performance of each component; The baseline steady-state performance model is corrected according to the relationship between the Reynolds number and the performance correction factors of each component; The calculation accuracy of the corrected baseline steady-state performance model is statistically compared to verify the effectiveness of the calculation results; The corrected baseline steady-state performance model is used to calculate the overall performance and the performance of each component under different working conditions; The calculation formula of the nonlinear gas path analysis is: Z = h(X) (4) If the performance of a component changes, the parameter change degree is represented by δ, and the first-order Taylor series expansion of h(x) is obtained at a given working condition point: h(X + δX) = h(X) + H·δX + HOT (5) The influence parameter matrix H is obtained, and its mathematical expression is: Ignoring the high-order term influence of the influence parameter matrix H, the following is obtained: h(X + δX) = h(X) + H·δX (7) The following is obtained through matrix conversion calculation: δX = (H T H) -1 H T δZ (8) Where h represents the functional relationship between the measurement parameters and the performance correction factors of each component, Z represents the measurement parameter vector, and X represents the performance correction factor vector of each component; According to the parameter relationship of formula (8), the Newton-Raphson algorithm is used to solve the nonlinear equation set to obtain the performance correction factor calculation value of each component that meets the measurement parameter calculation accuracy requirement of the objective function.

2. The method of claim 1, wherein: The typical test points include boundary points of the operating envelope and typical working condition points of the aircraft during take-off, continuous flight, climbing and cruising; the steady-state performance test data include working condition parameters, overall performance parameters, component cross-section parameters and control parameters; the calibration test performance of the engine before and after the high-altitude test should remain basically unchanged, the aircraft bleed air and power extraction are not performed, and the selected steady-state performance test data can ensure the effectiveness and accuracy of the subsequent calculation and analysis of the influence of the Reynolds number on the engine performance.

3. The method of claim 1, wherein the engine performance is determined by the following equation: ###0001### where, P = engine performance, Re = Reynolds number, and C = constant. The calculation formula of the parameter sensitivity is: In formula (1), Y i ref represents the baseline model calculation result of the i-th measurement parameter, Y i j and ΔY i j respectively represent the i-th parameter calculation result after the j-th component performance correction factor offset is implanted and the influence relative deviation amount. The calculation formula of the parameter correlation is: In formula (2), P and Q represent the vectors composed of the performance correction factors of each component corresponding to the measurement parameter change amount in the influence coefficient matrix; The calculation formula of the condition number is: In formula (3), H represents the influence coefficient matrix, and λ represents the condition number.

4. The method of claim 1, wherein the engine performance is determined by the following equation: ###0001### where, P = engine performance, Re = Reynolds number, and C = constant. The definition of the Reynolds number is: The Reynolds number is represented by the Reynolds number index RNI, and the following is obtained: where P represents the measured total pressure at the component inlet, T represents the measured total temperature at the component inlet, μ represents the dynamic viscosity coefficient, R represents the gas constant, P ref = 101.325 kPa, T ref = 288.15 K, R ref = 287 J(kg*K).

5. The method of claim 1, wherein the engine performance is determined by the following equation: ###0001### where, P = engine performance, Re = Reynolds number, and C = constant. The calculation method for verifying the effectiveness of the calculation results of the corrected steady-state performance model is: The threshold of the relative deviation is set, the test results of the engine intake total pressure P2, the intake total temperature T2, the ambient pressure Pamb and the low-pressure rotor conversion speed N1r are taken as the calculation input conditions of the steady-state performance model, the baseline steady-state performance model and the corrected steady-state performance model are respectively used to simulate and calculate each measured parameter, the relative deviations of the test results and the calculation results of each test point parameter are compared and counted, the specific algorithm is shown in formula (11), whether the relative deviation is within the set threshold range is judged, if yes, it is proved that the calculation result is effective; In Equation (11), Y mea represents the steady-state performance parameter measurement value, Y exp represents the corrected steady-state performance model parameter calculation value, Y e represents the performance parameter calculation relative deviation.

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