Impeller-machinery grid-type hybrid plane simulation method based on flux-conservation interpolation

Abstract

This application provides a grid-based hybrid plane simulation method for turbomachinery based on flux conservation interpolation, relating to the field of computational fluid dynamics. The method includes: performing circumferential averaging on the circumferentially non-uniform flow field at the rotor-stationary interface, simplifying the original grid into radial grid nodes and edges; constructing a secondary grid by taking the midpoints of the edges and determining the length of the secondary grid corresponding to each node; projecting the upstream blade row nodes onto the downstream region and calculating the overlap length of the secondary grids on both sides; determining the interpolation coefficients based on the ratio of the overlap length to the upstream secondary grid length, thereby achieving the conservation and transfer of flow field variables. This application strictly satisfies flux conservation, avoids the accumulation of errors in multi-level simulations, and provides better radial smoothness of the interpolation function. It can more accurately capture local flow field features in sparse grids and regions with strong curvature variations, improving numerical stability, convergence speed, and simulation accuracy.

Description

Technical Field

[0001] This application relates to the field of computational fluid dynamics, and in particular to a grid-type hybrid plane simulation method for turbomachinery based on flux conservation interpolation. Background Technology

[0002] Turbomachinery (such as compressors, turbines, and fans) is widely used in energy and power fields such as aero-engines and gas turbines. Hybrid plane simulation is a steady approximation method used to simulate the dynamic-static interference effect between the rotor and stator of turbomachinery. This method averages the circumferential non-uniform flow at the rotor outlet and stator inlet to obtain steady-averaged parameters distributed only radially. However, the mesh nodes at the upstream and downstream blade interface have their own independent radial coordinate distributions, which usually cannot be matched one-to-one. Therefore, interpolation methods are needed to transfer the flow field parameters at the interface. Existing linear interpolation methods cannot guarantee the strict conservation of total flux required by the hybrid plane, resulting in deviations in interstage flux and accumulation of errors in multi-stage environments. Furthermore, the smoothness of the interpolation function is insufficient, leading to limited accuracy in the end region and near the shock wave.

[0003] Therefore, how to achieve the conservation interpolation calculation of flow field variables in grid-type hybrid plane simulation of turbomachinery is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] The purpose of this application is to provide a grid-type hybrid planar simulation method for turbomachinery based on flux conservation interpolation, which can achieve complete conservation interpolation transfer of flow field variables under the strict requirement of flux conservation, thereby realizing planar simulation.

[0005] To address the aforementioned technical problems, this application provides a grid-type hybrid planar simulation method for turbomachinery based on flux conservation interpolation. The specific technical solution is as follows: A circumferential average is performed on the circumferential non-uniform flow at the interface between the upstream and downstream blade rows of the turbomachinery, simplifying the original mesh at the interface into a set of radially arranged mesh nodes and edges connecting adjacent mesh nodes; the interface is the interface between the rotor and the stator. For the original grid-type grid, take the midpoint of each edge, use each midpoint as the boundary of the secondary grid node, construct a set of secondary grids, and determine the secondary grid length corresponding to each grid node; Project each of the grid nodes of the upstream leaf row onto the grid area of ​​the downstream leaf row, and determine the overlap length between the first and second secondary grids of each grid node of the upstream leaf row and the second secondary grids of each grid node of the downstream leaf row. Based on the ratio of the overlap length to the secondary grid length corresponding to the grid node of the upstream leaf row, the interpolation coefficient of the grid node of the downstream leaf row relative to the grid node of the upstream leaf row is determined. Based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the upstream blade row are allocated to the grid nodes of the downstream blade row to achieve hybrid plane simulation of the turbomachinery.

[0006] Optionally, a set of secondary grids is constructed using each of the aforementioned midpoints as the boundary of the secondary grid nodes, including: Obtain the geometric midpoint of the edge between each adjacent grid node in the original grid; For each grid node at a non-boundary location, the midpoint of the preceding adjacent edge of the grid node is used as the starting boundary, and the midpoint of the following adjacent edge of the grid node is used as the ending boundary to determine the secondary grid corresponding to the grid node. For each of the grid nodes located at the radial end boundary, the secondary grid corresponding to the grid node is determined by taking the radial end boundary as one side boundary and the midpoint of the edge adjacent to the radial end boundary as the other side boundary.

[0007] Optionally, projecting each grid node of the upstream leaf row onto the grid region of the downstream leaf row, and determining the overlap length between the first and second secondary grids of each grid node of the upstream leaf row and the second and second secondary grids of each grid node of the downstream leaf row, includes: Using the downstream leaf row as the interpolation target side and the upstream leaf row as the interpolation source side, the first and second grids of each grid node of the upstream leaf row are radially projected onto the grid region of the downstream leaf row. Determine the radial overlap interval between the first and second secondary grids of each grid node in the upstream leaf row and the second and second secondary grids of each grid node in the downstream leaf row; Based on the length of the radial overlap interval, the overlap length between each grid node of the upstream leaf row and each grid node of the downstream leaf row is determined.

[0008] Optionally, based on the ratio of the overlap length to the quadratic grid length corresponding to the grid node of the upstream leaf row, the interpolation coefficients of the grid node of the downstream leaf row relative to the grid node of the upstream leaf row are determined, including: For the j-th grid node of the downstream leaf row, obtain the overlap lengths between the second and second quadratic grids of the j-th grid node of the downstream leaf row and the first and second quadratic grids of each grid node of the upstream leaf row; Divide each of the overlapping lengths by the first and second grid lengths of the corresponding upstream leaf row grid nodes to obtain the interpolation coefficients of the j-th grid node of the downstream leaf row relative to each grid node of the upstream leaf row.

[0009] Optional, also includes: Using the upstream leaf row as the interpolation target side and the downstream leaf row as the interpolation source side, the second and second grids of each grid node of the downstream leaf row are radially projected onto the grid region of the upstream leaf row. Determine the overlap lengths between the second and second-order grids of each grid node in the downstream leaf row and the first and second-order grids of each grid node in the upstream leaf row; Based on the ratio of each of the overlapping lengths to the second and second grid lengths corresponding to the grid nodes of the downstream leaf row, the interpolation coefficients of the grid nodes of the upstream leaf row relative to the grid nodes of the downstream leaf row are determined. Based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the downstream blade row are allocated to the grid nodes of the upstream blade row.

[0010] Optionally, the flow field variables include at least one of mass flow rate, momentum flux, and energy flux. Before allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row, the method further includes: Using the flow field variable values ​​at the grid nodes of the upstream blade row as the source values, and based on the interpolation coefficients, the values ​​of the flow field variables at each grid node of the downstream blade row are calculated by weighted summation.

[0011] Optionally, after determining the interpolation coefficients of the grid nodes of the downstream leaf row relative to the grid nodes of the upstream leaf row, the method further includes: Store the interpolation coefficients; In subsequent iterations, the interpolation coefficients are called to distribute the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row.

[0012] Optionally, based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the upstream blade row are allocated to the grid nodes of the downstream blade row, including: Using the mass flow rate, momentum flux, and energy flux values ​​at the grid nodes of the upstream leaf row as source values, and based on the interpolation coefficients, the mass flow rate, momentum flux, and energy flux values ​​at each grid node of the downstream leaf row are calculated by weighted summation.

[0013] Optionally, after allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row based on the interpolation coefficients, the method further includes: Based on the flow field variable values ​​assigned to the grid nodes of the downstream blade row, the interface boundary conditions of the downstream blade row are updated, and the flow field of the turbomachinery is iteratively solved based on the updated interface boundary conditions until the convergence criterion is met.

[0014] Optionally, after allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row based on the interpolation coefficients, the method further includes: The total flux on the source side is obtained by summing the product of the secondary grid length corresponding to each grid node of the upstream blade row and the flow field variable value at the grid node. The total flux on the target side is obtained by summing the product of the secondary grid length corresponding to each grid node of the downstream blade row and the flow field variable value already allocated at the grid node; wherein, the total flux on the source side is equal to the total flux on the target side.

[0015] This application achieves complete conservation interpolation transfer of flow field variables in gridded hybrid plane simulations. Compared with existing linear interpolation methods, it can strictly satisfy the requirement of flux conservation. The total flux of the upstream impeller can be completely and losslessly transferred to the downstream impeller through the interpolation process, without generating cumulative errors in the stage-by-stage simulation calculations of multi-stage turbomachinery. The interpolation function has better smoothness and physical rationality in radial distribution, avoiding the spurious gradient discontinuity problem introduced by the interpolation method itself, which is beneficial to improving the stability and convergence speed of numerical solutions. Especially in regions with sparse radial grid distribution and regions with strong curvature changes in flow field parameters, such as within the boundary layer of the hub and casing end region or near the shock wave train, the conservation interpolation method implemented in this application can more accurately capture the local variation characteristics of the flow field, improving the reliability and numerical accuracy of the simulation results. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 A flowchart of a grid-type hybrid plane simulation method for turbomachinery based on flux conservation interpolation provided in this application embodiment; Figure 2 A schematic diagram of a grid distributed only radially after circumferential averaging of the upstream and downstream interfaces provided in an embodiment of this application; Figure 3 This is a schematic diagram of the secondary mesh length construction provided in an embodiment of this application; Figure 4 This is a schematic diagram of the stage35 model provided in the embodiments of this application; Figure 5 This is a schematic diagram of the stage35 model mesh provided in the embodiments of this application; Figure 6 This is a schematic diagram of the stage35 to static interface provided in an embodiment of this application; Figure 7 This is a schematic diagram of the stage35 to static interface mesh provided in an embodiment of this application; Figure 8 The diagram shows the inlet and outlet flow rates of stage 35 and the inlet and outlet flow rates of the static interface provided in this application embodiment. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] This embodiment provides a grid-based hybrid plane simulation method for turbomachinery based on flux conservation interpolation, applied to the transfer of flow field parameters at the interface between the rotor and stator in grid-based hybrid plane simulation of turbomachinery. This embodiment ensures strict conservation of mass flow rate, momentum flux, and energy flux at the interface by constructing a secondary grid and determining the interpolation coefficients based on the spatial overlap ratio between the secondary grids. Unlike traditional linear methods based on geometric position interpolation, the core idea of ​​this application is to allocate flux using the ratio of the radial interval lengths represented by each grid node, thus ensuring the flux remains constant before and after interpolation in principle. See also... Figure 1 , Figure 1 A flowchart of a grid-type hybrid plane simulation method for turbomachinery based on flux conservation interpolation provided in this application embodiment is included, comprising the following steps: S101: Perform circumferential averaging on the circumferential non-uniform flow at the interface between the upstream and downstream blade rows of the turbomachinery, simplifying the original mesh at the interface into a set of radially arranged mesh nodes and edges connecting adjacent mesh nodes; the interface is the interface between the rotor and the stator. S102: For the original grid-type grid, take the midpoint of each edge, use each midpoint as the boundary of the secondary grid node, construct a set of secondary grids, and determine the secondary grid length corresponding to each grid node. S103: Project each of the grid nodes of the upstream leaf row onto the grid area of ​​the downstream leaf row, and determine the overlap length between the first and second secondary grids of each grid node of the upstream leaf row and the second secondary grids of each grid node of the downstream leaf row. S104: Based on the ratio of the overlap length to the secondary grid length corresponding to the grid node of the upstream leaf row, determine the interpolation coefficient of the grid node of the downstream leaf row relative to the grid node of the upstream leaf row. S105: Based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the upstream blade row are allocated to the grid nodes of the downstream blade row.

[0020] When performing hybrid plane simulations, the circumferential non-uniform flow at the rotor outlet and stator inlet first needs to be circumferentially averaged. In computational fluid dynamics simulations, the interference between the rotor blade wake and the stator blades is essentially an unsteady phenomenon, resulting in a significant non-uniform distribution of flow parameters along the circumferential direction. Circumferential averaging can neutralize this non-uniformity, reducing the flow parameters from a three-dimensional state with a non-uniform distribution in the circumferential direction to a steady state with parameters distributed only in the radial direction. After circumferential averaging, the original mesh at the upstream and downstream blade junctions can be simplified to a set of radially arranged mesh nodes and line segments connecting adjacent mesh nodes.

[0021] For lattice-centered grid nodes, each node naturally corresponds to the length of a grid cell; that is, the radial interval represented by two adjacent nodes is clearly and directly defined. However, for grid-point nodes, since the nodes are located at the vertices of the grid rather than the centers of the grid cells, each node does not naturally possess a corresponding grid cell area or length attribute. Therefore, a secondary grid needs to be constructed in subsequent steps to assign the spatial interval length represented by each grid-point node. Through circumferential averaging, the originally complex unsteady flow problem in three-dimensional space can be transformed into a radially steady one-dimensional problem. This fundamentally reduces the computational complexity of data transfer at the interface and provides a feasible one-dimensional grid basis for subsequent conservation interpolation calculations.

[0022] Based on the obtained radially distributed grid-type original mesh, the geometric midpoints of each original mesh edge need to be obtained first. For each line segment formed by connecting two adjacent mesh nodes, the midpoint of the line segment is taken as the geometric midpoint. Then, using these geometric midpoints as the boundary between each secondary mesh node, a set of secondary meshes continuously covering the entire interface region in the radial direction is constructed, such as... Figure 2 As shown, Figure 2 This is a schematic diagram of a grid distributed radially only after circumferential averaging of the upstream and downstream interfaces provided in an embodiment of this application.

[0023] In one feasible implementation, for each mesh node located at a non-boundary position, the geometric midpoint of the preceding adjacent edge of the mesh node is used as the starting boundary, and the geometric midpoint of the following adjacent edge of the mesh node is used as the ending boundary. The secondary mesh corresponding to the mesh node is determined by the interval between the starting and ending boundaries. For each mesh node located at the radial end boundary, such as a mesh node near the hub side or casing side end, since there is no adjacent mesh edge on one side, the radial end boundary itself is used as the boundary on one side, and the geometric midpoint of the edge adjacent to the radial end boundary is used as the boundary on the other side, thereby determining the secondary mesh interval corresponding to the end mesh node. After the secondary mesh interval is defined, for non-boundary nodes, the mesh length can be calculated from the coordinate interval from the midpoint of the preceding adjacent edge to the midpoint of the following adjacent edge; for end nodes, the mesh length is calculated from the coordinate interval from the radial end boundary coordinates to the midpoint of the adjacent edge. See also Figure 3 , Figure 3 This is a schematic diagram of the secondary mesh length construction provided in an embodiment of this application.

[0024] The aforementioned quadratic mesh construction method assigns a defined spatial occupancy range to each node in the gridded mesh, providing a precise geometric metric for determining the interpolation coefficients in the subsequent conservation interpolation process. Furthermore, since all quadratic meshes are connected end-to-end in the radial direction and do not overlap, they collectively and completely cover the entire radial region of the interface, ensuring that there are no gaps or overlapping coverage issues in the subsequent conservation interpolation process, thus providing a fundamental guarantee for the accuracy of conservation interpolation.

[0025] After constructing the secondary mesh, the mesh nodes and their corresponding secondary meshes of one blade row need to be projected onto the mesh region of the other blade row. In grid-based hybrid plane simulations, the radial coordinate distribution of the mesh nodes of the upstream and downstream blade rows is usually different, and the number of mesh nodes in each blade row may also differ. This mesh mismatch is one of the core problems that needs to be solved in hybrid plane simulations, namely, how to accurately transfer the values ​​of flow field variables between two blade rows with different radial mesh distributions. To solve this problem, this embodiment establishes the spatial correspondence between the mesh nodes on both sides by performing a radial projection operation across the blade rows.

[0026] In one feasible implementation, the downstream leaf row is used as the interpolation target side, and the upstream leaf row is used as the interpolation source side. The first and second quadratic grids of each grid node in the upstream leaf row are projected radially into the grid region of the downstream leaf row. The essence of the projection operation is to map the starting and ending boundary coordinates of each second quadratic grid in the upstream leaf row to the radial coordinate system of the downstream leaf row, thus repositioning the spatial positions of each upstream second quadratic grid within the coordinate frame of the downstream leaf row. After projection, each first and second quadratic grid in the upstream leaf row will have a radially overlapping region with one or more second quadratic grids in the grid region of the downstream leaf row. This one-to-many overlap relationship reflects the grid mismatch; an upstream grid node may have radial intersection with one or more downstream grid nodes.

[0027] For each pair of upstream and downstream leaf row grid node combinations that overlap radially, the radial overlap interval is determined, which is the common coverage interval of the two quadratic grids corresponding to the pair of grid nodes in the radial coordinate. Then, based on the length of this radial overlap interval, the overlap length between the upstream and downstream leaf row grid nodes is determined. Through the radial projection and overlap length calculation methods described above, the spatial coverage relationship between each upstream and downstream grid node can be quantitatively described, providing a reliable data foundation for the accurate calculation of subsequent interpolation coefficients. The overlap length is the intersection length of the upstream and downstream grid nodes in the radial interval, used to determine the flux allocation ratio.

[0028] After obtaining the overlap lengths between the first and second secondary grids of each grid node in the upstream leaf row and the second secondary grids of each grid node in the downstream leaf row, the interpolation coefficients can be finally determined based on the ratio of each overlap length to the secondary grid length corresponding to the source-side grid node.

[0029] Assume the upstream grid flow parameters are distributed radially as follows: The downstream grid flow parameters are distributed radially as follows: Where r is the radial coordinate variable. Upstream Taking a point as an example, The length of the quadratic grid is Projected downstream, corresponding to n points, respectively , … Points, respectively, correspond to the secondary grid length of the downstream points. , … The interpolation coefficients corresponding to the downstream points are respectively: , … Interpolation value As shown in the following formula, for point k, interpolation is performed on the downstream based on the upstream, and vice versa.

[0030] ; ; ; Assume the total number of upstream grid nodes is M, the total number of downstream grid nodes is N, the total radial length is L, and the secondary grid length corresponding to each point is... Corresponding to n downstream points, that is , … Point, where n is the total number of downstream grid nodes that intersect with a single upstream grid i, and represents the secondary grid length of each downstream point. , … The first formula represents single-point interpolation, i.e., linear interpolation weighted by grid length. The second formula represents discrete flux conservation: the sum of the grid lengths multiplied by the interpolation coefficients of all M upstream points equals the sum of the grid lengths multiplied by the interpolation coefficients of all N downstream points, meaning the total flux remains unchanged in a discrete sense before and after interpolation. The third formula shows that the integral of the interpolated distribution function over the entire radial length is equal to that of the downstream distribution function, i.e., flux conservation in a continuous sense. Therefore, interpolation using this method naturally satisfies the flux conservation requirement.

[0031] In one feasible implementation, for the j-th grid node of the downstream leaf row, the overlap lengths between the second and second quadratic grids of the j-th grid node of the downstream leaf row and the first and second quadratic grids of each grid node of the upstream leaf row are first obtained. For a downstream leaf row grid node, it may radially overlap with one or more grid nodes in the upstream leaf row; therefore, it is necessary to collect the overlap length information between the downstream node and all upstream nodes. Then, each obtained overlap length is divided by the first and second quadratic grid length of the corresponding grid node in the upstream leaf row, thereby obtaining the interpolation coefficients of the j-th grid node of the downstream leaf row relative to each grid node of the upstream leaf row.

[0032] The method for determining the interpolation coefficients possesses a crucial conservation property: for any grid node in the upstream blade row, its first and second grid lengths are divided into several segments, which are then distributed to the grid nodes of each downstream blade row that overlap with it. The distribution ratio is the interpolation coefficient for each segment. Therefore, the sum of the interpolation coefficients of all grid nodes in the downstream blade row relative to the upstream grid node equals 1. This ensures that the total flux remains strictly constant during the interpolation process from the upstream blade row to the downstream blade row, as the flow field variables are transferred through interpolation. Unlike traditional linear interpolation methods that determine interpolation weights based solely on the proportional relationship of geometric positions without considering flux conservation, this embodiment, based on the proportional allocation mechanism of the overlapping length of the second grid, ensures complete conservation of the interpolation process in principle.

[0033] After determining the interpolation coefficients, the flow field variable values ​​at each grid node of the upstream blade row are used as the source values. The flow field variable values ​​at each grid node of the upstream blade row are then transferred to each grid node of the downstream blade row through calculation according to the determined distribution ratio.

[0034] In one feasible implementation, flow field variables can include at least one of the following variable types: mass flow rate, momentum flux, and energy flux. In engineering applications involving hybrid planar simulation, mass flow rate reflects the amount of working fluid mass transported through the interface, momentum flux reflects the transport of fluid momentum and the effect of forces, and energy flux reflects the energy transfer process between stages. These flux-type variables are core physical quantities for evaluating the fluid exchange characteristics between stages, and it is necessary to ensure that their total amount at the interface is strictly conserved before and after interpolation. Specifically, using the flow field variable values ​​at the grid nodes of the upstream blade row as source values, and based on the determined interpolation coefficients, the flow field variable values ​​at each grid node of the downstream blade row are calculated by weighted summation.

[0035] For example, for the j-th grid node of the downstream blade row, the interpolation coefficients of the j-th grid node of the downstream blade row relative to each grid node of the upstream blade row are multiplied by the flow field variable values ​​at the corresponding grid nodes of the upstream blade row. Then, all products are summed, and the result is the flow field variable value at the j-th grid node of the downstream blade row. Through this weighted summation calculation method, the flow field variable values ​​of each upstream grid node are distributed according to the proportion of its secondary grid covered by each downstream grid node. The flow field variable values ​​strictly adhere to the principle of area ratio conservation during the transmission from upstream to downstream, ensuring that the total flux of mass flow rate, momentum flux, and energy flux at the interface remains strictly consistent with the actual total flux transmitted from upstream. This eliminates the flux deviation problem caused by the interpolation method itself in traditional linear interpolation methods.

[0036] Through the coordinated operation of steps S101 to S105, this embodiment achieves complete conservation interpolation transfer of flow field variables in gridded hybrid plane simulation. Compared with existing linear interpolation methods, it can strictly meet the requirement of flux conservation. The total flux of the upstream blade row can be completely and losslessly transferred to the downstream blade row through the interpolation process, without generating cumulative errors in the stage-by-stage simulation calculation of multi-stage turbomachinery. The interpolation function has better smoothness and physical rationality in radial distribution, avoiding the spurious gradient discontinuity problem introduced by the interpolation method itself, which is beneficial to improving the stability and convergence speed of numerical solutions. Especially in regions with sparse radial grid distribution and regions with strong curvature changes in flow field parameters, such as within the boundary layer of the hub and casing end region or near the shock wave train, the conservation interpolation method implemented in this application can more accurately capture the local variation characteristics of the flow field, improving the reliability and numerical accuracy of the simulation calculation results.

[0037] In one feasible implementation, the specific implementation of constructing the secondary mesh in step S102 can be further refined according to the following steps.

[0038] First, the geometric midpoints of the edges between adjacent grid nodes in the original grid are obtained. This involves taking the midpoint of each line segment connecting two adjacent grid nodes in the original grid; these midpoints will serve as the boundary points of the secondary grid. For grid nodes located outside the boundary, the midpoint of the preceding adjacent edge is used as the starting boundary, and the midpoint of the following adjacent edge is used as the ending boundary. The interval between the starting and ending boundaries is the secondary grid interval corresponding to that grid node. For grid nodes located at radial end boundaries, such as those on the hub or casing side, the endpoint of the radial end boundary is used as the boundary on one side, and the midpoint of the edge adjacent to that radial end boundary is used as the boundary on the other side, thus determining the secondary grid interval for the end grid node. Through this secondary grid construction method, each grid-type grid node is assigned a secondary grid with a clearly defined, non-overlapping, and continuously covering the entire radial interval, providing a precise geometric metric basis for determining subsequent interpolation coefficients. This construction method ensures that the entire radial interval is completely covered by each secondary grid without any overlapping or gaps. This gives each grid node a clear geometric and physical meaning for the length of the radial interval, preventing information omissions or redundant calculations during subsequent interpolation.

[0039] In one feasible implementation, the process of determining the projection and the coincidence length in step S103 can be performed as follows: At the interface of the hybrid plane, using the downstream blade row as the interpolation target side and the upstream blade row as the interpolation source side, the first and second secondary grids of each grid node of the upstream blade row are projected radially onto the grid region of the downstream blade row. The specific projection operation can be viewed as mapping the starting and ending boundary coordinates of each first and second secondary grid of the upstream blade row into the radial coordinate system of the downstream blade row, thereby determining the coverage area of ​​each secondary grid of the upstream blade row in the coordinate system of the downstream blade row. After projection, for each pair of upstream and downstream blade row grid nodes that may have a spatial coverage relationship, the radial overlap interval between their first and second secondary grids is determined, i.e., the common coverage interval of these two secondary grids on the radial coordinate axis. Then, based on the length of this radial overlap interval, the overlap length between the upstream and downstream blade row grid nodes is determined. The radial projection and overlap region calculation method adopted in this application fully utilizes the characteristic of the one-dimensional radial distribution of the grid at the interface, which can accurately quantify the spatial distribution ratio of the contribution of the upstream grid nodes to the flow field variables when transmitted downstream, laying a data foundation for the subsequent calculation of interpolation coefficients.

[0040] In one feasible implementation, the specific determination method for the interpolation coefficients in step S104 can be performed as follows: For the j-th grid node of the downstream leaf row, firstly, obtain the overlap lengths between the second and second quadratic grids of the j-th grid node of the downstream leaf row and the first and second quadratic grids of each grid node of the upstream leaf row. Considering that a grid node of the downstream leaf row may overlap radially with multiple grid nodes of the upstream leaf row, it is necessary to collect all related overlap length information. Then, divide each obtained overlap length by the first and second quadratic grid length of the corresponding grid node of the upstream leaf row, thereby obtaining the interpolation coefficients of the j-th grid node of the downstream leaf row relative to each grid node of the upstream leaf row. Since each interpolation coefficient represents the spatial proportion contributed to a specific downstream grid node from the second quadratic grid length of each upstream grid node, it can be mathematically proven that for any upstream grid node, the sum of the interpolation coefficients of all downstream grid nodes relative to that upstream node is numerically equal to 1. This corresponds to the complete and lossless distribution of the entire flux of the upstream grid node to all downstream locations, ensuring the complete transfer of the total flux. This method of determining interpolation coefficients based on area ratios mathematically guarantees the conservation of the interpolation process, which is the key difference between this application and traditional linear interpolation methods.

[0041] In one feasible implementation, after determining the interpolation coefficients, the process also includes storing them. Since the interpolation coefficients depend only on the radial coordinate distribution of the upstream and downstream blade row grid nodes and the geometric division of the secondary grid, and are independent of the specific values ​​of the flow field variables, the interpolation coefficients can be pre-calculated based on the grid geometry before performing hybrid plane simulation of the turbomachinery. The calculated interpolation coefficients are then stored in computer memory or a storage device. In subsequent iterations, the stored interpolation coefficients are directly retrieved from the storage device, and the flow field variable values ​​at the upstream blade row grid nodes are allocated to the downstream blade row grid nodes. By pre-calculating and storing the interpolation coefficients, the repetitive execution of geometrically related operations such as secondary grid construction and coincidence length calculation in each iteration can be avoided, thereby significantly reducing the computational overhead of each iteration and improving the overall computational efficiency of the hybrid plane simulation. This is particularly suitable for steady-state multi-stage simulation scenarios requiring numerous iterations, significantly shortening computation time while ensuring flux conservation.

[0042] In one feasible implementation, the flow field variables may include at least one variable type selected from mass flow rate, momentum flux, and energy flux. In the calculation of flow field parameter transfer at the mixed-plane interface, the conservation of flux-type variables has a decisive impact on the accuracy of the simulation. Before allocating the flow field variable values ​​at the upstream blade row grid nodes to the downstream blade row grid nodes, the flow field variable values ​​at the upstream blade row grid nodes are used as source values. Based on the determined interpolation coefficients, the flow field variable values ​​at each grid node of the downstream blade row are calculated through a weighted summation.

[0043] Specifically, for any grid node in the downstream blade row, the interpolation coefficients of this downstream blade row grid node relative to each grid node in the upstream blade row are multiplied by the flow field variable values ​​of the corresponding grid nodes in the upstream blade row. Then, all products are summed, and the resulting sum is the flow field variable value at that downstream blade row grid node. Since the weights used in the weighted summation process, i.e., the interpolation coefficients, are determined based on the ratio of the coincident length of the secondary grid to the length of the secondary grid on the source side, the weighted summation process strictly adheres to the principle of area conservation. Whether for mass flow rate, momentum flux, or energy flux, the total flux remains unchanged before and after interpolation, achieving true conservation interpolation.

[0044] Furthermore, in the process of allocating the flow field variable values ​​at the upstream blade row grid nodes to the downstream blade row grid nodes, the mass flow rate, momentum flux, and energy flux values ​​at the upstream blade row grid nodes are used as source values, and weighted summation calculations are performed based on the interpolation coefficients. For any grid node of the downstream blade row, the interpolation coefficients of that grid node relative to each grid node of the upstream blade row are multiplied by the mass flow rate value at the corresponding grid node of the upstream blade row, and then summed to obtain the mass flow rate value at that grid node. Using the same set of interpolation coefficients, the momentum flux and energy flux values ​​are subjected to the same weighted summation operation to obtain the momentum flux and energy flux values ​​at that grid node of the downstream blade row. Since the mass flow rate, momentum flux, and energy flux are allocated using the interpolation coefficients during the interpolation process, the fluxes of each of the three can be independently conserved before and after interpolation. In this way, the conservation of multiple physical fluxes can be guaranteed by calculating the interpolation coefficients only once, without having to perform different interpolation coefficient calculations for different variables, thus balancing conservation and computational efficiency.

[0045] In one feasible implementation, this application may further include a reverse interpolation process from the downstream blade row to the upstream blade row. Since the interaction between the upstream and downstream blade rows in hybrid plane simulation is not unidirectional but bidirectional, it is necessary not only to transmit the flow field information from the upstream to the downstream, but also, in some computational scenarios, to transmit the flow field information from the downstream blade row back to the upstream blade row to achieve complete closure of boundary conditions and stable convergence of iterative calculations. This reverse transmission process is symmetrical to the forward transmission, but differs in the interpolation direction and data flow direction.

[0046] Specifically, after constructing a set of secondary grids, the upstream blade row can be used as the interpolation target side, and the downstream blade row as the interpolation source side. The secondary grids of each grid node of the downstream blade row can be projected radially onto the grid region of the upstream blade row. After projection, the overlap lengths between the secondary grids of each grid node of the downstream blade row and the primary grids of each grid node of the upstream blade row are determined. For each upstream blade row grid node, the overlap length information between it and multiple downstream blade row grid nodes can be obtained. Then, based on the ratio of each overlap length to the secondary grid length corresponding to the downstream blade row grid node, the interpolation coefficients of the upstream blade row grid nodes relative to the downstream blade row grid nodes are determined. Finally, based on these interpolation coefficients, the flow field variable values ​​at the downstream blade row grid nodes are distributed to each grid node of the upstream blade row using the same weighted summation method as in forward interpolation. In backward interpolation, the interpolation coefficients also satisfy the conservation property, that is, the sum of the interpolation coefficients of all upstream grid nodes relative to a certain downstream grid node is equal to one, ensuring strict conservation of flux during the backward propagation process.

[0047] By adding this reverse interpolation process, this application can achieve bidirectional conservation and transfer of flow field variables between upstream and downstream blade rows, satisfying the complete requirements for upstream and downstream information exchange in mixed-plane boundary conditions. The combined use of forward and reverse interpolation constitutes a complete data transfer scheme for the mixed-plane interface, enabling each iteration of calculations between the rotor and stator in steady multi-stage turbomachinery simulations to be performed under strict conservation conditions, further improving the convergence speed and consistency of solution results in multi-stage simulations. Especially when dealing with compressors and turbine stages with strong dynamic-static interference effects, this bidirectional conservation and transfer characteristic has significant engineering practical value for maintaining the stability and accuracy of numerical calculations, effectively avoiding convergence difficulties caused by incomplete information transfer or flux non-conservation.

[0048] In one feasible implementation, after allocating the flow field variable values ​​at the upstream blade row grid nodes to the downstream blade row grid nodes based on interpolation coefficients, the interface boundary conditions of the downstream blade row can be updated according to the allocated flow field variable values. After the conservation interpolation calculation, new flow field variable values ​​are assigned to each grid node at the interface of the downstream blade row. These flow field variable values ​​serve as the boundary condition input for the downstream blade row and participate in the current iteration of the flow field solution within that blade row. After the downstream blade row completes the current flow field solution, its flow field variable values ​​at the interface are recalculated based on the updated flow field distribution. These values ​​are then used as source values ​​and passed back to the upstream blade row through reverse interpolation to update the interface boundary conditions of the upstream blade row. This process is repeated, with the aforementioned forward conservation interpolation and reverse conservation interpolation operations performed at the interface in each iteration, continuously updating the boundary conditions of the upstream and downstream blade rows until the flow field residual is reduced to below a preset threshold, at which point the solution process is deemed to have met the convergence criterion. By closely integrating conservation interpolation with the iterative solution process and maintaining strict flux conservation in each iteration, the numerical stability of hybrid plane simulation can be effectively improved, avoiding convergence difficulties or divergence problems caused by flux drift during boundary condition update.

[0049] To further reveal the actual technical effects of this application, the Stage 35 compressor model was used as a typical verification object to conduct hybrid planar simulation application tests. The Stage 35 model is a representative transonic axial-flow compressor stage, whose rotor blades and stator blades exhibit strong unsteady characteristics, requiring high conservation of parameters for the interpolation method at the interface. The structure of the Stage 35 model is as follows: Figure 4 As shown, Figure 4 This is a schematic diagram of the stage35 model provided in the embodiments of this application; the spatial mesh division for numerical calculation is as follows: Figure 5 As shown, Figure 5This is a schematic diagram of the stage35 model mesh provided in the embodiments of this application; the location of the rotor-stationary interface between the rotor and the stator is as follows. Figure 6 As shown, Figure 6 This is a schematic diagram of the stage 35 to static interface provided in an embodiment of this application; the mesh distribution details at the static interface are as follows: Figure 7 As shown, Figure 7 This is a schematic diagram of the stage 35 to static interface mesh provided in an embodiment of this application. The mesh distribution of this model has typical non-matching characteristics at the static interface, with different numbers of radial mesh nodes and coordinate distributions, making it very suitable for verifying the effectiveness of this application in real engineering cases.

[0050] When applying this application to perform hybrid plane simulation calculations of the stage35 model, the flow field variables at the transition-static interface are first subjected to forward interpolation according to steps S101 to S105, and simultaneously, reverse interpolation is performed according to the reverse interpolation process to ensure the bidirectional conservation and transfer of flow field information between upstream and downstream. During the iterative solution process of the hybrid plane simulation, each iteration performs the aforementioned forward and reverse conservation interpolation operations at the interface, ensuring that flux transfer between each stage remains strictly conserved throughout the iteration process.

[0051] In one feasible implementation, after allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row based on interpolation coefficients, flux conservation verification and correction can be performed on the interpolation allocation results. Specifically, firstly, the product of the quadratic grid length corresponding to each grid node of the upstream blade row and the flow field variable value at that grid node is summed to obtain the total flux on the source side; simultaneously, the product of the quadratic grid length corresponding to each grid node of the downstream blade row and the already allocated flow field variable value at that grid node is summed to obtain the total flux on the target side. At this point, the total flux on the source side is equal to the total flux on the target side.

[0052] See Figure 8 , Figure 8 The diagram shows the inlet and outlet flow rates of stage 35 and the inlet and outlet flow rates of the static interface provided in this application embodiment. The horizontal axis represents the number of iteration steps, and the vertical axis represents the main mass flow rate. Figure 8 The inlet mass flow rate, the R-side mass flow rate at the rotor-stationary interface (INTER_R-Massflow, where R refers to the rotor side, i.e., the mass flow rate through the rotor interface), the S-side mass flow rate at the rotor-stationary interface (INTER_S-Massflow, where S refers to the stator side, i.e., the mass flow rate through the stator interface), and the outlet mass flow rate are displayed respectively. Figure 8Quantitative analysis of the calculation results shows that the flow difference at the inlet and outlet of the stage35 model is approximately 0.095%, which meets the design requirement of flow error typically within 0.05% in engineering design. The flow difference at the interface between the inlet and outlet is approximately 0.024%, indicating that the flow error at the interface is controlled at a very low level. The flow error at the interface is a key factor affecting the total flow error at both inlet and outlet. Because this application implements strictly conserved interpolation based on the coincidence length of the quadratic mesh at the interface, the flow error at the interface is controlled at an extremely low level. Therefore, the overall inlet and outlet flow error is also controlled within the range that meets the design requirements.

[0053] Compared with traditional linear interpolation methods, this application has significant technical advantages in flux conservation, effectively avoiding the cumulative effect of interpolation errors in multi-stage turbomachinery calculations. In simulation scenarios involving multiple rows of blades, traditional linear interpolation methods introduce flux deviations at each interface. These deviations accumulate gradually after multiple stages are connected in series, potentially leading to significant deviations from the design point in the calculation results. This application, however, ensures strict flux conservation at each interface, effectively eliminating this source of cumulative error and making the multi-stage simulation results more consistent with physical reality. Furthermore, in regions where flow field parameters change drastically, such as the end boundary layer and near shock waves, this application employs a weighted allocation strategy based on secondary grid length, which more accurately restores the actual radial distribution characteristics of the flow field parameters compared to linear interpolation, avoiding local flux distortion caused by insufficient interpolation accuracy.

[0054] Furthermore, this application also boasts advantages in computational efficiency. Since the interpolation coefficients depend only on the radial coordinates of the mesh nodes and the secondary mesh length, they can be pre-calculated and stored before each simulation iteration, and directly called upon in each iteration without repeated calculations. This characteristic allows this application to maintain conservation while not significantly impacting overall computational efficiency, making it highly suitable for widespread application in the engineering simulation of large-scale multi-stage turbomachinery.

[0055] As can be seen from the above embodiments, this application has outstanding practical value in grid-type hybrid plane simulation of turbomachinery. By constructing a secondary mesh on the grid-type mesh at the interface and determining the interpolation coefficients based on the overlap ratio of the secondary mesh, the transfer of strictly conserved flow field variables can be achieved without increasing additional computing resources. Moreover, the implementation principle is clear and the implementation is simple, which can be directly integrated into the existing computational fluid dynamics simulation process, and it has broad engineering applicability and good prospects for promotion.

[0056] It is particularly noteworthy that this application has broad applicability to different types of turbomachinery. For axial compressors, this application can address the radial grid mismatch problem caused by the different number of blade rows between the rotor and stator; for centrifugal compressors, this application can adapt to the inconsistency in radial coordinate distribution caused by geometric differences between the impeller and diffuser; for turbomachinery, this application is also applicable to the transfer of interface parameters between guide vanes and moving blades. In different types of turbomachinery applications, the core principles of the secondary grid construction and coincident length ratio allocation on which this application is based remain unchanged; only corresponding coordinate mapping needs to be performed according to the specific grid distribution.

[0057] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. It should be noted that those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A grid-type hybrid planar simulation method for turbomachinery based on flux conservation interpolation, characterized in that, include: A circumferential average is performed on the circumferential non-uniform flow at the interface between the upstream and downstream blade rows of the turbomachinery, simplifying the original mesh at the interface into a set of radially arranged mesh nodes and edges connecting adjacent mesh nodes; the interface is the interface between the rotor and the stator. For the original grid-type grid, take the midpoint of each edge, use each midpoint as the boundary of the secondary grid node, construct a set of secondary grids, and determine the secondary grid length corresponding to each grid node; Project each of the grid nodes of the upstream leaf row onto the grid area of ​​the downstream leaf row, and determine the overlap length between the first and second secondary grids of each grid node of the upstream leaf row and the second secondary grids of each grid node of the downstream leaf row. Based on the ratio of the overlap length to the secondary grid length corresponding to the grid node of the upstream leaf row, the interpolation coefficient of the grid node of the downstream leaf row relative to the grid node of the upstream leaf row is determined. Based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the upstream blade row are allocated to the grid nodes of the downstream blade row to achieve hybrid plane simulation of the turbomachinery.

2. The method according to claim 1, characterized in that, Using the midpoints of each of the aforementioned points as the boundary of the secondary grid nodes, a set of secondary grids is constructed, including: Obtain the geometric midpoint of the edge between each adjacent grid node in the original grid; For each grid node at a non-boundary location, the midpoint of the preceding adjacent edge of the grid node is used as the starting boundary, and the midpoint of the following adjacent edge of the grid node is used as the ending boundary to determine the secondary grid corresponding to the grid node. For each of the grid nodes located at the radial end boundary, the secondary grid corresponding to the grid node is determined by taking the radial end boundary as one side boundary and the midpoint of the edge adjacent to the radial end boundary as the other side boundary.

3. The method according to claim 1, characterized in that, Projecting each grid node of the upstream leaf row onto the grid region of the downstream leaf row, and determining the overlap length between the first and second secondary grids of each grid node of the upstream leaf row and the second and second secondary grids of each grid node of the downstream leaf row, includes: Using the downstream leaf row as the interpolation target side and the upstream leaf row as the interpolation source side, the first and second grids of each grid node of the upstream leaf row are radially projected onto the grid region of the downstream leaf row. Determine the radial overlap interval between the first and second secondary grids of each grid node in the upstream leaf row and the second and second secondary grids of each grid node in the downstream leaf row; Based on the length of the radial overlap interval, the overlap length between each grid node of the upstream leaf row and each grid node of the downstream leaf row is determined.

4. The method according to claim 3, characterized in that, Based on the ratio of the overlap length to the secondary grid length corresponding to the grid node of the upstream leaf row, the interpolation coefficients of the grid node of the downstream leaf row relative to the grid node of the upstream leaf row are determined, including: For the j-th grid node of the downstream leaf row, obtain the overlap lengths between the second and second quadratic grids of the j-th grid node of the downstream leaf row and the first and second quadratic grids of each grid node of the upstream leaf row; Divide each of the overlapping lengths by the first and second grid lengths of the corresponding upstream leaf row grid nodes to obtain the interpolation coefficients of the j-th grid node of the downstream leaf row relative to each grid node of the upstream leaf row.

5. The method according to claim 1, characterized in that, After constructing a set of quadratic meshes, the following is also included: Using the upstream leaf row as the interpolation target side and the downstream leaf row as the interpolation source side, the second and second grids of each grid node of the downstream leaf row are radially projected onto the grid region of the upstream leaf row. Determine the overlap lengths between the second and second-order grids of each grid node in the downstream leaf row and the first and second-order grids of each grid node in the upstream leaf row; Based on the ratio of each of the overlapping lengths to the second and second grid lengths corresponding to the grid nodes of the downstream leaf row, the interpolation coefficients of the grid nodes of the upstream leaf row relative to the grid nodes of the downstream leaf row are determined. Based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the downstream blade row are allocated to the grid nodes of the upstream blade row.

6. The method according to claim 1, characterized in that, The flow field variables include at least one of mass flow rate, momentum flux, and energy flux. Before allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row, the method further includes: Using the flow field variable values ​​at the grid nodes of the upstream blade row as the source values, and based on the interpolation coefficients, the values ​​of the flow field variables at each grid node of the downstream blade row are calculated by weighted summation.

7. The method according to claim 1, characterized in that, After determining the interpolation coefficients of the grid nodes of the downstream leaf row relative to the grid nodes of the upstream leaf row, the method further includes: Store the interpolation coefficients; In subsequent iterations, the interpolation coefficients are called to distribute the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row.

8. The method according to claim 6, characterized in that, Based on the interpolation coefficients, the flow field variable values ​​at the grid nodes of the upstream blade row are distributed to the grid nodes of the downstream blade row, including: Using the mass flow rate, momentum flux, and energy flux values ​​at the grid nodes of the upstream leaf row as source values, and based on the interpolation coefficients, the mass flow rate, momentum flux, and energy flux values ​​at each grid node of the downstream leaf row are calculated by weighted summation.

9. The method according to claim 1, characterized in that, After allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row based on the interpolation coefficients, the method further includes: Based on the flow field variable values ​​assigned to the grid nodes of the downstream blade row, the interface boundary conditions of the downstream blade row are updated, and the flow field of the turbomachinery is iteratively solved based on the updated interface boundary conditions until the convergence criterion is met.

10. The method according to claim 1, characterized in that, After allocating the flow field variable values ​​at the grid nodes of the upstream blade row to the grid nodes of the downstream blade row based on the interpolation coefficients, the method further includes: The total flux on the source side is obtained by summing the product of the secondary grid length corresponding to each grid node of the upstream blade row and the flow field variable value at the grid node. The total flux on the target side is obtained by summing the product of the secondary grid length corresponding to each grid node of the downstream blade row and the flow field variable value already allocated at the grid node; wherein, the total flux on the source side is equal to the total flux on the target side.

Images