Method for determining and correcting sampling factors for aircraft engine emissions based on cross-scan

Abstract

This invention discloses a method for determining and correcting emission sampling factors for aero-engines based on transverse scanning, belonging to the field of aero-engine testing technology. The method includes: acquiring transverse scanning data, constructing an exhaust cross-section emission concentration distribution field, and calculating the true average emission value of the exhaust cross-section; establishing a virtual geometric model, mapping the positions of each sampling hole in the virtual geometric model to the emission concentration distribution field to obtain the emission value at each sampling hole position, and calculating the equivalent sampling value of a fixed sampling probe; performing virtual rotations of the virtual geometric model at multiple circumferential angles, calculating the equivalent sampling value at each angle, and constructing a sampling factor matrix; determining a global sampling factor based on the sampling factor matrix; and using the global sampling factor to correct the measured emission value or to make equivalent adjustments to the emission limit. This invention improves the representativeness of conventional emission measurement and certification judgment for aero-engines.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine testing technology, specifically relating to a method for determining and correcting aero-engine emission sampling factors based on transverse scanning. Background Technology

[0002] During operation, aircraft gas turbine engines emit various pollutants into the atmosphere, including carbon monoxide, nitrogen oxides, unburned hydrocarbons, and non-volatile particulate matter. To meet the emission control requirements of the International Civil Aviation Organization (ICAO) and national airworthiness authorities, emission measurements are required during type certification, production license approval, and ongoing airworthiness surveillance. Emission measurement involves obtaining the average emission level of the engine's exhaust section and comparing it with the corresponding emission limits to determine compliance. Currently, aircraft engine emission sampling primarily employs fixed sampling and transverse scanning sampling. Fixed sampling includes fixed multi-hole sampling probes, rake-type sampling probes, or cross-shaped sampling rakes. The probe has multiple sampling holes at several predetermined radial and circumferential positions on the engine's exhaust section. Each sampling hole simultaneously extracts sample gas from the exhaust flow, which is then combined and mixed through sampling pipelines before being sent to a gas analyzer for concentration measurement. Because the sampling is performed simultaneously and the pipelines converge, the obtained concentration is essentially a comprehensive result of the emission concentrations at each sampling hole location mixed according to a certain weighting relationship. Transverse scanning sampling uses a movable single-point probe or sampling mechanism to sample point by point at multiple radial and circumferential positions within the exhaust section, obtaining the spatial distribution of emission concentration at the outlet section, and then calculating the true average emission concentration of the section through area-weighted averaging.

[0003] However, both of the above sampling methods have limitations in engineering applications. While transverse scanning can relatively completely reflect the spatial distribution of pollutant concentrations within the exhaust cross-section and obtain near-true cross-sectional average emission levels, its implementation is complex. It requires precise spatial positioning and point-by-point sampling of the probe in a high-temperature, high-speed exhaust environment, resulting in long testing times, high costs, and stringent requirements for engine stability and test bench conditions, making it unsuitable for repeated testing in every routine emission measurement. Fixed sampling probes, while structurally stable, easy to operate, and highly efficient, are suitable for routine emission testing, but the number and position of their sampling holes are predetermined. When there is significant radial or circumferential concentration non-uniformity at the engine outlet cross-section, the concentration measured by the fixed sampling probe may systematically deviate from the true average value of the exhaust cross-section, resulting in representativeness bias. In existing technologies, transverse scanning is mainly used to verify the acceptability of a fixed sampling probe design. However, after verification, routine tests still directly use the measurement results from the fixed sampling probe, lacking a method to systematically convert existing transverse scanning data into a fixed sampling representativeness bias coefficient, and failing to establish a closed-loop data processing flow for correcting routine measurements or making equivalent adjustments to emission limits using this coefficient. This can lead to unquantified sampling representativeness bias in routine emissions measurement results, affecting the consistency and conservatism of emissions compliance judgments across different engines and test batches. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for determining and correcting emission sampling factors for aero-engines based on transverse scanning, thereby resolving the issues present in the background art.

[0005] To achieve the aforementioned objectives, this invention proposes a method for determining and correcting emission sampling factors for aero-engines based on transverse scanning, comprising: Acquire exhaust cross-section transverse scan data of multiple aero-engines under multiple power states and multiple emission components, construct exhaust cross-section emission concentration distribution field based on transverse scan data, and calculate the true average emission value of exhaust cross-section by area weighted average; A virtual geometric model of the fixed sampling probe is established, and the position of each sampling hole in the virtual geometric model is mapped to the emission concentration distribution field to obtain the emission value at each sampling hole position. The equivalent sampling value of the fixed sampling probe is calculated according to the weight of each sampling hole. The virtual geometric model is virtually rotated at multiple circumferential angles, and the equivalent sampled value at each angle is calculated. The ratio of the equivalent sampled value at each angle to the actual average emission value is used as a single sampling factor to construct a sampling factor matrix. Multi-level statistical processing is performed on the sampling factor matrix, and the global sampling factor is determined by combining the preset risk level and statistical confidence coefficient. The global sampling factor is used to correct the measured emission values ​​obtained from fixed sampling probes in conventional emission measurements, or to make equivalent adjustments to emission limits.

[0006] The beneficial effects of this invention are as follows: This invention superimposes a virtual geometric model of a fixed sampling probe onto an emission concentration distribution field formed by existing transverse scanning data. This maps the positions of each sampling aperture of the fixed sampling probe to the concentration field for interpolation calculations, thereby obtaining equivalent sampling values ​​from the fixed sampling probe without repeating the complete transverse scan. Subsequently, a sampling factor matrix is ​​constructed by virtually rotating the virtual geometric model at multiple circumferential angles. Then, a global sampling factor is determined by performing multi-level statistical processing on the sampling factor matrix, combined with a preset risk level and a t-distribution confidence coefficient. Finally, the global sampling factor is used to make representative corrections to the measured emission values ​​of the fixed sampling probe or to make equivalent adjustments to the emission limits, thereby improving the representativeness, consistency, and conservatism of conventional emission measurements and certification judgments for aero-engines. Attached Figure Description

[0007] Figure 1 This is a flowchart of the steps of a method for determining and correcting emission sampling factors for aero-engines based on transverse scanning according to the present invention. Figure 2 This is a schematic diagram of the contour lines of the concentration distribution field of the present invention; Figure 3 This is a schematic diagram illustrating the principle of the sampling arm of the present invention; Figure 4 This is a schematic diagram illustrating the principle of the sampling arm rotation of the present invention. Detailed Implementation

[0008] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0009] like Figure 1 As shown, a method for determining and correcting emission sampling factors for aero-engines based on transverse scanning includes: S1: Acquire exhaust cross-section transverse scan data of multiple aero engines under multiple power states and multiple emission components, construct an exhaust cross-section emission concentration distribution field based on the transverse scan data, and calculate the true average emission value of the exhaust cross-section through area weighted averaging.

[0010] The transverse scan data includes the two-dimensional spatial coordinates of each measuring point on the exhaust cross section, the emission component concentration value or emission index value corresponding to each measuring point, and the area weight represented by each measuring point.

[0011] The engines analyzed in this embodiment include large and small engines with non-mixed exhaust types. Large non-mixed exhaust engines include JT9D, RB211, CFM56-3, M45H, CF6-50, and JT3D, while small non-mixed exhaust engines include ALF502 and TFE731-3. Large engines with mixed exhaust types are also included, such as JT8D-9, JT8D-217, JT8D-11, JT8D-9A, JT8D-17R, and JT8D-209.

[0012] The lateral scan data for each engine is acquired at least in both idle and high-power states, and in some embodiments, also in takeoff and climb states. The measured emission components include carbon monoxide (CO), nitrogen oxides (NOx), unburned hydrocarbons (THC), and smoke index (SN). For each emission component, a corresponding emission concentration or emission index value is obtained at each measurement point. In the field of aero-engine emission measurement, emission concentration refers to the volume or mass proportion of a specific pollutant in the exhaust gas mixture, reflecting the level of that pollutant in the exhaust gas at the sampling point. The emission index is the mass of a specific pollutant emitted per unit mass of fuel consumed.

[0013] When determining the spatial coordinates, the origin is taken as the geometric center of the engine exhaust cross-section, with the x-axis and y-axis along two orthogonal directions of the exhaust cross-section. The area weight corresponding to each measuring point is a key parameter for transforming the emission data of discrete measuring points into the average emission level of the exhaust cross-section. The area weight represents the size of the local area of ​​the exhaust cross-section represented by the measuring point. The larger the area weight, the larger the exhaust cross-section area represented by the measuring point, and the greater its contribution to the average emission level of the cross-section. The area weight is calculated using Voronoi partitioning, that is, constructing an influence area centered on each measuring point, where the distance from all locations within this area to the measuring point is less than the distance to any other measuring point. The area of ​​this Voronoi cell is the area weight of the corresponding measuring point.

[0014] After acquiring the raw transverse scan data, data preprocessing is required to ensure the consistency and reliability of subsequent calculations. The preprocessing process includes anomaly identification, removing obvious abnormal data points caused by sampling system malfunctions, probe blockage, or fluctuations in engine operating conditions. Secondly, the coordinates of the measurement points for different engines are standardized, normalizing the radial coordinates of the exhaust cross-sections of each engine to the same dimensionless range, facilitating consistent comparison of data from engines of different sizes in subsequent virtual sampling calculations. Simultaneously, the effective boundary of the exhaust cross-section for each engine is determined, i.e., the cross-sectional area actually covered by the exhaust flow. Finally, the data under different power states are organized and archived separately, forming a structured dataset indexed by engine number, emission composition, and power state, serving as the data foundation for subsequent calculations.

[0015] An exhaust cross-section emission concentration distribution field was constructed based on transverse scan data, including: For each engine, each emission component, and each power state, spatial interpolation is performed on the measurement point data to obtain a continuous concentration distribution field covering the exhaust cross section.

[0016] Since the transverse scanning obtains the emission concentration or emission index at discrete measurement points within the exhaust cross section, and the sampling hole position of the fixed sampling probe in the subsequent virtual sampling calculation usually does not completely coincide with the original measurement point of the transverse scanning, it is necessary to use spatial interpolation methods to extend the discrete measurement point data into a continuous concentration distribution field covering the entire effective area of ​​the exhaust cross section.

[0017] For each engine, each emission component, and each power state, spatial interpolation is performed independently. The input for interpolation is the two-dimensional coordinates of all transverse scan measurement points under that condition, along with their corresponding emission concentration or emission index values. The output is an estimate of the emission value at any location within the effective area of ​​the exhaust cross-section. In this embodiment, the interpolation method used is spatial interpolation based on radial basis functions. This method can handle irregularly distributed measurement point data and generate a smooth and continuous concentration distribution surface between measurement points. In other embodiments, Kriging interpolation, natural neighborhood interpolation, bilinear interpolation, or inverse distance weighted interpolation can also be used; the specific choice depends on the measurement point distribution density and the spatial variation characteristics of the emission concentration field. Figure 2 As shown, the concentration distribution field can be visualized using contour maps, where each line represents the location trajectory where the emission concentration is equal within the exhaust cross section.

[0018] Based on the constructed emission concentration distribution field, the true average emission value of the exhaust cross section is calculated using area-weighted averaging. Area-weighted averaging involves summing the emission concentrations of each local area within the exhaust cross section according to their respective area proportions, resulting in a single value that represents the overall emission level of the exhaust cross section. When using concentration data, the formula for calculating the true average emission value is: ,in, The true cross-sectional average concentration of the p-th emission component obtained by transverse scanning under the k-th operating condition. Let i be the concentration value at the i-th transverse scan point. Here, n represents the area weight of the i-th measurement point, and n is the number of measurement points in the transverse scan. When using emission index data, the calculation method is the same; simply replace the concentration value with the emission index value.

[0019] For each engine included in the analysis, the true average emission values ​​of each emission component under each power state were calculated using the method described above, forming a dataset of true average emission values ​​indexed by engine number, emission component, and power state. In this embodiment, the true average emission value is considered the best estimate of the emission level at the engine outlet section. Because transverse scanning performs sufficient spatial sampling within the exhaust section, its area-weighted average result can more completely reflect the spatial distribution information of pollutant concentrations within the exhaust section compared to a fixed sampling probe, and is therefore used as a reference benchmark for evaluating the representativeness of fixed sampling.

[0020] S2: Establish a virtual geometric model of the fixed sampling probe, map the position of each sampling hole in the virtual geometric model to the emission concentration distribution field to obtain the emission value at each sampling hole position, and calculate the equivalent sampling value of the fixed sampling probe according to the weight of each sampling hole.

[0021] After constructing the emission concentration distribution field of the exhaust section and calculating the true average emission value, it is necessary to establish a virtual geometric model of the fixed sampling probe to simulate the sampling results that the fixed sampling probe may obtain on the exhaust section in conventional emission measurement.

[0022] The establishment of the virtual geometric model first requires determining the structural parameters of the fixed sampling probe. In this embodiment, the fixed sampling probe adopts a cross-shaped sampling rake structure, such as... Figure 3 As shown, the structure consists of two mutually orthogonal sampling arms, with the intersection of the two arms located at the geometric center of the engine exhaust section. Several sampling holes are arranged radially on each sampling arm, and the radial positions of the sampling holes are determined according to the principle of equal-area arrangement. Equal-area arrangement means dividing the effective annular region of the engine exhaust section radially into several concentric annular sub-regions of equal area, with each sampling hole located at the centroid radius of its corresponding annular sub-region. In this embodiment, a central sampling hole located at the geometric center of the exhaust section is not provided because some central regions of the engine outlet section are obstructed by a central body or structure, making a central sampling hole potentially unrealizable or unable to represent the true flow field in actual installation.

[0023] To evaluate the impact of different sampling hole numbers on sampling representativeness, this embodiment establishes virtual geometric models for various sampling hole number schemes. For example, 3 sampling holes per arm correspond to 12 sampling holes for the entire probe, 4 sampling holes per arm correspond to 16 sampling holes for the entire probe, and 5 sampling holes per arm correspond to 20 sampling holes for the entire probe. Each scheme uses the principle of equal area arrangement to determine the radial position of each sampling hole. The only difference between the different schemes lies in the number of annular sub-regions, resulting in variations in the radial position and spacing of the sampling holes. The two-dimensional coordinates of each sampling hole on the exhaust cross-section can be obtained by converting polar coordinates to rectangular coordinates based on the circumferential angle and radial position of its respective sampling arm.

[0024] After determining the spatial coordinates of each sampling well, these coordinates are mapped onto the emission concentration distribution field. Since the sampling well positions of the fixed sampling probes typically do not completely coincide with the original measurement points of the transverse scan, it is necessary to use the interpolation function of the emission concentration distribution field to obtain the emission concentration or emission index values ​​at each sampling well position. For the j-th sampling well, its position coordinates are known; substituting these coordinates into the interpolation function of the emission concentration distribution field yields the emission value of the p-th emission component at that sampling well position under the k-th power state. This process is performed one by one for each sampling well in the virtual geometric model, ultimately obtaining the set of emission values ​​at all sampling well positions.

[0025] After obtaining the emission values ​​at each sampling hole location, the equivalent sampling value of the fixed sampling probe is calculated based on the weight of each sampling hole. The equivalent sampling value represents the comprehensive emission concentration that the fixed sampling probe can measure after mixing the sample gas extracted from all sampling holes under this arrangement. In this embodiment, each sampling hole is weighted equally, meaning that each sampling hole contributes equally to the final mixing result, and the equivalent sampling value is the arithmetic mean of the emission values ​​at all sampling hole locations. The formula for calculating the equivalent sampling value is the sum of the emission values ​​at all sampling hole locations divided by the total number of sampling holes. In other embodiments, the weight of each sampling hole can also be set differently according to the area proportion it represents or the exhaust flow rate proportion at that location. In this case, the equivalent sampling value is the weighted sum of the emission values ​​of each sampling hole according to their respective weights, divided by the total weight.

[0026] For each engine, emission component, and power state included in the analysis, a virtual geometric model was established and equivalent sampled values ​​were calculated using the method described above. Each sampling hole number scheme was evaluated as an independent candidate scheme, ultimately forming an equivalent sampled value dataset indexed by engine number, emission component, power state, and sampling hole number scheme.

[0027] S3: Perform virtual rotations on the virtual geometric model at multiple circumferential angles, calculate the equivalent sampled values ​​at each angle, and use the ratio of the equivalent sampled values ​​at each angle to the actual average emission values ​​as individual sampling factors to construct a sampling factor matrix.

[0028] In this embodiment, the sampling factor matrix is ​​constructed, including: Using the geometric center of the engine exhaust section as the rotation center, the overall structure of the fixed sampling probe is rotated around the geometric center in the exhaust section plane by multiple preset angles. For each rotation angle, the new coordinates of each sampling hole after rotation are substituted into the interpolation function of the emission concentration distribution field to obtain the emission value at the corresponding position. The equivalent sampling value at the corresponding angle is calculated, and the ratio of the equivalent sampling value at each angle to the true average emission value is used as a single sampling factor. All single sampling factors are arranged according to the circumferential angle and the number of sampling holes to construct a sampling factor matrix.

[0029] Because the emission concentration distribution within the engine exhaust cross-section is typically not perfectly axisymmetric but exhibits a degree of circumferential non-uniformity, the circumferential installation angle of the fixed sampling probe on the exhaust cross-section directly affects the local concentration level at each sampling port location, leading to differences in the equivalent sampling values ​​obtained at different installation angles. In actual emission testing, the installation angle of the fixed sampling probe is often determined by the bench structure, probe interface position, or engineering practices, and may not necessarily be able to select the most representative circumferential position. Therefore, to comprehensively evaluate the sampling representativeness of the fixed sampling probe at different installation angles, this embodiment performs virtual rotations of the virtual geometric model at multiple circumferential angles, recalculates the spatial coordinates of each sampling port at each rotation angle, obtains the emission value at the corresponding location based on the emission concentration distribution field, and then calculates the equivalent sampling value at that angle.

[0030] The implementation method of virtual rotation is as follows: Figure 4 As shown, the entire structure of the cross-shaped sampling rake is rotated around the geometric center of the engine exhaust section by a preset angle within the exhaust section plane, with the geometric center of the exhaust section as the rotation center. After rotation, the radial position of each sampling hole remains unchanged, but its circumferential position changes, and the corresponding two-dimensional coordinates are recalculated through coordinate rotation transformation. In this embodiment, six virtual rotation angles are selected: 0°, 15°, 30°, 45°, 60°, and 75°. For each virtual rotation angle, the new coordinates of each sampling hole after rotation are substituted into the interpolation function of the emission concentration distribution field to obtain the emission concentration value or emission index value of each sampling hole at the new position, and then the equivalent sampling value at that angle is calculated. Thus, for each engine, each emission component, each power state, and each sampling hole number scheme, equivalent sampling values ​​at six different circumferential angles can be obtained.

[0031] After obtaining the equivalent sampling values ​​at each angle, the ratio of each equivalent sampling value to the corresponding true average emission value is used as a single sampling factor. Therefore, the physical meaning of the single sampling factor is the proportional relationship between the equivalent emission value measured by the fixed sampling probe and the true average emission value of the exhaust section, given a given engine, emission composition, power state, number of sampling holes, and circumferential installation angle. When the single sampling factor is greater than 1, it indicates that the emission value measured by the fixed sampling probe at that angle is higher than the true average value of the section; when the single sampling factor is less than 1, it indicates that the emission value measured by the fixed sampling probe is lower than the true average value of the section.

[0032] All the aforementioned individual sampling factors are arranged according to two dimensions: the number of sampling holes and the circumferential angle, to obtain a sampling factor matrix. The rows of this matrix correspond to different circumferential angles, and the columns correspond to different numbers of sampling holes. Each element in the matrix is ​​the value of an individual sampling factor under the corresponding condition. A sampling factor matrix is ​​provided for each engine, each emission component, and each power state included in the analysis.

[0033] S4: Perform multi-level statistical processing on the sampling factor matrix, and determine the global sampling factor by combining the preset risk level and statistical confidence coefficient.

[0034] In this embodiment, multi-level statistical processing is performed on the sampling factor matrix, including: For the same engine, the same emission component, and the same number of sampling holes, the standard deviation of the individual sampling factor under different circumferential angles is calculated to obtain the angular dispersion.

[0035] For the same engine and the same emission component, the angular dispersion under each sampling hole number scheme is regarded as multiple independent estimates of the circumferential non-uniformity of the same engine and then combined to obtain the combined standard deviation of the engine's internal angles.

[0036] For the same emission component, the standard deviation of the engine intra-engine angles corresponding to all engines included in the analysis is further merged to obtain the cross-engine angle merged discreteness.

[0037] For each engine, the average sampling factor of the engine is obtained by arithmetically averaging all individual sampling factors in the sampling factor matrix. The average sampling factor of the emission components is obtained by arithmetically averaging the average sampling factors of all engines. The standard deviation of the average sampling factor of each engine relative to the average sampling factor of the emission components is calculated to obtain the dispersion of the average sampling factor among engines.

[0038] Since individual sampling factors obtained under a single engine, single power state, single number of sampling holes, and single circumferential angle can only reflect local representativeness deviations under specific conditions, they cannot be directly used for general corrections in routine emission testing. To make the sampling factors universal across engines, operating conditions, and probe schemes, multi-level statistical processing of the sampling factor matrix is ​​required. The influence of different sources of variation on the sampling factors should be quantified layer by layer to finally obtain the global sampling factors.

[0039] The first layer of multi-level statistical processing is the calculation of angular dispersion. Specifically, for the same engine, the same emission component, the same power state, and the same number of sampling holes, the standard deviation of the single sampling factor under different circumferential angles is calculated. This standard deviation is the angular dispersion under that condition, and its calculation formula is as follows: ,in, The angular dispersion is given by the e-th engine, the p-th emission component, the k-th power state, and the s-th sampling hole number scheme. For the corresponding conditions, the first A single sampling factor for each circumferential angle. This is the arithmetic mean of all circumferential angle sampling factors under this condition. This represents the number of circumferential angles.

[0040] Angular dispersion is used to characterize the fluctuation range of the sampling factor caused by different circumferential installation angles of a fixed sampling probe. The greater the angular dispersion, the more significant the circumferential non-uniformity of the engine exhaust section, and the more sensitive the measurement results of the fixed sampling probe are to the installation angle.

[0041] The second layer of multi-level statistical processing is the calculation of intra-engine merging dispersion. For the same engine and the same emission component, the first layer has already obtained the angular dispersion under each sampling aperture number scheme. Since different sampling aperture number schemes reflect the angular sensitivity of the same emission concentration field under different spatial sampling densities, these angular dispersions can be regarded as multiple independent estimates of the circumferential non-uniformity of the same engine. The angular dispersions of all sampling aperture number schemes for the same engine are merged to obtain the intra-engine angular merging standard deviation, which is calculated using the following formula: ,in, The combined standard deviation of the engine internal angles for the e-th engine and the p-th emission component is given. The total number of sampling wells is given by the number of degrees of freedom corresponding to the combined standard deviation. ,in, Let e ​​be the combined degrees of freedom of the engine's internal angles.

[0042] The third layer of multi-level statistical processing is the cross-engine angle merging dispersion calculation. For the same emission component, the second layer has already obtained the combined standard deviation of the engine angles for each engine. The combined standard deviations of the engine angles corresponding to all engines included in the analysis are further merged to obtain the cross-engine angle merging dispersion, and its calculation formula is as follows: ,in, For the cross-engine angle combined discreteness of the p-th emission component, Let be the combined standard deviation of the internal angles of the e-th engine. This quantity characterizes the overall sampling factor uncertainty level caused by the variation of the circumferential installation angle of the fixed sampling probe across the entire engine group, and its corresponding degrees of freedom are . ,in, The total degrees of freedom for combining discreteness across engine angles.

[0043] The fourth layer of multi-level statistical processing is the calculation of the dispersion of the average sampling factor among engines. For each engine, the arithmetic mean of all individual sampling factors in its sampling factor matrix is ​​taken to obtain the average sampling factor of that engine. The calculation formula is as follows: ,in, Let be the average sampling factor for the e-th engine. This average sampling factor reflects the average representativeness deviation level of the engine across all sampling aperture schemes and all circumferential angles.

[0044] The average sampling factor of all engines is arithmetically averaged to obtain the average sampling factor of emission components. The calculation formula is as follows: ,in, Let be the average sampling factor for the p-th emission component. Simultaneously, calculate the standard deviation of each engine's average sampling factor relative to the average sampling factor of the emission components, i.e., the dispersion of the average sampling factor among engines. The formula for this is: ,in, Let represent the dispersion of the average sampling factor among engines. This dispersion characterizes the systematic differences in sampling factors among different engines due to differences in outlet emission distribution characteristics, and its corresponding degrees of freedom are . ,in, For the discrete degrees of freedom between engines.

[0045] In this embodiment, the global sampling factor is determined by combining a preset risk level and a statistical confidence coefficient, including: Based on the average sampling factor of emission components, the statistical uncertainty term, which is composed of the dispersion of cross-engine perspective merging and the dispersion of average sampling factor between engines, is deducted. The magnitude of the statistical uncertainty term is determined by the one-sided quantile and effective degrees of freedom of the t-distribution corresponding to the preset risk level.

[0046] After completing the above four-level statistical processing, the global sampling factor is determined by combining the preset risk level and statistical confidence coefficient. The preset risk level represents the upper limit of the allowable probability of misjudgment in emission compliance assessment. In this embodiment, a risk level of 2.5% is adopted, which requires the determination of the global sampling factor to have a confidence level of 97.5% to ensure the conservatism of the correction results. When sampling is performed using only a single circumferential angle in conventional emission testing, the formula for calculating the global sampling factor is as follows: ,in, A global sampling factor from a single perspective. The one-sided quantiles of the t-distribution related to the preset risk level and effective degrees of freedom v. To combine discreteness across engine angles, The dispersion of the average sampling factor among engines is represented. The corresponding effective degrees of freedom are determined using the Welch-Satterthwaite approximation formula. , where v is the effective degrees of freedom.

[0047] When averaging sampling results from N different circumferential angles in conventional emissions testing, the contribution of angular dispersion to the final result should decrease as the number of averaging angles increases, because multi-angle averaging can reduce the influence of random deviations from a single angle. In this case, the formula for calculating the global sampling factor is: ,in, Let be the global sampling factor averaged from N angles, where N is the number of circumferential angles used in conventional testing. The corresponding effective degrees of freedom are: After determining the effective degrees of freedom, the corresponding statistical confidence coefficients are obtained by looking up tables or calculating based on the t-distribution at a 2.5% one-sided risk level. Substituting this into the global sampling factor calculation formula yields the final result. The physical meaning of the global sampling factor is the ratio of the measurement result of the fixed sampling probe to the true average emission level of the exhaust section. If it is less than or equal to 1, it indicates that the fixed sampling probe tends to underestimate the true average emission level of the exhaust section in a statistical sense.

[0048] S5: Use the global sampling factor to correct the measured emission values ​​obtained by the fixed sampling probe in conventional emission measurements, or to make equivalent adjustments to the emission limits.

[0049] The corrected emission value is obtained by dividing the measured emission value of the fixed sampling probe by the global sampling factor, or by multiplying the original emission limit by the global sampling factor to obtain the equivalent emission limit.

[0050] There are two equivalent ways to apply the global sampling factor: one is to make a representative correction to the measured emission values ​​of a fixed sampling probe, and the other is to make an equivalent adjustment to the emission limits.

[0051] In the first application method, when conventional emission testing uses a fixed sampling probe to obtain the measured emission value of the p-th emission component at the k-th power state. In some cases, the measured value may be lower than the true average emission level of the exhaust section because the sampling orifice of the fixed sampling probe may not completely cover the high-concentration area within the exhaust section. To eliminate this representativeness bias, the measured emission value is corrected using a global sampling factor for the corresponding emission component. The formula for calculating the corrected emission value is as follows: ,in, These are emission values ​​that have been corrected for representativeness. This refers to the emission concentration or emission index directly measured by a fixed sampling probe in routine emission testing. Let be the global sampling factor corresponding to the p-th emission component. Due to the global sampling factor... Typically less than 1, corrected emission value Will be greater than the measured value This means that the correction process compensates for any underestimation effect that might exist with a fixed sampling probe, making the corrected result closer to the true average emission level of the exhaust cross section. When averaging the sampling results from N different circumferential angles in conventional emission testing, the corresponding multi-angle global sampling factor is used. Alternative Make corrections, and the correction formula is now: .

[0052] In the second application method, let the original emission limit of the p-th emission component at the k-th power state be _____. This limit is based on the true average emission level of the exhaust cross section. When using a fixed sampling probe for routine emission measurements, since there is a proportional relationship between the measured value of the fixed sampling probe and the true average value of the exhaust cross section, represented by the global sampling factor, multiplying the original emission limit by the global sampling factor yields an equivalent limit that is directly comparable to the fixed sampling measurement value. The calculation formula is as follows: ,in, This is the equivalent emission limit after taking into account the representativeness bias of the sampling. Because... Typically less than 1, equivalent limit Less than the original limit This signifies that a more stringent judgment standard has been applied to the measured emission values ​​from fixed sampling probes, thereby compensating for any potential underestimation effect from fixed sampling probes. In emission compliance judgments, the measured emission values ​​from fixed sampling probes are... Direct and equivalent limits If a comparison is made, If the emission component meets the emission requirements under the current power state, then it is determined that the emission component meets the emission requirements. If so, it is determined that the emission requirements are not met. This method is mathematically equivalent to the first correction method because... and These are two expressions of the same inequality.

[0053] It should be noted that the global sampling factor correction in this step and other corrections that may be involved in aero-engine emission measurements belong to different levels of data processing. For example, for the emission measurement of non-volatile particulate matter (NVPM), particles may experience transmission losses in the sampling system through components such as sampling lines, splitters, diluents, volatile particulate removers, and particle counters. These losses need to be compensated for by a sampling system loss correction factor. This system loss correction addresses the extent of particle loss during sampling and transmission, while the global sampling factor correction in this step addresses whether the sampling orifice position of the fixed sampling probe can represent the average emission level of the exhaust cross-section. These two types of corrections target different sources of error and can be used sequentially or independently within the same emission data processing flow; they are not interchangeable. In actual data processing, the measured emission values ​​can be corrected for sampling system losses first, and then the result after loss correction can be corrected for representativeness in this step. Alternatively, the two types of correction factors can be combined into a comprehensive correction factor and applied to the measured emission values ​​all at once.

[0054] When establishing the global sampling factor, different combinations of variables can be calculated separately, forming multiple result sets to allow for the selection of a suitable sampling factor based on the specific application scenario. Variable combinations include, but are not limited to, risk level (e.g., 2.5% or 10%), number of sampling angles (e.g., single angle or average of three angles), data unit (e.g., emission index or concentration level), whether a central sampling hole is included, whether a small engine is included, whether a mixed-flow engine is included, the radial arrangement of sampling holes (e.g., equal area or equal spacing), and the number of sampling holes on each cross-shaped sampling arm (e.g., 3, 4, 5, or 10). For each variable combination, the corresponding single-angle or multi-angle global sampling factor is obtained following the aforementioned multi-level statistical processing flow. These results can be used to compare the impact of different sampling strategies on sampling representativeness and to select a sampling factor suitable for the specific engine type, emission composition, and testing objective.

[0055] The complete calculation process from a fixed sampling concentration matrix to the final sampling factor is given below. This embodiment is only used to illustrate the calculation steps of the method of this application and does not limit this application to NOx, nor does it limit this application to using only this group of engines, this type of probe hole number, or this type of statistical conditions. The calculation object of this embodiment is NOx, the engine sample number is Eng. 7, and the concentration level data, equal area sampling hole arrangement, 2.5% risk level, excluding mixed flow engines, excluding small engines, excluding the central sampling point, and the calculation is performed using a single probe position as an example.

[0056] An outlet cross-sectional concentration field is generated based on existing transverse scanning data, and a fixed sampling probe aperture position is superimposed on this concentration field. Interpolation calculations are performed for different probe angles and different numbers of sampling apertures to obtain the fixed sampling concentration matrix of NOx.

[0057] Table 1 NOx Fixed Sampling Concentration Matrix Probe angle 12 16 20 40 0° 165.35 165.28 165.37 165.33 15° 167.85 168.00 168.13 168.30 30° 172.61 172.83 172.86 173.08 45° 179.71 179.58 179.58 179.66 60° 167.10 166.93 167.13 167.02 75° 162.30 162.17 162.40 162.24

[0058] Note: The area-weighted average of the NOx transverse scan for this engine is 166.6.

[0059] Table 2 NOx Single-Item Sampling Factor Matrix Probe angle 12 16 20 40 0° 0.99250 0.99208 0.99262 0.99238 15° 1.00732 1.00840 1.00918 1.01020 30° 1.03607 1.03739 1.03758 1.03890 45° 1.07869 1.07791 1.07791 1.07839 60° 1.00300 1.00198 1.00318 1.00252 75° 0.97419 0.97341 0.97479 0.97383

[0060] For each sampling aperture number scheme, the standard deviation of the sampling factor at six probe angles is calculated to characterize the dispersion of the sampling factor caused by changes in the circumferential angle of the probe. The calculated standard deviations of the angles for each sampling aperture number scheme are as follows:

[0061] Table 3. Standard deviation of angle under different sampling hole numbers Sampling hole scheme Sampling factor 12 0.0371 16 0.0372 20 0.0368 40 0.0373

[0062] After combining the standard deviations of the angles under the four sampling hole number schemes, the combined standard deviation of the engine's internal angles is obtained as 0.0371. Following the same method, the combined standard deviations of the engine's internal angles were calculated for multiple engines, yielding the following results.

[0063] Table 4. Combined Standard Deviation of Engine Internal Angles for Each Engine Engine number 12 16 20 40 Angle combined standard deviation Degrees of freedom 7 0.0371 0.0372 0.0368 0.0373 0.0371 20 11 0.0229 0.0485 0.0576 0.0138 0.0400 20 1 0.0278 0.0245 0.0209 0.0226 0.0241 20 8 0.00339 0.00339 0.00358 0.00378 0.00353 20 4 0.0501 0.0537 0.0542 0.0436 0.0506 20

[0064] Furthermore, by merging the angles of different engines, the cross-engine angle merging discreteness is 0.035, and the degree of freedom is 100.

[0065] For each engine, the average of its 24 individual sampling factors is calculated to obtain the engine's average sampling factor:

[0066] Table 5 Average sampling factors for each engine Engine number Average sampling factor 7 1.015 11 1.012 1 1.002 8 1.006 4 1.002

[0067] The average sampling factor across engines is calculated to be 1.0074, and the standard deviation of the average sampling factor between engines is calculated to be 0.0059. In this example, after substituting into the formula, the final sampling factor is 0.936, and the degrees of freedom are 103.

[0068] It should be noted that the specific numerical parameters involved in the various embodiments of the present invention, including but not limited to the number and values ​​of circumferential rotation angles, the number of sampling holes, the percentage of risk level, the statistical confidence coefficient, and the merging method in each layer of statistical processing, are all preferred examples of this embodiment. Those skilled in the art can adaptively adjust the above parameters based on the actual engine type, emission component characteristics, test conditions, and accuracy requirements through conventional experiments or engineering experience, without departing from the technical concept of the present invention. In addition, the data preprocessing methods involved in the present invention, such as coordinate normalization, area weight calculation, and selection of spatial interpolation methods, are all conventional technical operations in the field. Those skilled in the art can choose appropriate implementation methods according to specific data characteristics. At the same time, for the sake of brevity, the formulas of the present invention do not specifically explain the mathematical degradation cases such as zero denominators. In actual engineering implementation, those skilled in the art will handle such boundary conditions accordingly according to conventional numerical calculation specifications. For example, when the sample size of a certain statistic is insufficient or the variance is zero, a preset default value or skipping the calculation of that layer is adopted. These treatments are common knowledge in the field and do not affect the integrity and feasibility of the technical solution of the present invention.

Claims

1. A method for determining and correcting emission sampling factors for aero-engines based on transverse scanning, characterized in that, include: Acquire exhaust cross-section transverse scan data of multiple aero-engines under multiple power states and multiple emission components, construct exhaust cross-section emission concentration distribution field based on transverse scan data, and calculate the true average emission value of exhaust cross-section by area weighted average; A virtual geometric model of a fixed sampling probe is established, and the position of each sampling hole in the virtual geometric model is mapped to the emission concentration distribution field to obtain the emission value at each sampling hole position. The equivalent sampling value of the fixed sampling probe is calculated according to the weight of each sampling hole. The equivalent sampling value represents the comprehensive emission concentration measured after mixing the sample gas extracted from all sampling holes. The virtual geometric model is virtually rotated at multiple circumferential angles, and the equivalent sampled value at each angle is calculated. The ratio of the equivalent sampled value at each angle to the actual average emission value is used as a single sampling factor to construct a sampling factor matrix. Multi-level statistical processing is performed on the sampling factor matrix, and the global sampling factor is determined by combining the preset risk level and statistical confidence coefficient. The global sampling factor is used to correct the measured emission values ​​obtained by fixed sampling probes in conventional emission measurements, or to make equivalent adjustments to emission limits. The sampling factor matrix undergoes multi-level statistical processing, including: for the same engine, the same emission component, and the same number of sampling holes, calculating the standard deviation of individual sampling factors under different circumferential angles to obtain angular dispersion; for the same engine and the same emission component, treating the angular dispersion under each sampling hole number scheme as multiple independent estimates of the circumferential non-uniformity of the same engine and merging them to obtain the combined standard deviation of angles within the engine; for the same emission component, further merging the combined standard deviations of angles within the engine corresponding to all engines included in the analysis to obtain the combined dispersion of angles across engines; for each engine, arithmetically averaging all individual sampling factors in the sampling factor matrix to obtain the engine's average sampling factor, arithmetically averaging the average sampling factors of all engines to obtain the emission component's average sampling factor, and calculating the standard deviation of each engine's average sampling factor relative to the emission component's average sampling factor to obtain the dispersion of the average sampling factor between engines. The global sampling factor is determined by combining the preset risk level and the statistical confidence coefficient. This includes: using the average sampling factor of emission components as a benchmark, deducting the statistical uncertainty term composed of the combined dispersion from the cross-engine perspective and the dispersion of the average sampling factor between engines. The magnitude of the statistical uncertainty term is determined by the one-sided quantile and effective degrees of freedom of the t-distribution corresponding to the preset risk level.

2. The method according to claim 1, characterized in that, The transverse scan data includes the two-dimensional spatial coordinates of each measuring point on the exhaust cross section, the emission component concentration value or emission index value corresponding to each measuring point, and the area weight represented by each measuring point.

3. The method according to claim 1, characterized in that, An exhaust cross-section emission concentration distribution field was constructed based on transverse scan data, including: For each engine, each emission component, and each power state, spatial interpolation is performed on the measurement point data to obtain a continuous concentration distribution field covering the exhaust cross section.

4. The method according to claim 1, characterized in that, Construct the sampling factor matrix, including: Using the geometric center of the engine exhaust section as the rotation center, the overall structure of the fixed sampling probe is rotated around the geometric center in the exhaust section plane by multiple preset angles. For each rotation angle, the new coordinates of each sampling hole after rotation are substituted into the interpolation function of the emission concentration distribution field to obtain the emission value at the corresponding position. The equivalent sampling value at the corresponding angle is calculated, and the ratio of the equivalent sampling value at each angle to the true average emission value is used as a single sampling factor. All single sampling factors are arranged according to the circumferential angle and the number of sampling holes to construct a sampling factor matrix.

5. The method according to claim 1, characterized in that, Using a global sampling factor to correct measured emission values ​​obtained from fixed sampling probes in conventional emission measurements, or to make equivalent adjustments to emission limits, includes: The corrected emission value is obtained by dividing the measured emission value of the fixed sampling probe by the global sampling factor, or by multiplying the original emission limit by the global sampling factor to obtain the equivalent emission limit.

Images