Method for constructing a three-dimensional tip clearance model for compressor system stability calculations

Abstract

The present application relates to the technical field of impeller machinery, and discloses a construction method of a three-dimensional tip clearance model for compression system stability calculation.The present application can calculate the direction and size of a tip vortex and the pressure rise characteristic in the tip vortex according to the known geometry of a planar cascade at the tip, the correlation of inlet and outlet flow angles and the pressure rise characteristic.The calculated geometric characteristics and pressure rise characteristics can be correlated with the inlet and outlet flow parameters of the blade row in the tip vortex area during the compression system stability calculation, so that the influence of the tip clearance can be reflected in the three-dimensional numerical simulation of the compression system.Especially, the blade row can be modeled in the three-dimensional numerical simulation of the compression system, and the influence of the tip clearance on the performance, stability boundary and stall initiation process of the compression system can be reflected, so that the present application can be used for the compression system stability calculation.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology and discloses a method for constructing a three-dimensional tip clearance model for calculating the stability of a compression system. Background Technology

[0002] Rotating stall and surge are two unstable flow states unique to compressors, leading to reduced compressor performance and, in severe cases, engine shutdown. Studies have shown a close relationship between compressor instability processes and tip clearance leakage flow; for example, the morphology of the leakage flow determines the form of the initial disturbance; and the instability of the leakage vortex itself, and its breakup, significantly influence the stall initiation process. Currently, the mechanism by which tip clearance leakage flow affects the stall initiation process is not fully understood. Therefore, developing a tip clearance leakage flow model that can be used for compressive system stability calculations is of great significance.

[0003] Existing tip clearance models, such as those by Yaras and Sjolander and by Storer and Cumpsty, almost all treat tip clearance as a flow loss, lacking a description of the specific flow field under the influence of the clearance. Therefore, they cannot be used to study the impact of tip leakage flow on the flow field during instability dynamics. Cao Renjing et al. (Cao Renjing, Tao Deping, Zhou Sheng. The Influence of Tip Clearance on the Stability of Axial Compression Systems) developed a computational model that considers the influence of tip clearance on the stability of axial compression systems, modeling the end losses caused by tip clearance. However, they used the inviscid Moore-Greitzer model to calculate the instability dynamics, thus only considering the changes in time delay parameters caused by the loss, failing to reflect the performance degradation and flow field changes caused by the loss, and cannot be used for three-dimensional numerical simulation of compression systems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a three-dimensional blade tip clearance model for compressive system stability calculation. In the process of compressive system stability calculation, the calculated geometric features and pressure rise characteristics can be correlated with the inlet and outlet airflow parameters of the blade row in the blade tip vortex region, thereby realizing the influence of blade tip clearance in the three-dimensional numerical simulation of the compressive system.

[0005] To achieve the above-mentioned technical effects, the technical solution adopted by the present invention is as follows:

[0006] A method for constructing a three-dimensional tip clearance model for compressive system stability calculation is proposed, which calculates the geometric characteristics and pressure rise characteristics of the tip vortex based on the geometric characteristics of the planar blade cascade at the blade tip, the inlet and outlet airflow angles, and the pressure rise characteristics.

[0007] Furthermore, the construction method includes the following steps:

[0008] Step S1: Calculate the Zweifel efficiency, i.e. the dimensionless pressure difference between the two sides of the blade, based on the inlet and outlet airflow angles of the planar blade cascade at the blade tip.

[0009] Step S2: Based on the geometric characteristics of the planar blade cascade at the blade tip, the inlet and outlet airflow angles and pressure rise characteristics, and the calculated Zweifel efficiency, calculate the geometric characteristics and pressure rise characteristics of the blade tip vortex respectively.

[0010] The geometric characteristics of a tip vortex include the angle between the airflow direction within the tip vortex and the blade, as well as the cross-sectional radius of the tip vortex.

[0011] Furthermore, the method for calculating the angle between the airflow direction in the tip vortex and the blade is as follows: calculate the lift coefficient of the planar blade cascade based on the Zweifel efficiency, and calculate the angle between the airflow direction in the tip vortex and the blade based on the obtained lift coefficient of the planar blade cascade.

[0012] Furthermore, the angle between the airflow direction within the tip vortex and the blade. The lift coefficient of the planar blade cascade ,in, It is the dimensionless pressure difference across the blade, i.e., the Zweifel efficiency; It is the inlet airflow angle of the planar blade cascade. It is the outlet airflow angle of the planar blade cascade.

[0013] Furthermore, the dimensionless pressure difference across the blades ,in It is the blade spacing, It is the axial chord length of the blade row. It is the inlet airflow angle of the planar blade cascade. It is the outlet airflow angle of the planar blade cascade.

[0014] Furthermore, the cross-sectional radius of the tip vortex ,in The angle between the airflow direction within the tip vortex and the blade. It is the thickness of the tip jet, that is, the width of the tip gap; This is the distance from the vertical projection point of the tip vortex onto the blade to the leading edge of the blade.

[0015] Furthermore, the pressure rise characteristic within the tip vortex is defined as the total-static pressure rise coefficient. ,in It is the total static pressure rise coefficient of the planar blade cascade at the blade tip. The dimensionless pressure difference across the blades is calculated based on the inlet and outlet airflow angles of the planar blade cascade. It is the jet flow rate coefficient. The flow coefficient at the inlet of the blade exhaust is . It is the outlet airflow angle of the planar blade cascade.

[0016] Compared with the prior art, the beneficial effects of this invention are:

[0017] 1. This invention can calculate the direction, size, and pressure rise characteristics of the tip vortex based on the known geometry, inlet and outlet airflow angle correlation, and pressure rise characteristics of the planar blade cascade at the blade tip. During the stability calculation of the compression system, the calculated geometric features and pressure rise characteristics can be correlated with the inlet and outlet airflow parameters of the blade row within the tip vortex region, thereby reflecting the influence of the tip clearance in the three-dimensional numerical simulation of the compression system.

[0018] 2. This invention can be used to model the blade row in the three-dimensional numerical simulation of the compression system and reflect the influence of the blade tip clearance on the performance, stability boundary and stall initiation process of the compression system, thereby being used for the stability calculation of the compression system. Attached Figure Description

[0019] Figure 1a The curves showing the correlation between the inlet and outlet airflow angles at the blade tip and within the tip vortex of the rotor in Example 2;

[0020] Figure 1b The curves showing the correlation between the inlet and outlet airflow angles at the blade tip and within the blade tip vortex of the stator in Example 2;

[0021] Figure 2a The total-static pressure rise characteristic curves at the blade tip and within the blade tip vortex of the rotor in Example 2 under different inlet airflow angles are shown.

[0022] Figure 2b The total-static pressure rise characteristics at the blade tip and within the blade tip vortex of the stator in Example 2 under different inlet airflow angles;

[0023] Figure 3 The total-static pressure rise characteristic curves of the compressor stage in Example 2 under different blade tip clearances are shown.

[0024] Figure 4 This is a schematic diagram of the pressure distribution at different moments in the rotor outlet section during the stall process without blade tip clearance in Example 2;

[0025] Figure 5 This is a schematic diagram of the pressure distribution at different times at the rotor outlet section during the 1% blade tip clearance stall process in Example 2. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0027] Example 1

[0028] A method for constructing a three-dimensional tip clearance model for compressive system stability calculation is proposed, which calculates the geometric characteristics and pressure rise characteristics of the tip vortex based on the geometric characteristics of the planar blade cascade at the blade tip, the inlet and outlet airflow angles, and the pressure rise characteristics.

[0029] The calculation process includes the following steps:

[0030] Step S1: Calculate the Zweifel efficiency, i.e. the dimensionless pressure difference between the two sides of the blade, based on the inlet and outlet airflow angles of the planar blade cascade at the blade tip.

[0031] Step S2: Based on the geometric characteristics of the planar blade cascade at the blade tip, the inlet and outlet airflow angles and pressure rise characteristics, and the calculated Zweifel efficiency, calculate the geometric characteristics and pressure rise characteristics of the blade tip vortex respectively.

[0032] The geometric characteristics of a tip vortex include the angle between the airflow direction within the tip vortex and the blade, as well as the cross-sectional radius of the tip vortex.

[0033] In this embodiment, based on the known geometry, inlet and outlet airflow angle correlation, and pressure rise characteristics of the planar blade cascade at the blade tip, the direction, size, and pressure rise characteristics within the blade tip vortex can be calculated. During the stability calculation of the compression system, the calculated geometric features and pressure rise characteristics can be correlated with the inlet and outlet airflow parameters of the blade row within the blade tip vortex region, thereby reflecting the influence of the blade tip clearance in the three-dimensional numerical simulation of the compression system. For example, in the three-dimensional numerical simulation of the compression system, the inlet and outlet airflow angle correlation and pressure rise characteristics of the blade row are used to correlate the inlet and outlet airflow parameters of the blade row, and the width of the blade tip region is... The calculated airflow angle correlation and pressure rise characteristics within the tip vortex are used to reflect the influence of tip clearance on the performance, stability boundary and stall initiation process of the compression system, and thus it is used for compression system stability calculation.

[0034] Example 2:

[0035] The method for constructing a three-dimensional blade tip clearance model for stability calculation of a compression system includes the following steps:

[0036] Phase 1: Calculating the geometric characteristics of tip vortices:

[0037] Step 1. Calculate the Zweifel efficiency based on the inlet and outlet airflow angles of the planar blade cascade. Where Zw is the dimensionless pressure difference across the blade. and These are the average pressures on the pressure surface and the suction surface, respectively. It is the relative total pressure at the inlet. It is the outlet static pressure;

[0038] In this embodiment, based on the assumptions of non-adhesive and thin blades, the Zweifel efficiency can be given by the airflow angle:

[0039] ,in It is the blade spacing, It is the axial chord length of the blade row. and These are the inlet and outlet airflow angles, respectively.

[0040] Step 2. Calculate the lift coefficient of the planar blade cascade:

[0041] In this embodiment, based on the inviscid assumption, the lift coefficient can be estimated by the Zweifel efficiency.

[0042] Step 3. Calculate the angle between the airflow direction within the tip vortex and the blade.

[0043] Step 4. Calculate the cross-sectional radius of the tip vortex:

[0044] In this embodiment, the tip vortex is modeled as a semi-cylindrical ideal vortex, and its cross-sectional radius is:

[0045]

[0046] in It is the thickness of the tip jet, that is, the width of the tip gap; It is the coordinate along the blade direction, that is, the distance from the vertical projection point of the tip vortex on the blade to the leading edge of the blade.

[0047] Phase Two: Calculating the Pressure Rise Characteristics within the Tip Vortex

[0048] First, define the total-static pressure rise coefficient. ,in For the static pressure at the blade outlet, For the total pressure at the entrance, For the density at the entrance, Let be the entrainment velocity at the mid-diameter of the rotor blade; define the flow coefficient at the blade inlet as . ,in For traffic, This refers to the cross-sectional area of ​​the flow passage at the import point. The axial velocity at the inlet.

[0049] If we assume no loss, the velocity component perpendicular to the chord length when the tip vortex leaves the blade...

[0050] Assuming that the tip jet experiences instantaneous shear with the mainstream immediately upon leaving the blade, resulting in a certain total pressure loss, and then immediately mixes into the mainstream, the subsequent pressure rise characteristics are the same as those of a planar blade cascade. Using the jet flow coefficient... Reflecting the above total pressure loss, the true... for ;therefore, The total pressure loss caused by the loss is

[0051]

[0052] Based on the inviscid assumption, the pressure difference across the blade can be written as:

[0053]

[0054] Therefore, the total static pressure rise coefficient within the tip vortex is: ,in It is the total static pressure rise coefficient of the planar blade cascade at the blade tip. This is the Zweifel efficiency calculated previously. This is the jet flow coefficient, which can be taken from the potential flow calculation results of Heyes et al. (Heyes F.JG, Hodson HP, Dailey GM. The Effect of Blade Tip Geometry on the TipLeakage Flow in Axial Turbine Cascades). ,but .

[0055] Using the three-dimensional tip clearance model constructed in this embodiment, the correlation of airflow angles within the rotor and stator tip vortices in a low-pressure compressor stage was calculated and compared with the correlation of inlet and outlet airflow angles of the planar blade cascade at the blade tip. Figure 1a , Figure 1b As shown in the figure, the outlet airflow angle in the blade tip vortex is always greater than that in the mainstream region. As the inlet airflow angle increases, the airflow in the mainstream region separates, and the outlet airflow angle in the mainstream region increases significantly. At this time, due to the slowing upward trend of lift, the rise of the outlet airflow angle of the blade tip vortex slows down, or even decreases.

[0056] Figure 2a and Figure 2b The total-static pressure rise characteristics of a planar blade cascade, as well as the total-static pressure rise characteristics within the tip vortex under different inlet airflow angles, are presented. It is evident that as the inlet airflow angle increases, the losses caused by the tip vortex also increase, leading to a decrease in the total-static pressure rise coefficient within the tip vortex.

[0057] The flow within the airflow channels before and after the blade assembly is calculated using the Euler equation solver. The airflow parameters at the blade assembly inlet and outlet are correlated using airflow angle correlation and pressure rise characteristics, thus simulating the compressor stage operation and obtaining the total-static pressure rise characteristics of the stage with different tip clearance widths. (See...) Figure 3The width of the tip clearance is measured as a percentage of the blade passage height. It is evident that the introduction of tip clearance reduces the pressure ratio and shifts the stability boundary to the right during stable stage operation, and this trend increases with increasing tip clearance. The curve corresponding to the "experiment" was obtained on a single-stage compressor with a tip clearance width of 2 mm, approximately 1% of the passage height, and a rotational speed of 1500 rpm.

[0058] Figure 4 and Figure 5 The pressure distribution (in kPa) at the rotor outlet section at different times during stall is shown for both zero clearance and 1% clearance conditions. It can be seen that in the zero clearance condition, the stall cluster is a single cluster occupying about 50% of the circumferential space; in the clearance condition, the stall cluster splits into three, and the radial height occupied is reduced.

[0059] The numerical experiments described above show that the tip clearance model in this embodiment can calculate the inlet and outlet airflow angle correlation and pressure rise characteristics of the tip vortex, and its performance is consistent with the actual physical mechanism; it can be used for three-dimensional numerical calculation of compression systems and can reflect the influence of tip clearance on the stability boundary and stall initiation process.

[0060] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constructing a three-dimensional tip clearance model for stability calculation of a compression system, characterized in that, Based on the geometric characteristics of the planar blade cascade at the blade tip, the inlet and outlet airflow angles, and the pressure rise characteristics, the geometric characteristics and pressure rise characteristics of the blade tip vortex are calculated; the construction method includes the following steps: Step S1: Calculate the Zweifel efficiency, i.e. the dimensionless pressure difference between the two sides of the blade, based on the inlet and outlet airflow angles of the planar blade cascade at the blade tip. Step S2: Based on the geometric characteristics of the planar blade cascade at the blade tip, the inlet and outlet airflow angles and pressure rise characteristics, and the calculated Zweifel efficiency, calculate the geometric characteristics and pressure rise characteristics of the blade tip vortex respectively. The geometric characteristics of a tip vortex include the angle between the airflow direction within the tip vortex and the blade, as well as the cross-sectional radius of the tip vortex; the pressure rise characteristic within the tip vortex is defined as the total-static pressure rise coefficient. ,in It is the total static pressure rise coefficient of the planar blade cascade at the blade tip. The dimensionless pressure difference across the blades is calculated based on the inlet and outlet airflow angles of the planar blade cascade. It is the jet flow rate coefficient. The flow coefficient at the inlet of the blade exhaust is . It is the outlet airflow angle of the planar blade cascade.

2. The method for constructing a three-dimensional tip clearance model for compressive system stability calculation according to claim 1, characterized in that, The method for calculating the angle between the airflow direction within the blade tip vortex and the blade is as follows: The lift coefficient of the planar blade cascade is calculated based on the Zweifel efficiency. Based on the lift coefficient of the planar blade cascade, the angle between the airflow direction in the tip vortex and the blade is calculated.

3. The method for constructing a three-dimensional tip clearance model for compressive system stability calculation according to claim 2, characterized in that, The angle between the airflow direction within the tip vortex and the blade. The lift coefficient of the planar blade cascade ,in, It is the dimensionless pressure difference across the blade, i.e., the Zweifel efficiency; It is the inlet airflow angle of the planar blade cascade. It is the outlet airflow angle of the planar blade cascade.

4. The method for constructing a three-dimensional tip clearance model for stability calculation of a compression system according to any one of claims 2-3, characterized in that, Dimensionless pressure difference across the blade ,in It is the blade spacing, It is the axial chord length of the blade row. It is the inlet airflow angle of the planar blade cascade. It is the outlet airflow angle of the planar blade cascade.

5. The method for constructing a three-dimensional tip clearance model for calculating the stability of a compression system according to claim 1, characterized in that, Cross-sectional radius of the tip vortex ,in The angle between the airflow direction within the tip vortex and the blade. It is the thickness of the tip jet, that is, the width of the tip gap; This is the distance from the vertical projection point of the tip vortex onto the blade to the leading edge of the blade.

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