Effects of tip clearance on non-synchronous aerodynamic excitation of compressor rotor blades

The unstable tip flow of compressor rotor may cause the aeroelastic problems, inducing the non-synchronous vibration with high amplitude level, which has a significant effect on blade high cycle fatigue and safety. In order to investigate the effects of tip clearance on non-synchronous aerodynamic excitation of compressor rotor blades, the full annular numerical simulations were conducted for the unsteady flow field of a 1.5-stage compressor under near stall conditions. The frequency characteristics of non-synchronous aerodynamic excitation and tip unstable flow structure were analysed for different tip clearances (0.5%C, 1.0%C, 2.0%C, and 3.0%C). The results showed that the frequency and amplitude are strongly influenced by the tip clearance size. For 0.5%C tip clearance, the main frequency of non-synchronous aerodynamic excitation is the low-frequency aerodynamic excitation frequency, which is mainly caused by tornado-like vortex in the tip suction side, the dominant aerodynamic disturbance mode number is 19. For 2.0%C and 3.0%C tip clearance, the dominant aerodynamic disturbance mode number is 47, and the main aerodynamic excitation frequency is high frequency non-synchronous aerodynamic excitation frequency, mainly caused by the shedding vortices propagating circumferentially at the blade tip, exhibiting the feature of “rotating instability”.


Introduction
The compressor is the core component of an aircraft engine, as the increasing aerodynamic load of high-performance compressor, the tangential velocity of the blade tip is increasing, making the blades more susceptible to unsteady flow excitation in the flow field, ultimately leading to prominent flow induced vibration problem.In recent years, a new problem of flow induced vibration non-synchronous vibration (NSV) has been reported by many scholars [1][2][3][4][5].The unstable flow at the blade tip is considered an important factor inducing NSV, and the tip clearance has a significant impact on the development of tip unstable flow.Therefore, it has great significance to study the effect of tip clearance (TC) on the non-synchronous aerodynamic excitation of compressor rotor blades.
The size and shape of tip clearance have a significant effect on tip flow.The tip clearance not only affects the leakage flow, but also changes the flow structure in the passage.Wear, corrosion, dirt, and other factors may change the blade tip clearance [6]，especially in near stall conditions, it may lead to the occurrence of NSV.In recent years, many studies have focused on the tip region unsteady flow of NSV.Vo considers that rotational instability is caused by the impact of tip clearance reflux on the pressure surface behind the blade [7].Drolet studied the effects of tip clearance size and operating temperature on prediction of critical NSV speed, and proposed a new method to improve prediction of the critical speed [8].Im used the unsteady Reynolds averaged Navier-Stokes (URANS) model to simulate a 1.5-stage compressor and studied the effects of three types of blade tip clearances on NSV.The results showed that the size and shape of tip clearance have a significant effect on the frequency and amplitude of NSV, and the tornado-like tip vortex oscillating along the flow direction is the main cause of NSV [9].In 2014, he further validated this viewpoint using the delayed detached eddy simulation (DDES) model [10].Espinal conducted a full annular numerical simulation of a 1.5-stage compressor and found that NSV is a full annular phenomenon, with unstable vortices in circumferential motion near the rotor blade tip being the main cause of NSV [11].Patel used the scale adaptive simulation (SAS) turbulence model for NSV simulation, and the simulation results is in good agreement with the experiment.Research has shown that the vortex shedding from the leading edge (LE) leads to NSV [12].Stapelfeldt believes that under highly throttled conditions, the tip leakage flow blocks the passage and causes the disturbance, which propagates circumferentially in the LE plane, will lead to NSV [13].Patel conducted an NSV study using the improved delayed detached eddy simulation (IDDES), and he believes that the tip vortex in the upper 75% span of the rotor passage moves in a circumferential direction, resulting in NSV [14].Yang used the URANS model to study the compressor under near stall conditions.A possible cause of RI was proposed: the spiral breakdown of the tip leakage vortex at different positions resulted in a cross-passage structure, which propagates into circumferential direction [15].
The above research indicates that there is an important connection between NSV and the unsteady flow in the tip clearance region.These literatures tend to study how tip clearance flow affects NSV, and there is less research on the effect of tip clearance on the non-synchronous aerodynamic excitation.Moreover, most studies have not used full annular numerical simulation, making it difficult to simulate the circumferential unsteady flow characteristics.This paper conducted a full annular numerical simulation to study the unsteady flow field of a 1.5-stage compressor under near stall conditions.The unsteady flow characteristics and instability aerodynamic excitation of four types of blade tip clearances were compared and analyzed, revealing the mechanism of the influence of blade tip clearance on the non-synchronous aerodynamic excitation of rotor blades.

Research object and numerical model
The research object is a 1.5-stage compressor, with blade numbers of 52 (IGV), 47 (R1), and 68 (S1).To investigate the effect of tip clearance on non-synchronous aerodynamic excitation, four types of blade tip clearance values were selected for numerical simulation.The tip clearance values were 0.5%, 1.0%, 2.0%, and 3.0% times the tip chord length, abbreviated as 0.5%C, 1.0%C, 2.0%C, and 3.0%C.The numerical simulation is completed using ANSYS CFX, and k-ε turbulence model is used to solve the computational domain.The wall function is used to handle the flow near the wall area.This method ensures calculation accuracy while reducing the amount of mesh.NSV is a phenomenon caused by unstable flow circumferential propagation, therefore, a full-annulus passage model is used to capture the circumferential unsteady flow of non-blade periods.The full-annulus passage mesh is copied from the circumferential direction of the single passage, the full-annulus mesh is shown in figure 1.The total number of full-annulus passage mesh after mesh independence verification is about 3.5 × 10 7 .The inlet boundary is a constant total temperature and total pressure, the outlet boundary condition is a constant static pressure, and the wall boundary is set as a non-slip, adiabatic solid wall boundary condition.The transient calculation uses the steady-state results as the initial flow field, with a transient time step of 0.000004s, which is less than 1/30 of the time for a rotor to rotate one passage.Figure 3 shows time history of the outlet mass flow rate for 0.5%C tip clearance.In this study, the unsteady solutions between 6 and 20 rotor revolutions are used for frequency analysis since the predicted mass flows show periodic oscillations roughly.Meanwhile, all of the static pressure presented and used for frequency analysis in this study is normalized by the IGV inlet dynamic pressure.

Results and discussion
The Spatial Fast Fourier Transform (SFFT) was used to analyze the circumferential mode number of aerodynamic disturbance.The SFFT result was performed on circumferential pressure signals with different spans, and 2048 data were taken in the circumferential direction for analysis to improve the accuracy of pulsation signal data, as shown in figure 4. For 0.5%C and 1.0%C tip clearances, the circumferential modal number is 19 at different spans.For 0.5%C tip clearance, the amplitude of 19 modes order is significantly higher than that of 47.For 1.0%C tip clearance, the amplitude of modal number 19 decreases.For 2.0%C and 3.0%C tip clearances, there are also low mode number disturbances, but the amplitude is relatively low.At this time, the disturbances in the flow field are still mainly caused by the rotor blades; Comparing the SFFT results for different spans, it found that the amplitude of the 90% span curve is basically the highest, indicating that the 90% span is closer to the strong non-blade periods disturbance source in the flow field.Therefore, when conducting subsequent Fast Fourier Transform (FFT) studies, the pressure signal comes from the probes located at 90% span.SFFT results at50% SW of R1. Figure 5 shows FFT results at 90% span near LE for 0.5%C tip clearance (in relative frame).The pressure fluctuations of each passage are very similar with the same frequency.Therefore, the probes located at passage of blade 1 will be used for subsequent comparative analysis.Figure 6 shows the frequency spectral of the pressure signal at 90% span.For 0.5%C and 1.0%C tip clearances, there is a significant low frequency about 1.4EO (engine order), and the amplitude of LE is significantly higher than that of 30% SW and 80% SW, indicating that the non-synchronous aerodynamic excitation source in the flow field is mainly located at the leading edge.For 1.0%C tip clearance, the low-frequency spectrum is more abundant and the amplitude of 1.4EO is 35% lower than that at tip clearance of 0.5%C; For 2.0%C and 3.0%C tip clearances, the frequencies of non-synchronous aerodynamic excitation are greater than 20EO.Meanwhile, the amplitudes of 30% and 80% SW are higher, indicating that the main non-synchronous aerodynamic excitation source is located in the passage. .FFT results at 90% span (in relative frame).Figure 7 shows the frequency spectral of the probes located at LE near the casing wall.For 0.5%C tip clearance, the amplitude of 17.57EO is significantly higher than that of 47EO.For 1.0%C tip clearance, there is also a non-synchronous aerodynamic excitation of the same frequency here, with a certain decrease in amplitude, and a new non-synchronous aerodynamic excitation (23.86EO) appears in the flow field.For 2.0%C tip clearance, the frequency of non-synchronous aerodynamic excitation is 36.53EO,and the amplitude is small; For 3%C tip clearance, the frequency of non-synchronous aerodynamic excitation changes to 26.67EO and the amplitude increases.It can summary that the size of tip clearance significantly affects the frequency and amplitude of non-synchronous aerodynamic excitation.During the process of increasing tip clearance from 0.5%C to 3.0%C, the amplitude of non-synchronous aerodynamic excitation first decreases and then increases, indicating the existence of an optimal tip clearance, where the impact of non-synchronous aerodynamic excitation is minimal.Among the four tip clearances studied, 2.0%C is the optimal value, the amplitude of non-synchronous aerodynamic excitation is the smallest, and the spectral information is relatively single, which is conducive to avoiding NSV during design.The relative Mach number contours at rotor 95% span are shown in figure 8. Figure 9 shows the vorticity contours at 95% span.For 0.5%C and 1.0%C tip clearances, the flow in each passage is extremely different, and the flow field has obvious circumferential non-uniformity.For 2.0%C and 3.0%C tip clearances, the flow field similarity between passages is very high.The flow field distribution of the four tip clearances has the following commonalities: The low velocity zones in the flow field are divided into two parts, one part is caused by leakage flow, starting from the leading edge of the blade, gradually occupying the middle of the passage, and the other part is caused by the separation of the suction surface boundary layer, gradually interacting with the leakage flow in the process of developing towards the middle of the passage; The areas with high vorticity value are mainly located at the leading edge of the rotor, caused by leakage vortex at the leading edge, and a small portion are located at the trailing edge of the blade, originating from the flow mixing of the pressure surface and suction surface.When the leading edge leakage vortex travels along the flow direction, it will suck up the surrounding airflow and interact with the tip leakage flow and mainstream flow, gradually expanding its influence range and weakening the vortex strength; The vorticity value in the area affected by the leading edge leakage flow is higher than that in the boundary layer separation area of the suction surface, indicating that the leading edge leakage vortex is an important cause of flow instability.For tip clearance of 0.5%C, the airflow distribution difference between passages is the largest.The vorticity value near the suction surface boundary layer is not high, which indicates that the airflow disturbance here is weak.The flow distribution in 1.0%C tip clearance is similar to that in 0.5%C tip clearance, and there is significant unsteady flow in each passage, but the distribution difference between passages is weakened; When tip clearance increases to 2.0%C, the vorticity value at the leading edge decreases, and the vorticity value in the passage is generally higher.When tip clearance is 3.0%C, the flow consistency between different passages is higher, and the vorticity at the leading edge is enhanced to a certain extent.The distribution of the flow field in each passage is highly consistent.The intensity of the vortex in the passage with a frequency equal to the passing frequency of the rotor blade is greater, and in practice, the probes at LE feels more obvious disturbance, the amplitude of R1-BPF is higher, which is consistent with the results in figure 7.
Figure 10 shows 3D streamline near tip region with streamline starting from the first tip clearance.For tip clearance of 0.5%C, the disturbance of tip leakage flow is strong, and the leakage flow forms tornado-like vortex in the passage, which is very different from the common streamwise tip clearance vortex.The tornado-like vortex wake adheres closely to the blade surface, causing damage to the flow near blade surface.Tornado-like vortex also exists in passages with a 1.0%C tip clearance, but its strength is weaker.It should be noted that the tornado tip vortex does not exist in each blade passage, which leads to strong circumferential non-uniform flow；For tip clearance of 2.0%C and 3.0%C, there is no tornado-like vortex in the passages, and the flow in each passage is very similar.The leakage flow near the leading edge forms a leading edge leakage vortex during its travel, and the leakage flow at the rear is sucked together with the mainstream fluid under shear, forming an induced vortex.The leakage vortex and induced vortex intersect with each other in the passage, and rupture occurs at the intersection, resulting in a large amount of low-energy fluid that forms a passage vortex during moving along the flow direction.As tip clearance increases, the space for leakage flow to enter the next passage is larger, and the entrainment capacity of the passage vortex is weaker compared to tornado-like vortex.Therefore, more leakage flow can cross the passage and enter the next passage, participating in the synthesis of vortex in the next passage.Figure 11 shows surface streamlines near suction surface.For 0.5%C tip clearance, due to the presence of tornado-like vortex, the flow near suction surface is significantly disrupted, and there is a noticeable vortex-like streamline at the intersection of tornado-like vortex wake and blade surface.For 1.0%C tip clearance, this phenomenon also exists near the blade surface, as the weakening of tornado-like vortex, the damage to the flow near suction surface has been reduced.For 2.0%C and 3.0%C tip clearance, there is no tornado-like vortex here, the streamlines separation phenomenon near suction surface basically disappears, and the similarity of streamlines distribution near different blade is high.

Conclusions
The frequency and amplitude are strongly influenced by the tip clearance size, there exists an optimal tip clearance where the impact of non-synchronous aerodynamic excitation is minimal.Among the four tip clearances, 2.0%C is the optimal value, the amplitude of non-synchronous aerodynamic excitation is the smallest, and the spectral information is relatively single, which is conducive to avoiding NSV during design.
Under near stall conditions, for 0.5%C tip clearance, the main frequency of non-synchronous aerodynamic excitation is the low-frequency aerodynamic excitation frequency, which is mainly caused by tornado-like vortex in the suction surface tip area.The dominant aerodynamic disturbance mode number is 19.For 2.0%C and 3.0%C large tip clearances, the dominant aerodynamic disturbance mode number is 47, and the main aerodynamic excitation frequency is high-frequency non-synchronous aerodynamic excitation frequency, mainly caused by the shedding vortices propagating circumferentially at the blade tip, exhibiting the feature of "rotating instability".

Figure 1 .
Figure 1.Computational mesh.During the unsteady simulation, a series of numerical probes are arranged in the circumferential and axial directions to obtain time-domain pressure signals in the flow field.The position distribution of each probe is shown in figure 2. The three probes for flow direction are located at the leading edge, 30% streamwise (SW), and 80% SW, to record the pressure pulsation on the rotor surface (in relative frame).Meanwhile, numerical probes were set at different passages and different span positions, according to the distribution in figure 2.

Figure 2 .
Figure 2. Numerical probes of the compressor.Figure3shows time history of the outlet mass flow rate for 0.5%C tip clearance.In this study, the unsteady solutions between 6 and 20 rotor revolutions are used for frequency analysis since the predicted mass flows show periodic oscillations roughly.Meanwhile, all of the static pressure presented and used for frequency analysis in this study is normalized by the IGV inlet dynamic pressure.

Figure 3 .
Figure 3. History of the outlet mass flow for 0.5%C tip clearance.

Figure 4 .
Figure 4. SFFT results at50% SW of R1.Figure5shows FFT results at 90% span near LE for 0.5%C tip clearance (in relative frame).The pressure fluctuations of each passage are very similar with the same frequency.Therefore, the probes located at passage of blade 1 will be used for subsequent comparative analysis.

Figure 5 .
Figure5.FFT results at 90% span near LE for 0.5%C tip clearance.Figure6shows the frequency spectral of the pressure signal at 90% span.For 0.5%C and 1.0%C tip clearances, there is a significant low frequency about 1.4EO (engine order), and the amplitude of LE is significantly higher than that of 30% SW and 80% SW, indicating that the non-synchronous aerodynamic excitation source in the flow field is mainly located at the leading edge.For 1.0%C tip clearance, the low-frequency spectrum is more abundant and the amplitude of 1.4EO is 35% lower than that at tip clearance of 0.5%C; For 2.0%C and 3.0%C tip clearances, the frequencies of non-synchronous aerodynamic excitation are greater than 20EO.Meanwhile, the amplitudes of 30% and 80% SW are higher, indicating that the main non-synchronous aerodynamic excitation source is located in the passage.

Figure 6
Figure 6.FFT results at 90% span (in relative frame).Figure7shows the frequency spectral of the probes located at LE near the casing wall.For 0.5%C tip clearance, the amplitude of 17.57EO is significantly higher than that of 47EO.For 1.0%C tip clearance, there is also a non-synchronous aerodynamic excitation of the same frequency here, with a certain decrease in amplitude, and a new non-synchronous aerodynamic excitation (23.86EO) appears in the flow field.For 2.0%C tip clearance, the frequency of non-synchronous aerodynamic excitation is 36.53EO,and the amplitude is small; For 3%C tip clearance, the frequency of non-synchronous aerodynamic excitation changes to 26.67EO and the amplitude increases.It can summary that the size of tip clearance significantly affects the frequency and amplitude of non-synchronous aerodynamic excitation.During the process of increasing tip clearance from 0.5%C to 3.0%C, the amplitude of non-synchronous aerodynamic excitation first decreases and then increases, indicating the existence of an optimal tip clearance, where the impact of non-synchronous aerodynamic excitation is minimal.Among the four tip clearances studied, 2.0%C is the optimal value, the amplitude of non-synchronous aerodynamic excitation is the smallest, and the spectral information is relatively single, which is conducive to avoiding NSV during design.

Figure 7 .
Figure 7. FFT results at LE of R1 near shroud (in absolute frame).The relative Mach number contours at rotor 95% span are shown in figure8.Figure9shows the vorticity contours at 95% span.For 0.5%C and 1.0%C tip clearances, the flow in each passage is extremely different, and the flow field has obvious circumferential non-uniformity.For 2.0%C and 3.0%C tip clearances, the flow field similarity between passages is very high.The flow field distribution of the four tip clearances has the following commonalities: The low velocity zones in the flow field are divided into two parts, one part is caused by leakage flow, starting from the leading edge of the blade, gradually occupying the middle of the passage, and the other part is caused by the separation of the suction surface boundary layer, gradually interacting with the leakage flow in the process of developing towards the middle of the passage; The areas with high vorticity value are mainly located at the leading edge of the rotor, caused by leakage vortex at the leading edge, and a small portion are located at the trailing edge of the blade, originating from the flow mixing of the pressure surface and suction surface.When the leading edge leakage vortex travels along the flow direction, it will suck up the surrounding airflow and interact with the tip leakage flow and mainstream flow, gradually expanding its influence range and weakening the vortex strength; The vorticity value in the area affected by the leading edge leakage flow is higher than that in the boundary layer separation area of the suction surface, indicating that the leading edge leakage vortex is an important cause of flow instability.

Figure 10 .
Figure 10.3D streamlines near tip region.Figure11shows surface streamlines near suction surface.For 0.5%C tip clearance, due to the presence of tornado-like vortex, the flow near suction surface is significantly disrupted, and there is a noticeable vortex-like streamline at the intersection of tornado-like vortex wake and blade surface.For 1.0%C tip clearance, this phenomenon also exists near the blade surface, as the weakening of tornado-like vortex, the damage to the flow near suction surface has been reduced.For 2.0%C and 3.0%C tip clearance, there is no tornado-like vortex here, the streamlines separation phenomenon near suction surface basically disappears, and the similarity of streamlines distribution near different blade is high.