An aviation fuel gear pump tip clearance region pressure reconstruction analysis method

Abstract

The novel application discloses an aviation fuel gear pump tooth tip clearance area pressure reconstruction analysis method, which comprises the following steps: step one: deriving an aviation engine fuel gear pump fluid domain three-dimensional model; step two: carrying out grid independence test and simulation calculation of multiple typical working conditions, and carrying out test verification on the calculation results; step three: combining a time function with a POD orthogonal basis to complete pressure reconstruction of the gear pump tooth tip clearance area. The simulation time of the fuel gear pump is reduced, the simulation calculation stability is increased, and the continuous change of pressure and other parameters on a smaller simulation time scale has obvious advantages. The specific work is that, for the tooth tip clearance area, the pressure of the selected plane part time observation point is analyzed by combining the POD modal analysis method, the continuous change value of the pressure under a shorter time interval is obtained, the time cost of the unsteady flow field calculation in the CFD is reduced, and the linear heat map and the spectrum analysis are used to find that the pressure of the tooth tip clearance periodically changes with the rotation of the gear.

Description

Technical Field

[0001] This invention relates to the field of optimized design of fuel gear pumps for aero engines, and in particular to a method for pressure reconstruction analysis of the tooth tip clearance region of an aero fuel gear pump. Background Technology

[0002] The working environment of aero-engine fuel gear pumps is harsh and affected by vibration and other factors. Their optimized design requires multiple iterations and improvements, resulting in a longer design cycle. Researchers typically use computational fluid dynamics (CFD) methods for fuel pump design and optimization. While CFD technology has many advantages, its application to rotating fuel gear pumps requires consideration of internal flow field changes, demanding high computer performance. When performing refined fuel pump design, fluid-structure interaction, heat, and environmental factors must be considered. Simulation calculation time increases exponentially with the increase of design variables and the coupling of multiple factors, extending the development cycle and impacting progress. Furthermore, during the iterative optimization of fuel gear pumps, their structural parameters often change to varying degrees. If traditional CFD methods are used for simulation analysis, the gear pump flow field mesh needs to be redrawn based on these changes, significantly increasing the workload for designers. Therefore, to reduce workload and shorten simulation time, the design paradigm needs to be updated within permissible accuracy limits.

[0003] In addition, when designing fuel gear pumps for aero-engines, besides focusing on steady-state performance under rated operating conditions, special attention is also paid to transient performance at multiple non-rated operating condition design points. Currently, the common research method is to use CFD to conduct unsteady flow field calculations of fuel gear pumps under different operating conditions. The problems in simulation are that, on the one hand, it requires continuous mesh reconstruction and iterative calculation, resulting in extremely long calculation cycles; on the other hand, the gear meshing region is prone to negative volume during reconstruction, which leads to the insufficiency of calculation divergence. The paper "Simulation Calculation of Internal Flow Field of External Meshing Gear Pump Based on Fluent" published by Nie Rui et al. in 2017 only solved the internal flow field characteristics of the gear pump and obtained the pressure distribution cloud map of the internal flow, but the above-mentioned problems still exist.

[0004] The POD method employed in this invention demonstrates significant theoretical advantages in reducing simulation time for fuel gear pumps, increasing simulation stability, and obtaining continuous changes in parameters such as pressure over smaller simulation timescales. Taking aero-engine fuel gear pumps as the research object, this invention combines the POD method with CFD, greatly reducing the time cost of unsteady flow field calculations in CFD. This method can capture flow field information within the fuel gear pump over shorter time intervals, predict changes in flow field parameters at any time point, improve the efficiency of transient flow field calculations for aero-engine fuel gear pumps, and provide a theoretical basis for efficient fuel pump design.

[0005] Invention Content

[0006] The novel purpose of this invention is to address the shortcomings of existing technologies by proposing a method for pressure reconstruction analysis of the tooth tip clearance region in aviation fuel gear pumps.

[0007] To achieve the above objectives, the present invention novelly adopts the following technical solution:

[0008] A method for pressure reconstruction analysis in the tooth tip clearance region of an aviation fuel gear pump includes the following steps:

[0009] Step 1: Export the 3D model of the fluid domain of the fuel gear pump in the aero-engine;

[0010] Step 2: Conduct mesh independence tests and simulation calculations for multiple typical working conditions, and verify the calculation results experimentally;

[0011] Step 3: Combine the time function with the POD orthogonal basis to complete the pressure reconstruction of the gear pump tooth tip clearance region.

[0012] Preferably, the fuel gear pump fluid domain in step one consists of four parts: inlet, gear, outlet, and unloading groove.

[0013] Preferably, in step two, a hexahedral structure mesh is drawn for the gear part, and a hexahedral Cartesian hybrid mesh is drawn for the inlet and outlet areas and the unloading groove part. The gear part structure mesh drawn by the Cartesian method based on the binary tree method has high accuracy, and the mesh is densified in the tooth tip clearance and gear meshing area, which can meet the complex changes in the flow field when the gear rotates or meshes.

[0014] Preferably, in step two, to avoid the number of grids having a significant impact on the simulation results, a grid independence test is required to detect the changes in minimum flow rate, average flow rate, and maximum flow rate as the number of grids increases. The left and right vertical axes represent the flow rate of the gear pump and its error at the average flow rate, respectively. The minimum flow rate, average flow rate, and maximum flow rate of the gear pump are different under different grid numbers, and they gradually tend to stabilize as the number of grids increases.

[0015] Preferably, in step three, based on the initial flow field data obtained from simulation and the POD modal analysis method, the time function a at each node obtained by POD decomposition is... i (t j ), i∈[1,K], j∈[1,N t Smooth spline fitting is performed to extend the original time interval, calculate the time function under the new time interval, and combine it with the corresponding POD mode to interpolate and reconstruct the initial flow field data to obtain the flow field data value under a shorter time interval.

[0016] Preferably, in order to further analyze the results after POD interpolation reconstruction, points with significant pressure changes are selected based on the results, and spectral analysis is performed on the reconstructed pressure values. The closer to the outlet, the greater the amplitude of the pressure change.

[0017] Preferably, this indicates that the fuel pressurization in the gear pump is a gradual process over time, not a linear relationship with time. Instead, most of the pressurization is concentrated near the gear pump outlet area, which is consistent with the numerical simulation results. The spectrum of the observation point near the gear outlet area has a larger amplitude compared with other areas, which is consistent with the motion law of the fuel gear pump.

[0018] Preferably, the pressure value at the observation point closer to the outlet area is greater. That is, during the operation of the gear pump, the pressure at the tooth tip clearance changes periodically, and its period is related to the rotational speed of the gear. That is, every time the gear rotates past an observation point, the pressure at that point undergoes a periodic change.

[0019] Preferably, this phenomenon also conforms to the motion law of the gear pump. When the gear moves to the point of observation, it will compress the volume around that point, causing the surrounding oil pressure to increase.

[0020] Preferably, when the movement is about to leave the observation point, the volume around that point will increase and the oil pressure will decrease.

[0021] The present invention has the following beneficial effects:

[0022] This invention provides a novel method for pressure reconstruction analysis in the tooth tip clearance region of an aviation fuel gear pump. This method offers significant advantages in reducing simulation time, increasing simulation stability, and obtaining continuous changes in parameters such as pressure over a smaller simulation timescale. Specifically, it analyzes the pressure at selected time points in the tooth tip clearance region using POD modal analysis, obtaining continuous pressure changes over shorter time intervals. This significantly reduces the time cost of calculating unsteady flow fields in CFD. Furthermore, using linear heatmaps and spectral analysis, it is found that the pressure in the tooth tip clearance changes periodically with gear rotation, and under various operating conditions, the pressure change frequency corresponds to the gear meshing period at the corresponding rotational speed. Compared to traditional methods, this method provides an efficient and convenient new approach for rapid analysis of the transient flow field inside an aviation fuel gear pump, effectively reducing the time spent on repetitive calculations in practical engineering and significantly improving simulation efficiency while ensuring accuracy. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the implementation scheme proposed in this invention;

[0024] Figure 2 This is a schematic diagram of the fluid domain of the aviation fuel gear pump proposed in this invention;

[0025] Figure 3 This is a schematic diagram of the fluid domain mesh division of the fuel gear pump proposed in this invention;

[0026] Figure 4 This is a schematic diagram of the mesh independence test results proposed in this invention;

[0027] Figure 5 This is a schematic diagram of the observation surface and observation point positions on the gear proposed in this invention;

[0028] Figure 6 This is a schematic diagram illustrating the pressure magnitude at observation points under different rotational speeds proposed in this invention.

[0029] Figure 7 This is a schematic diagram illustrating the magnitude of POD pressure reconstruction under different rotational speeds proposed in this invention.

[0030] Figure 8 This is a schematic diagram of the pressure spectrum values ​​at different rotational speeds proposed in this invention. Detailed Implementation

[0031] The technical solutions of the novel embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the novel embodiments of the present invention, and not all embodiments.

[0032] Reference Figure 1-8 A method for pressure reconstruction analysis in the tooth tip clearance region of an aviation fuel gear pump includes the following steps:

[0033] Step 1: Export the 3D model of the fluid domain of the fuel gear pump in the aero-engine;

[0034] Step 2: Conduct mesh independence tests and simulation calculations for multiple typical working conditions, and verify the calculation results experimentally;

[0035] Step 3: Combine the time function with the POD orthogonal basis to complete the pressure reconstruction of the gear pump tooth tip clearance region.

[0036] The study selected four grid schemes with a grid number of 10×10. 4 43×10 4 80×10 4 110×10 4Simulations were performed at 12000 rpm to examine the changes in minimum, average, and maximum flow rates as the number of grid cells increased. The left and right ordinates represent the flow rate of the gear pump and its error at the average flow rate, respectively. The minimum, average, and maximum flow rates of the gear pump differed for different grid cell counts, gradually stabilizing with increasing grid cell count. Pressure reconstruction of the gear pump's tooth tip clearance region was achieved by combining the time function and the POD orthogonal basis. Based on the initial flow field data obtained from the simulation and the POD modal analysis method, the time function 'a' at each node obtained from the POD decomposition was analyzed. i (t j ), i∈[1,K], j∈[1,N t Smooth spline fitting was performed to extend the original time interval, and the time function under the new time interval was calculated. The initial flow field data was then interpolated and reconstructed using the corresponding POD mode to obtain flow field data values ​​under shorter time intervals. To observe the change in pressure at the tooth tip clearance of the fuel gear pump during operation, three planes in the gear fluid region were selected, with 38 observation points equally spaced on each plane. Numerical simulations were performed at 9000, 12000, and 15000 rpm, and the pressure values ​​at the observation points were extracted. The pressure distribution in the tooth tip clearance exhibits strong symmetry; the pressure values ​​at the observation points on the driving wheel side and the driven wheel side on the same plane are basically consistent, differing only due to the gear... The meshing relationship has a phase difference. Therefore, to shorten the research time, 20 points on the driven wheel side were selected to plot the pressure changes at different speeds. The observed pressure changes have strong periodicity, but the amplitude of the periodic changes varies greatly. The pressure change amplitude is largest on plane 2. The symmetry of the gear structure makes the pressure distribution on the upper plane 1 and the lower plane 3 also symmetrical. To further analyze the pressure pulsation during gear movement, the pressure at different times of the observation points was decomposed by POD and then interpolated and reconstructed, expanding the time points to 100. Linear heat maps were plotted on the three planes under the conditions of 9000, 12000, and 15000 rpm, where p / p nmaxThis represents the ratio of the pressure at a given point to the maximum pressure on its corresponding plane. A larger ratio indicates a higher relative pressure at that point, and a darker color. As the time step increases, the pressure at observation points on different planes exhibits a clear periodic color change, with the change period being approximately consistent. This indicates that during the operation of the gear pump, the pressure at the point on the gear tooth clearance changes periodically with time, and the change period at different points is approximately the same. The closer to the outlet, the greater the pressure change amplitude. This suggests that fuel pressurization within the gear pump is a gradual process over time, not linearly related to time, but rather concentrates most of the pressurization near the gear pump outlet area. This is consistent with the numerical simulation results. Further analysis of the POD interpolation reconstruction results reveals that five points with significant pressure changes were selected, and the reconstructed pressure values ​​were analyzed using a spectrum. Analysis shows that under all three speed conditions, the spectral amplitude of the observation points appears in the low-frequency region, with observation points 15 and 17 exhibiting higher amplitudes. The spectral amplitude of observation points closer to the gear outlet region is larger compared to other regions, consistent with the motion law of the fuel gear pump. The closer the observation point is to the outlet region, the greater the pressure value. Furthermore, it was found that the highest amplitude frequencies at 9000, 12000, and 15000 rpm are 1500, 2000, and 2500 Hz respectively, consistent with the gear motion law at these speeds. That is, during the operation of the gear pump, the pressure at the tooth tip clearance changes periodically, and its period is related to the gear speed. For example, at 15000 rpm, the gear rotation period is 0.004s, and with 10 teeth, the rotation frequency of each tooth is 1 / (0.004 / 10) = 2500Hz. Figure 8 (c) It can be seen that the pressure dominance frequency at the observation points on planes 1, 2, and 3 is 2500Hz, which is consistent with the rotational frequency of the gear at that speed. That is, the pressure at the observation point undergoes a periodic change every time the gear rotates past the observation point. This phenomenon is also consistent with the motion law of the gear pump. When the gear is about to pass the observation point, it will compress the volume around the point, causing the surrounding oil pressure to increase. When it is about to leave the observation point, it will cause the volume around the point to increase, and the oil pressure to decrease. Therefore, the results show that the pressure change frequency at the observation point is consistent with the rotational frequency of the gear, which is consistent with the motion theory of the gear pump, proving the accuracy of the POD interpolation reconstruction method.

[0037] Intrinsic Orthogonal Decomposition (POD) is a vector-based statistical method that calculates a set of orthogonal bases from existing data. The subspace formed by these bases can approximate the original data with high fidelity and low degrees of freedom. It is widely used in data dimensionality reduction and flow field reconstruction. When applied to flow field analysis, it decomposes the flow field into a linear superposition of a series of time functions and spatial orthogonal base products. Based on the above principle, three POD methods have been developed, including direct POD, snapshot POD, and singular value decomposition-based POD. Among them, the singular value decomposition-based POD method has more accurate calculation results and has a significant advantage in reducing the amount of simulation computation. Therefore, this invention selects the singular value decomposition-based POD method.

[0038] For high-dimensional data matrix C m×n To centralize the data, subtract the average value from each column:

[0039] C′=CC (1)

[0040] (2) The centered data matrix is ​​processed using Singular Value Decomposition (SVD) to obtain the left singular matrix, singular value matrix, and right singular matrix:

[0041] C′=P∑Q T (2)

[0042] Where P is an m×m matrix, ∑ is an m×n matrix whose elements are all 0 except for those on the main diagonal, each element on the main diagonal is called a singular value, and Q is an n×n matrix. Both P and Q are unitary matrices, i.e.:

[0043] P T P = IQ T Q = I (3)

[0044] (3) Solve for the time coefficient a, i.e.:

[0045] a=P·∑ (4)

[0046] (4) Solve for the eigenvalue λ, that is, the energy of each mode:

[0047]

[0048] (5) The basis function Q obtained by solving i (x) and the corresponding time coefficient a i (t), reconstruct the data matrix:

[0049]

[0050] The novel method of use and advantages of this invention: The working process of this method for pressure reconstruction analysis in the tooth tip clearance region of an aviation fuel gear pump is as follows:

[0051] like Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 and Figure 8 As shown,

[0052] Step 1: Export the 3D model of the fluid domain of the aero-engine fuel gear pump. Figure 2 The diagram shows the fluid domain of the fuel gear pump used in this paper, which consists of four parts: inlet, gear, outlet, and unloading groove.

[0053] Step Two: Conduct mesh independence checks and simulation calculations for multiple typical working conditions, and experimentally verify the calculation results. For the gear section, a hexahedral mesh is drawn; for the inlet / outlet regions and the unloading groove section, a mixed hexahedral and Cartesian mesh is drawn. The meshed results are shown below. Figure 3 As shown in the figure, the gear structure mesh drawn by the Cartesian method based on the binary tree method has high accuracy. The mesh is refined in the tooth tip clearance and gear meshing area, which can meet the complex changes in the flow field when the gear rotates or meshes.

[0054] To avoid the significant impact of mesh number on the simulation results, a mesh independence test is necessary. Four mesh schemes were selected, with mesh numbers of 10 × 10⁻⁶ and 10⁻⁶ respectively. 4 43×10 4 80×10 4 110×10 4 Simulations were performed at 12000 rpm to examine how the minimum, average, and maximum flow rates changed with increasing grid number. The results are as follows: Figure 4 As shown, the left and right vertical axes represent the flow rate of the gear pump and its error at the average flow rate, respectively.

[0055] As shown in the figure, the minimum flow rate, average flow rate, and maximum flow rate of the gear pump are different under different grid numbers. As the number of grids increases, they gradually tend to stabilize. Among them, the average flow rate errors of Scheme 3 and Scheme 4 are 0.072 and 0.07, respectively, indicating that Scheme 3 can perform calculations that meet the simulation accuracy with lower computer performance and shorter calculation time. Therefore, this invention adopts the grid number of Scheme 3 for simulation analysis.

[0056] Step 3: Combine the time function with the POD orthogonal basis to complete the pressure reconstruction in the gear pump tooth tip clearance region. Based on the initial flow field data obtained from the simulation and the POD modal analysis method, reconstruct the time function a at each node obtained from the POD decomposition. i (tj ), i∈[1,K], j∈[1,N t Smooth spline fitting is performed to extend the original time interval, calculate the time function under the new time interval, and combine it with the corresponding POD mode to interpolate and reconstruct the initial flow field data to obtain the flow field data value under a shorter time interval.

[0057] To observe the change in the tooth clearance pressure of the fuel gear pump during operation as the gear rotates, such as... Figure 5 As shown, three planes were selected in the gear fluid region, with 38 observation points equally spaced on each plane. Numerical simulations were performed at 9000, 12000, and 15000 rpm to extract pressure values ​​at the observation points. The pressure distribution in the tooth tip clearance exhibits strong symmetry. The pressure values ​​at the observation points on the driving gear side and the driven gear side on the same plane are basically consistent, with only a phase difference due to the gear meshing relationship. Therefore, to shorten the research time, 20 points on the driven gear side were selected, and their pressure changes at different speeds were plotted as shown below. Figure 6 As shown, the observed pressure changes have a strong periodicity, but the amplitude of the periodic changes varies greatly. The pressure change amplitude is the largest on plane 2. The symmetry of the gear structure makes the pressure distribution on the upper plane 1 and the lower plane 3 also symmetrical.

[0058] To analyze the pressure pulsation during gear motion in depth, the pressure at different times of the observation point was decomposed using POD and then interpolated and reconstructed, expanding the time points to 100. Linear heat maps were then plotted on three planes under operating conditions of 9000, 12000, and 15000 rpm, as shown below. Figure 7 As shown, where p / p nmax This represents the ratio of the pressure at a given point to the maximum pressure on its plane at that moment. A larger ratio indicates a greater relative pressure at that point, and the color is darker.

[0059] As the time step increases, the pressure at observation points on different planes exhibits obvious periodic color changes, and the change period is approximately consistent. This indicates that during the operation of the gear pump, the pressure at the point on the tooth tip clearance changes periodically with time, and the change period at different points is approximately the same. The closer to the outlet position, the greater the pressure change amplitude. This suggests that the fuel pressurization in the gear pump is a gradual process over time, not a linear relationship with time. Instead, most of the pressurization is concentrated near the gear pump outlet area, which is consistent with the numerical simulation results.

[0060] To further analyze the results after POD interpolation reconstruction, based on Figure 6 Five points with significant pressure changes were selected from the results, and spectral analysis was performed on the reconstructed pressure values. The results are as follows: Figure 8As shown in the figure, under the three speed conditions, the spectral amplitude of the observation points all appear in the low-frequency region, and observation points 15 and 17 have higher amplitudes. Figure 5 The observation points shown have higher amplitude spectra closer to the gear outlet area compared to other areas, consistent with the motion characteristics of the fuel gear pump. The closer the observation point is to the outlet area, the higher the pressure value. Furthermore, it was found that the highest amplitude frequencies at 9000, 12000, and 15000 rpm were 1500, 2000, and 2500 Hz respectively, consistent with the gear motion characteristics at these speeds. That is, during the operation of the gear pump, the pressure at the tooth tip clearance changes periodically, and its period is related to the gear speed. For example, at 15000 rpm, the gear rotation period is 0.004s, and with 10 teeth, the rotation frequency of each tooth is 1 / (0.004 / 10) = 2500Hz. Figure 8 (c) It can be seen that the pressure dominance frequency at the observation points on planes 1, 2, and 3 is 2500Hz, which is consistent with the rotational frequency of the gear at that speed. That is, the pressure at the observation point undergoes a periodic change every time the gear rotates past the observation point. This phenomenon is also consistent with the motion law of the gear pump. When the gear is about to pass the observation point, it will compress the volume around the point, causing the surrounding oil pressure to increase; when it is about to leave the observation point, it will cause the volume around the point to increase, and the oil pressure to decrease. Therefore, the results show that the pressure change frequency at the observation point is consistent with the rotational frequency of the gear, which is consistent with the motion theory of the gear pump, proving the accuracy of the POD interpolation reconstruction method.

[0061] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for pressure reconstruction analysis in the tooth tip clearance region of an aviation fuel gear pump, characterized in that... Includes the following steps: Step 1: Export the 3D model of the fluid domain of the fuel gear pump in the aero-engine; Step 2: Conduct mesh independence tests and simulation calculations for multiple typical working conditions, and verify the calculation results experimentally; Step 3: Combine the time function with the POD orthogonal basis to complete the pressure reconstruction in the gear pump tooth tip clearance region; The three-dimensional model of the fluid domain of the aero-engine fuel gear pump in step one consists of four parts: inlet, gear, outlet, and unloading groove. Step two involves mesh independence testing and simulation calculations for multiple typical working conditions, including drawing a hexahedral structure mesh for the gear part, and drawing a hexahedral Cartesian hybrid mesh for the inlet and outlet areas and the unloading groove part. The gear part structure mesh drawn by the Cartesian method based on the binary tree method has high accuracy. The mesh is also refined in the tooth tip clearance and gear meshing area, which can meet the complex changes in the flow field when the gear rotates or meshes. In step two, to avoid the influence of the number of grids on the simulation results, a grid independence test is performed to detect the changes in minimum flow, average flow and maximum flow as the number of grids increases, and the number of simulation grids is determined based on the average flow error. Step three, combining the time function with the POD orthogonal basis to complete the pressure reconstruction of the gear pump tooth tip clearance region, specifically involves: based on the initial flow field data obtained from the simulation and the POD modal analysis method, reconstructing the time function at each node obtained from the POD decomposition. Smooth spline fitting is performed to extend the original time interval, the time function under the new time interval is calculated, and the initial flow field data is reconstructed by interpolation in combination with the corresponding POD mode to obtain the flow field data value under a shorter time interval.

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