A cascade test cascade rear non-uniform measuring point layout method based on model error driving

Abstract

The application discloses a model error driving-based non-uniform test point layout method behind a cascade, and belongs to the technical field of turbomachinery testing. The method removes test points with the least contribution to the model error of performance parameters through iteration, and realizes non-uniform layout with minimized error under the constraint of the number of test points. The core steps include: analysis of the distribution characteristics of the flow field parameters behind the cascade, non-uniform construction of initial dense test points, left and right partitioned alternating iteration optimization, and test point screening based on error constraint. The method takes the calculation error of performance parameters as a direct optimization target, does not depend on the density distribution rule of test points preset by people, forms the test point distribution with encrypted wake zone and sparse main flow zone through a data driving mode, and is suitable for test point layout of the flow field behind a planar cascade and a ring cascade.

Description

Technical Field

[0001] This invention relates to testing methods for turbomachinery, specifically to a method for arranging probe measuring points behind the blade cascade in a test. Background Technology

[0002] Blade cascade testing is a key method for obtaining the aerodynamic performance of turbomachinery. The accurate measurement of flow field parameters behind the cascade (such as total pressure, static pressure, and airflow angle) directly affects the calculation accuracy of core performance parameters such as airfoil loss coefficient and energy loss coefficient.

[0003] In traditional blade cascade tests, the layout of measurement points behind the cascade often adopts a uniform distribution strategy, with points spaced at equal intervals along the cascade direction, such as 10%~15% of the cascade pitch. This method suffers from the following technical bottlenecks:

[0004] (1) Unstable model error: When the number of measurement points is small, the uniform layout cannot adapt to the difference between the high gradient in the wake region and the gentle gradient in the mainstream region, resulting in a significant error in the calculation of performance parameters (>2%) in some working conditions.

[0005] (2) The non-uniform layout lacks quantitative basis: Although it is known that the wake region needs to be densified, the densification location and degree depend on experience, and it cannot be guaranteed that the performance parameter calculation error meets the requirements.

[0006] (3) Lack of objective criteria for screening measurement points: When reducing the number of measurement points under the constraint of experimental cost, there is a lack of quantitative methods to judge "which measurement points can be eliminated and which must be retained", which can easily lead to the loss of key information.

[0007] In existing technologies, although some studies have employed non-uniform point distribution based on flow field gradients, these methods only optimize the flow field characteristic resolution and do not establish a direct correlation with the calculation error of the cascade performance parameters. Other techniques refine the location of shock waves, but these techniques presuppose that the shock wave is a key physical feature, thus limiting their applicability. Summary of the Invention

[0008] Purpose of the invention: To address the high-precision measurement requirements under limited measurement point conditions in blade cascade performance testing, this invention proposes a model error-driven method for the layout of measurement points behind the cascade, which minimizes the error under a limited number of measurement points through iterative optimization.

[0009] Technical solution: A method for laying out measurement points behind the cascade in a blade cascade test based on model error-driven approach, comprising the following steps:

[0010] Step 1: Analysis of the distribution characteristics of flow field parameters behind the gate

[0011] The flow field parameters of the cascade are obtained through CFD numerical simulation or experimental measurement. At the target measurement section behind the cascade (e.g., 0.4 to 1.0 times the chord length), the total pressure and static pressure distribution curves in the cascade direction within a cascade pitch range are extracted and normalized to 0% to 100% according to the cascade pitch percentage. The curve has the following characteristics:

[0012] 1. The centerline of the wake is approximately located in the middle of the curve, determined by the position of the minimum total pressure within one grid pitch range after passing through the grid;

[0013] 2. The wake region is determined by the total pressure loss amplitude exceeding a preset threshold (e.g., 5%~10%);

[0014] 3. The remaining area is the mainstream area.

[0015] Step 2: Non-uniform construction of the initial dense measurement point set

[0016] Using the centerline of the wake as the boundary, the area one grid pitch behind the grid is divided into the left region Ω. L and the right region Ω R Let the grid widths of the left and right regions be W respectively. L W R The initial number of measuring points N in the left and right regions is allocated according to the width ratio. L N R :

[0017] N L =round[N total ×W L / (W L +W R )] ;

[0018] N R =N total -N L ;

[0019] Where N total The initial total number of measurement points is set to 50-200, with 100 being preferred; round is the rounding operation.

[0020] The measuring points are uniformly distributed in the left and right regions, forming an initial non-uniform measuring point set S0=S 0L ∪S 0R S 0L S 0R These are the initial measurement point sets for the left and right regions, respectively.

[0021] Calculate the baseline value Y0 of the performance parameter under this initial non-uniform measurement point set. The performance parameter is the total pressure loss coefficient. or energy loss coefficient .

[0022] Step 3: Iterative optimization based on minimizing model error

[0023] Perform single-point elimination operations on the left and right measurement point sets in sequence, that is, eliminate individual measurement points in the current side measurement point set one by one, and combine them with the measurement point set on the other side to form a candidate subset. Calculate the performance parameter values ​​of each candidate subset and their errors with the benchmark values, and retain the subset with the smallest error.

[0024] The mathematical expression for iterative optimization is:

[0025] Let S be the set of measurement points in the current k-th iteration. k =S kL ∪S kR S kL S kR These are the left and right measurement point sets for the k-th iteration, respectively, with N measurement points each. kL N kR .

[0026] 3.1 Left Region Removal Operation

[0027] In the left measurement point set S kL In the process, the i-th measurement point is removed one by one, i=1,2,...,N kL This generates the set S after removing measurement point i. kL (i), S kL (i) Combine with the set of right measurement points to form a candidate subset S k (i)=S kL (i)∪S kR .

[0028] Calculate candidate subset S k (i) Performance parameter value Y k (i) When the performance parameter value Y k (i) Selecting the total pressure loss coefficient When, the calculation formula is:

[0029]

[0030] In the formula This is the total pressure loss coefficient. These are the average total pressure at the inlet of the blade cascade, the average total pressure at the outlet, and the average static pressure at the outlet. The average parameters can be calculated using either linear weighted averaging or flow rate weighted averaging.

[0031] When the performance parameter value Y k (i) Selecting the energy loss coefficient When, the calculation formula is:

[0032]

[0033] In the formula The energy loss coefficient, Specific heat ratio.

[0034] Calculate the performance parameter value Y k (i) The error Δk(i) from the reference value Y0 is |Y k (i)-Y0| / Y0×100%, select the set S that minimizes Δk(i). kL (i*), the corresponding deleted measurement point number i*=argmin(Δk(i)).

[0035] Delete the measurement point with index i* and update it to the current left measurement point set.

[0036] 3.2 Right Region Removal Operation

[0037] Perform the same operation in the right region: in S kR In the process, the j-th measurement point is removed one by one, where j=1,2,...,N kR Generate candidate subset S kR (j) is combined with the updated set of left measurement points to form a candidate subset S. k (j)=S kR (j)∪S kL (i*).

[0038] Calculate candidate subset S k (j) performance parameter value Y k (j), and then calculate the performance parameter value Y. k (j) The model error Δk(j) between the reference value Y0 and the standard value Y0 is |Y k (j)-Y0| / Y0×100%, select the set S that minimizes Δk(j). kR (j*), the corresponding deleted measurement point number j*=argmin(Δk(j)).

[0039] Delete the measurement point with index j* and update it to the current right measurement point set.

[0040] 3.3 Alternating Iteration

[0041] The removal operation is performed alternately in the left and right regions.

[0042] Repeat the iteration until the convergence condition of step 4 is met.

[0043] Step 4: Measurement point selection based on constraint determination

[0044] Convergence criteria include one or a combination of the following:

[0045] (a) Target measurement point number constraint: Current number of measurement points N k To reach the preset target value N target ; where the current number of measurement points N kThis is the sum of the number of measurement points in the left and right measurement point sets of the current iteration.

[0046] (b) Error threshold constraint: The performance parameter error in the single-point elimination operation on the current side is less than or equal to the preset threshold ε. max Furthermore, the performance parameter error obtained from the subsequent single-point elimination operation on the other side is greater than the preset threshold ε. max Among them, the preset threshold ε is used when the performance parameters are the total pressure loss coefficient and the energy loss coefficient, respectively. max Take 1% for each.

[0047] Preferably, a combination constraint is used: first set N target If the iteration reaches the current number of measurement points N k Below N target And the performance parameter error in the current single-point removal operation is greater than ε. max Then relax N target The value or tightening of ε max After determining the value, iterate again.

[0048] Step 5: Determine the optimal distribution scheme of measuring points

[0049] Output the set of measurement points S that satisfy the convergence condition. opt Its distribution scheme, including the grid-direction position coordinates of each measuring point.

[0050] Beneficial effects: Existing technologies that densify measurement points based on shock wave location or flow field gradient presuppose specific physical features as key areas, identifying feature locations and strategically placing measurement points. The fundamental difference between this method and such existing technologies lies in:

[0051] 1. This method does not pre-set the density distribution rule of "the wake region must be dense and the main region must be sparse", that is, it does not rely on the human-preset density distribution rule of measurement points;

[0052] 2. This method determines the contribution of measurement points to performance parameter errors solely through model error calculation, discarding points with low contribution and retaining points with high contribution, thus representing a purely data-driven optimization.

[0053] 3. This method uses performance parameter error as the sole optimization objective, and the quantitative basis for non-uniform layout is clear;

[0054] 4. This method uses error minimization to filter, so that the distribution of measurement points after iterative optimization naturally shows a dense wake region and a sparse mainstream region. This structure is not artificially set.

[0055] Therefore, this invention is applicable to any flow field with parameter gradient differences, and has wider applicability. Compared with the prior art, this invention has the following advantages:

[0056] 1. Through iterative optimization, the performance parameter error is minimized under the constraint of a limited number of measurement points. With 10 to 14 measurement points, the error can be controlled within a reasonable range, and the model error is controllable.

[0057] 2. Compared with a uniform layout of the same number of measuring points, the optimized layout results in a more concentrated error distribution under various working conditions, avoiding situations where the error is significantly larger in individual working conditions, and significantly reducing error fluctuation.

[0058] 3. The contribution of each measuring point to the performance parameter error can be quantitatively calculated, and the selection of measuring points is based on objective evidence, avoiding the subjectivity of human experience judgment. Attached Figure Description

[0059] Figures 1-7 The following diagram illustrates the iterative optimization process of the non-uniform point distribution method in the example. It sequentially shows the true value calculated with 10 points, the result of deleting 1 point and leaving 9 points, the result of deleting 1 more point after optimization and leaving 8 points, the result of deleting 1 more point after optimization and leaving 7 points, the result of deleting 1 more point after optimization and leaving 6 points, the result of deleting 1 more point after optimization and leaving 5 points, and the result of deleting 1 more point after optimization and leaving 4 points.

[0060] Figure 8 A statistical chart showing the minimum number of measuring points required for different error requirements under various test conditions;

[0061] Figure 9 This is a schematic diagram of the optimized distribution of typical measuring points;

[0062] Figure 10 This is a flowchart of the iterative optimization algorithm. Detailed Implementation

[0063] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0064] The specific implementation process of this invention will be described in detail below. For example... Figure 10As shown, this embodiment uses the cross-section at 0.6 times the chord length behind a certain blade as the measurement target, and targets multiple operating conditions: angle of attack -10° to 10°, Mach number 0.4 to 1.2, Reynolds number 1×10⁻⁶. 4 ~3×10 5 To meet the flow field parameter measurement requirements, this paper demonstrates a measurement point layout method based on non-uniform distribution and uncertainty optimization. The example below uses the I0M12R30 engine under the following conditions: angle of attack 0°, Mach number 1.2, Reynolds number 3 × 10⁻⁶. 5 .

[0065] I. Analysis of the distribution characteristics of flow field parameters behind the gate

[0066] Numerical calculations were performed using CFD methods to obtain the spatial distribution data of total pressure and static pressure in the flow field behind the grid. A total pressure distribution curve within a grid pitch was obtained. This curve is characterized by: the wake centerline being approximately located in the middle of the curve, and its position determined by the minimum total pressure value; the wake region's extent being determined by a total pressure deficit amplitude > 8%, calculated using the following formula: ,in Total import pressure, The measurement point represents the total pressure; the rest represent the mainstream pressure area.

[0067] II. Iterative Optimization Layout of Non-Uniform Measurement Points

[0068] 1. Characteristic zoning of the flow field behind the gate

[0069] The flow field measurement points behind the grid are divided into two regions, left and right, by the wake centerline. Each region contains a semi-wake region and a semi-mainstream region. In this embodiment, the wake centerline is located at 52% of the grid pitch.

[0070] 2. Construction of the initial high-density measurement point set

[0071] Set the initial total number of measurement points N total = 100, width ratio W L :W R = 52:48.

[0072] N L =round[100 * 0.52] = 52;

[0073] N R = 48;

[0074] The 52 measuring points in the left region are evenly distributed between 0% and 52% of the grid pitch (inclusive), while the 48 measuring points in the right region are evenly distributed between 52% and 100% of the grid pitch (exclusive).

[0075] Calculate the baseline value: Use a line weighted average to obtain the baseline value ω0 of the total pressure loss coefficient.

[0076] 3. Iteratively eliminate low-contribution measurement points

[0077] The measurement points in the left and right partitions are iteratively eliminated in turn until the model error requirements of the performance parameters are met.

[0078] Iterative elimination: Perform single-point elimination operations on the left and right measurement point sets sequentially, that is, eliminate individual measurement points in the current set one by one, merge with the other set to form a candidate subset, and calculate the model value Y of each candidate subset. k (i) and model error Δk(i) = |Y k (i)-Y0| / Y0×100%. Select the measurement point that minimizes Δk(i) and remove it, keeping the remaining measurement points to enter the next round.

[0079] Figures 1 to 7 The iterative optimization process is shown using 10 initial measurement points as an example. The actual calculation is based on an initial set of 100 points; this is just an illustration of the method.

[0080] III. Measurement Point Selection Based on Constraint Decision

[0081] Set the relative error threshold ε for the total pressure loss coefficient max = 1%, minimum number of measurement points greater than 10.

[0082] During the iterative optimization process, the number of measurement points gradually decreases, while the model error gradually increases. When the number of measurement points drops to a certain value, the model error approaches or exceeds the threshold, or the number of measurement points equals the minimum number of measurement points. This number of measurement points is the minimum number of measurement points that satisfies the constraints.

[0083] Figure 8 The statistical results of the number of measuring points under different error requirements are presented. It can be seen that, with the goal of the relative error of the total pressure loss coefficient being less than 1%, more than 10 measuring points are required for the test conditions.

[0084] IV. Optimal Measurement Point Distribution Scheme

[0085] Taking 12 measuring points as an example, the optimized typical distribution is as follows:

[0086] Left region, points 6-7: mainly distributed near the center line of the wake and the boundary of the main flow area;

[0087] Right region, points 5-6: The wake region is denser, while the mainstream region is sparser;

[0088] The distribution of measurement points naturally forms a non-uniform characteristic with dense wake regions and sparse mainstream regions. However, this characteristic is not pre-set by humans, but is the result of iterative minimization of model error.

[0089] Figure 9 The diagram shows the optimized distribution of typical measuring points. It can be seen that the spacing between measuring points in the wake region is significantly smaller than that in the mainstream region.

[0090] 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 method for arranging measurement points behind a cascade in a test based on model error-driven methods, characterized in that, include: S1: Obtain the aerodynamic parameter distribution within one grid pitch of the target measurement section behind the grid, and identify the wake centerline, wake region and main stream region; wherein, the wake centerline is located within ±5% of the midpoint of the grid pitch; S2: Divide the grid direction into left and right regions with the center line of the wake as the boundary, allocate the number of measurement points according to the width ratio of the left and right regions, construct an initial measurement point set, and calculate the benchmark values ​​of performance parameters under this measurement point set; S3: Perform single-point elimination operation on the left and right measurement point sets in sequence, that is, eliminate individual measurement points in the current measurement point set one by one, and combine them with the measurement point set on the other side to form a candidate subset. Calculate the error between the performance parameter value of the candidate subset and the benchmark value, and retain the subset with the smallest error as the updated measurement point set. Iterate alternately in this process. S4: Determine whether the performance parameter error in the current iteration meets the preset threshold, or whether the number of measurement points in the current measurement point set is lower than the preset target value N. target ; S5.: Output the set of measurement points that satisfy the constraint criteria and their distribution scheme.

2. The method according to claim 1, characterized in that, In step S1, the center line of the wake is determined by the position of the minimum total pressure within one grid pitch range after the grid.

3. The method according to claim 1, characterized in that, The performance parameters include the total pressure loss coefficient or the energy loss coefficient.

4. The method according to claim 1, characterized in that, In step S3, the mathematical expression of the alternating iteration is: Let S be the set of measurement points in the current k-th iteration. k =S kL ∪S kR S kL S kR These are the left and right measurement point sets, respectively; For the set of left test points, the set S after removing test point i will be... kL (i) Combine with the set of right messenger points to form a candidate subset S k (i)=S kL (i)∪S kR ; Calculate candidate subset S k (i) Performance parameter value Y k (i), Y k (i) The error between the reference value Y0 and the standard value Y0 is: Δk(i) = |Y0|0. k (i)-Y0| / Y0×100%; Select the set S that minimizes Δk(i) kL (i*) is updated to the current left set of points; Perform the same single-point elimination operation on the right measurement point set, and then perform the same operation on the left and right measurement point sets alternately until the convergence condition is met.

5. The method according to claim 4, characterized in that, When the performance parameter is selected as the total pressure loss coefficient When, the calculation method is as follows: When the performance parameter is selected as energy loss coefficient When, the calculation method is as follows: In the formula These are the average total pressure at the inlet of the blade cascade, the average total pressure at the outlet, the average static pressure at the outlet, and the specific heat ratio.

6. The method according to claim 1, characterized in that, In step S4, it is determined whether the performance parameter error in the current iteration meets the preset threshold. Specifically, the performance parameter error in the single-point elimination operation on the current side is less than or equal to the preset threshold ε. max Furthermore, the performance parameter error obtained from the subsequent single-point elimination operation on the other side is greater than the preset threshold ε. max .

7. The method according to claim 6, characterized in that, If the iteration reaches the current number of measurement points N k Below N target And the performance parameter error in the current single-point removal operation is greater than ε. max Then relax N target The value or tightening of ε max The value is then iterated again; where the current number of measurement points N is N. k This is the sum of the number of measurement points in the left and right measurement point sets of the current iteration.

8. The method according to claim 6, characterized in that, In step S5, the distribution scheme includes the grid-direction position coordinates of each measuring point.

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