Rotor boundary layer development in a two-stage compressor

The unsteady flow field around and in the wakes of the rotor and stator blades embedded within a multistage turbomachine is dominated by the interaction of the upstream rotor and stator wakes with the downstream blades and wakes. These interactions have a significant impact on the vibration and acoustic characteristics of the machinery and on the boundary layer transition of the blades. Therefore, obtaining reliable and detailed experimental data on the interaction of the rotor and stator blades in a multistage turbomachine is critical not only for understanding the physical mechanisms involved but also for the development of reliable and accurate computational methods.

The performance of a turbomachine depends strongly on the behavior of the nominally two-dimensional boundary layer over the blade suction surfaces. Axial compressors rely fundamentally on aerodynamic diffusion to achieve a pressure rise. Since the adverse pressure gradients associated with diffusion become strong at the high loading levels of modern designs, boundary layers tend to separate. This has a negative impact on the stall margin and pressure rise capability. In addition, the boundary layer behavior influences the efficiency and loss of the whole compressor.^1,2

The development of unsteady boundary layers on turbomachinery blades is influenced significantly by the laminar-to-turbulent transition.^3,4 The transition process^5,6 is complicated by the unsteadiness of the flow in a multistage turbomachine. For attached flow with low freestream turbulence levels, the transition process proceeds via the natural transition route. Selective frequencies of background disturbances are gradually amplified, generating two-dimensional Tollmien–Schlichting (TS) waves, which develop three-dimensional secondary instabilities. Local flow breakdown occurs in regions of high shear, forming turbulent spots, which grow and coalesce into a fully turbulent boundary layer.⁷ In many turbomachinery flows, this natural transition route is bypassed by other mechanisms; nevertheless, the TS instability can play an important role in the ultimate breakdown to transition, particularly in compressors. In a more realistic environment, the bypass transition is more common in turbomachines. Turbulent spots are formed directly owing to the high freestream turbulence intensity and upstream wakes, and they then spread and convect downstream, merging to turbulence.⁸ In strongly decelerating flow, a laminar boundary layer will separate from the surface.^9,10 In a similar manner to inflectional attached boundary layers, the separated shear layer exhibits inviscid instability due to the strongly inflectional profile. This instability is referred to as the Kelvin–Helmholtz (KH) instability because of the similarities with a free shear layer, and it tends to drive the roll-up of the separated shear layer into coherent vortices, which finally break down to turbulence. This transition route is called the separation transition.¹¹ Owing to the complex flow environment in a turbomachine, all three transition routes exist and are observed in experiments.

In a multistage turbomachine environment, the upstream wakes are chopped into segments as they pass through rotor and stator blade rows.^12,13 The wake segments are then transported through the rotor–stator gaps and blade passages, while interacting with wakes generated by other blades as well as with the boundary layers of the blades themselves.^14,15 In the absolute (stator) frame of reference, the wakes have a lower velocity than the freestream flow; in the relative (rotor) frame of reference, this velocity deficit may be considered as a negative jet superimposed onto the freestream flow. As the stator wakes convect through the downstream rotor passage in the turbine,¹⁶ they impinge on the suction surface boundary layer, causing the freestream velocity to first increase and then decrease. In addition to this large-scale velocity perturbation, the negative jet transports the turbulent wake fluid to the edge of the boundary layer. These disturbances periodically induce early transition in the boundary layer, a process typically referred to as the wake-induced transition.^17,18 In addition to the wakes arriving from the blade row immediately upstream, the background turbulence is also high in a turbomachine. The transition process in the suction surface boundary layer is therefore multimodal and periodic in time.

Numerous numerical and experimental studies have already focused on blade–wake and wake–wake interactions in turbines and compressors.^19–24 Both the velocity deficit and the high level of turbulence within the incoming wakes can change the boundary layer behavior of the downstream blade. For an attached flow, the direct numerical simulation (DNS) results of Wu et al.²⁵ showed that the fluid structures generated by the wake are similar to those involved in the bypass transition. The wake-induced structure stretches into a streaky structure as it convects downstream at a fraction of the mainstream velocity. The convection rates of the leading and trailing edges of the streak are similar to those of the leading and trailing edge of a turbulent spot in the zero pressure gradient. Zhong et al.²⁶ also found the formation of turbulent spots with wake impingement using a thermally sensitive liquid crystal. These turbulent spots coalesce into a wake-induced strip as they convect downstream along the suction surface. There is a calmed region with higher shear stresses and fuller velocity profiles following the turbulent strip.

In the context of separated flow, Hodson and Howell^27,28 obtained a number of valuable results from experimental research on the wake–blade interaction. The experimental results of Coull and Hodson²⁹ showed that the wake generates a region of amplified Klebanoff streaks, which induce a second type of disturbance in the form of short-span KH structures. Behind the wake-amplified Klebanoff streaks, a calmed region is observed. Both the turbulent strip and the calmed region are effective in suppressing flow separation. As the calmed region convects further downstream, the boundary layer separates again owing to the strong adverse pressure gradient. The boundary layer is more likely to separate in the compressor passage because of the strong adverse pressure gradient there. Hilgenfeld and Pfitzner³⁰ studied the combined effects of impinging wakes and background turbulence on the development of the suction surface boundary layer. A periodic reduction in the size of the separation bubble was observed on the suction surface. Wissink et al.³¹ found that separation was intermittently suppressed with stronger wake disturbances that triggered turbulent spots upstream of the location of separation. The interaction of a convected wake with a compressor stator blade boundary layer was investigated by Wheeler et al.³² The wake-leading edge interaction led to the formation of a thickened laminar boundary layer, within which turbulent spots formed.

Particle image velocimetry (PIV) is a whole-field technique that provides quantitative measurement and visualization of a two-dimensional velocity field.^33,34 PIV measurements of wake-blade interactions around a rotating blade in a multistage turbomachine were performed by Uzol et al.³⁵ and Chow et al.³⁶ A refractive-index-matched facility was employed to obtain an unobstructed view of the entire stage. The results showed that the boundary layer became significantly thinner, with lower momentum thickness and a more stable profile, during the upstream wake impingement. The rotor wake was sheared by the nonuniformities in the horizontal velocity distributions, which were a direct result of the discontinuities in the trajectories of the stator wake across the rotor wake. This shearing created a kink in the trajectory of the rotor wake, a quadrupole structure in the distribution of strain, regions with concentrated vorticity, high turbulence levels, and high shear stresses.³⁷ Jia et al.³⁸ studied the effects of wake strengths and the reduced frequency on unsteady boundary layer development in a low-speed axial compressor using PIV. They showed that the boundary layer displacement first became thicker owing to a negative jet effect. Then, as the disturbances developed underneath the wake, the boundary layer thickness gradually decreased.

Previous studies of wake–blade interactions have focused mainly on the boundary stationary interfaces. The boundary layer development under wake impingement over a rotating blade has not been thoroughly investigated, especially in air. Furthermore, many of the experiments on rotating blades have been performed in single-stage facilities. The effects of wake–wake interactions and multistage blade rows on downstream flow have not been extensively studied. The detailed physics of the unsteady laminar–turbulent transition and the influence of the wake–wake interaction promoted by periodic wakes in compressor blades still need experimental validation. As an unobstructed technique can be realized only in water or in single-stage turbomachines, it is necessary to develop new PIV techniques to investigate the flow in the multistage turbomachines in air. Additionally, near-wall PIV measurements^39,40 can provide the velocity distribution in the near-wall region and in the blade passage, which will be helpful in understanding the mechanism of wake–blade and wake–wake interactions.

The aim of the present work is to extend the knowledge of the complex flow and turbulence structures in multistage turbomachines. Near-wall PIV measurements were performed on the second-stage rotor blades of a two-stage compressor. The passage flow and boundary layer development of the second-stage rotor blades are studied in detail. This paper presents a description of wake–blade and wake–wake interaction processes differing from those in previous studies.

The experiments reported in this paper were conducted in a two-stage axial compressor rig that consists of four blade rows forming two similar stages. Each stage blade row had 20 rotor blades followed by 20 stator blades with C4-series airfoil. The hub and tip diameters were 375 mm and 500 mm, respectively, with a hub–tip ratio of 0.75. The designed rotational speed was 1500 rpm, and the mass flow was 2 kg/s. The chords of the rotor and stator were 35.5 mm and 36.5 mm, respectively. The rotor blade axial chord was 30 mm, and the rotor blade suction surface length S was 36.5 mm. The gap between each blade row was 5 mm. The Reynolds number, Re_2i, based on the inlet relative velocity of the second-stage rotors U_2i (42.7 m/s) and the rotor chord length, was 1.024 × 10⁵. The characteristic Mach number was obviously low, based on the inlet relative velocity, about 0.1256.

In our PIV measurement, we used the phase-lock technique to acquire images. The PIV measurement setup of the two-stage axial compressor rig is shown in Fig. 1. The light source was a 120 mJ/pulse dual-head Nd:YAG laser whose beam was expanded to generate a 1 mm thick light sheet. An endoscopic probe enabled us to introduce a laser sheet at the 50% span position of the blade. The diameter of the endoscopic laser arm was 10 mm. Three mounting holes were located at the front of the first stage rotor blades, about 300 mm. According to the location of the measurement area, we chose the most suitable mounting hole to fix the endoscopic laser arm. A double-frame 16-bit digital camera with a 2160 × 2560 sCMOS array was used to acquire two successive images of the illuminated flow. The sampling rate of the system was 10 Hz, which was too low to obtain sequential images of the flow field, and, instead, phase-lock measurements were performed at fixed intervals of the rotor blades. An initial delay generated by a DG645 digital delay/pulse generator was applied to the trigger signal generated by a shaft encoder connected with the generator rotor shaft. Consequently, we were able to acquire data at any desired rotor phase. The concentration and homogeneity with which particles are introduced into the flow is the primary factor in determining the quality of PIV images. A large quantity of smoke, with a mean particle diameter of 1 µm, was introduced in front of the compressor rig to ensure uniformity of the seeding particles in the blade passage of interest. Three hundred instantaneous measurements were collected at each phase. The processing used a final interrogation window size of 32 × 32 pixels, with a 75% overlap.

In this paper, we present data for the midspan plane and at 1500 rpm. The measurements covered the entire second-stage rotor row. Data were obtained at 20 rotor phases, with circumferential interval 0.9°, covering an entire rotor blade passage of 18°. The measurement window size was approximately 38 mm × 32 mm and covered a large proportion of the second stage rotor suction surface, giving a spatial resolution of approximately 0.1 mm, as shown in Fig. 2. The time delay dt between the firings of the two lasers was adjusted to produce a detectable displacement of the particles in the two successive images. In the present study, the time delay was 6 µs.

For stationary turbulence, the instantaneous velocity u_i(t) is separated into a time-averaged component $ui¯$ and a fluctuating component $ui′$(t),

In periodic flow, it is more appropriate to perform a decomposition relative to the phase-averaged velocity ⟨u_i(t)⟩ such that

where $ui(t)̃$ is the velocity perturbation and

is the time-mean of the phase average. The root-mean-squared (RMS) level of the fluctuation is defined for both steady and periodic flows as

For phase-locked instantaneous PIV measurements, the time-averaged and phase-averaged parameters can be calculated as follows:

where P = 20 is the number of phases, N = 300 is the number of instantaneous vector maps for each phase, x and y are the axial and lateral coordinates, respectively, and ϕ is the phase angle. The subscript i takes a value of 1 or 2, indicating the axial and almost circumferential velocity components, respectively. The coefficient $34$ in the turbulent kinetic energy (TKE) is selected to account for the contribution of the plane velocity component, assuming that this is an average of the available measured components. The phase-averaged vorticity of the z component, ⟨ω(x, y, ϕ)⟩, is also calculated.

The boundary layer integral parameters are calculated from the PIV measurement results. The displacement thickness δ^* is defined as

where δ₉₅ is the distance from the blade surface at which the velocity is 95% of the freestream velocity U_∞ and $u(y)¯$ is the time-averaged velocity.

The momentum thickness θ is defined as

For the phase-locked PIV measurements, the phase-averaged velocity profiles and integral parameters are obtained as in Eqs. (11) and (12) on replacing $u(y)¯$ by ⟨u(y)⟩.

The whole process of the wake–blade and wake–wake interactions in a wake passing period can be clearly revealed by analyzing the distributions of phase-averaged parameters and integral parameters, together with the variation of the instant velocity profiles.

We first present results on the complex flow and the turbulence structure in the second-stage rotor blades passage. Figure 3 shows the distributions of phase-averaged results at selected instants during one wake passing cycle. We choose three representative phases in a wake passing period, phases P04, P13, and P16, which correspond to no wake, a wake impinging on the blade, and a wake impinging on the rotor wake.

At phase P04, there is no wake caused by the first-stage blade rows in the measurement areas. The flow is quiet, with no distinct flow structure in the second-stage rotor blades passage. The relative velocity distribution shows that the relative velocity decreases from the passage entrance to the exit. The RMS of the velocity in the mainstream is probably about 5%. From the distributions of turbulent kinetic energy and vorticity, the turbulent kinetic energy and vorticity in the mainstream flow are relatively low and are mainly concentrated in the boundary layer and wake. In addition, the area of low momentum around the rotor blade is large at the trailing edge, which means that the boundary layer is separated. The wake of the second-stage rotor blade shedding is observed. The velocity of the wake is low compared with that of the surrounding fluid, but it has much higher turbulence intensity and turbulent kinetic energy. As many experimental results have shown, the wake is a negative jet with high turbulence.³⁸ In addition, it is observed that the vorticity of the wake is opposite around the centerline, but it is not symmetrical because the flows of the suction surface and the pressure surface at the trailing edge are not the same.

The stator wakes are transported downstream through the rotor blades passage after they have been chopped off by the rotor blades. The wake of the first-stage stator is clearly visible at phase P13. The upper black dashed line is the leading edge of the first-stage stator wake, labeled as LE, and the lower one is the trailing edge, labeled as TE. The distributions of the phase-averaged results shows that the turbulence level and turbulent kinetic energy are high in the wake compared with the mainstream flow. It is obvious that the wake is impinging on the rotor blade at phase P13. The stator wake is distorted and produces a kink structure that is caused by the interaction of the upstream wakes, outlined by the red line zone, labeled as S. The kink is also called a “turbulent hot spot”³⁷ because it is more active than the surrounding fluid. Compared with the phase-averaged results in the wake, the turbulent hot spot has concentrated vorticity, high turbulence level, and high turbulence kinetic energy. The results are similar to those from the experiments by Chow et al.,³⁷ who observed the turbulent hot spots at downstream of the rotor blade. From the velocity distribution, we observed a high-speed region and a low-speed region around the turbulent hot spot, labeled as HS and LS, respectively. These two regions resulted from wake–wake interactions, and they moved downstream with the turbulent hot spot. In addition, we confirmed that when the stator wake impinged on the blade, the boundary became thicker compared with the no-wake condition, and a thickened boundary layer region with high turbulence level and high turbulent kinetic energy was formed, labeled as A. These flow structures will be discussed in detail in Subsections III B and III C.

The first-stage stator wakes move to the trailing edge and interact with the second-stage rotor wakes; it is shown at phase P16. From the velocity distributions, a large low-momentum region is observed at the trailing edge. It is clear that the second-stage rotor wake widens, and the velocity defect is aggravated. The turbulence level and turbulent kinetic energy in the rotor wake increase because of interactions between the rotor wake and the upstream wake. From the distribution of vorticity, it can be seen that there is an obvious asymmetry of the vorticity in the rotor wake. The negative-vorticity region increases greatly, but the positive-vorticity region remains unchanged compared with phase P13. Furthermore, there still exists a kink structure in the upstream stator wake. A high-speed region and a low-speed region around the turbulent hot spot are noticeable, and these flow structures together move downstream with the stator wake.

A kink, also called a turbulent hot spot, results from the first-stage rotor wake and the stator wake. Chow et al.³⁷ observed a kink structure in the rotor wake and attributed the kink structure to the discontinuous velocity of the wake segments. The first-stage rotor wake is advected to the first-stage stator passage, where it is chopped by the stator blades and transported downstream. However, the velocities of the wake segments around the suction surface and of those around the pressure surface are different. When the rotor wake segments reach the trailing edge and interact with the stator wake, the discontinuities in the wake segment velocities cause a kink in the stator wake. The phase-averaged results in Fig. 3 confirm that the turbulent hot spot is an unstable structure with the high turbulence level, high turbulent kinetic energy, and concentrated vorticity.

Plots of the perturbation velocity field at selected phases calculated using Eq. (7) are shown in Fig. 4. The turbulent hot spot is a region with concentrated positive vorticity, and the center has the strongest vorticity. It is obvious that the perturbation velocity is counterclockwise around the turbulent hot spot, and its magnitude is greatest at the edge of the spot. Considering these characteristics of the turbulent hot spot, we guess that it has some properties similar to those of a point vortex. Considering the radial direction, the turbulent hot spot may be seen like a vortex tube. In addition, it is observed that the magnitude of the perturbation velocity around the turbulent hot spot is much larger than that in the wake. Even in the region that is around the turbulent hot spot but outside the wake, the magnitude of the perturbation velocity is still high. Furthermore, the disturbance caused by the positive vorticity in the turbulent hot spot is larger than that caused by the negative jet in the wake. Therefore, the local impact of the turbulent hot spot on the passage flow is much stronger than that of the wake.

The direction of the perturbation velocity in the wake is from the suction surface to the pressure surface in the compressor because of the negative jet, which is contrary to that in the turbine. In Fig. 4, the perturbation velocity in the wake but far from the turbulent hot spot is directed from the suction surface to the pressure surface. This is consistent with the results of Jia et al.³⁸ However, the perturbation velocity is counterclockwise around the turbulent hot spot. This difference in the direction of the perturbation velocity could explain the existence of the high-speed and low-speed regions. The results are presented here in a rotational relative coordinate system, and so, the direction of the relative velocity is along the blade passage to downstream. At the lower right of the turbulent hot spot, the direction of the perturbation velocity is consistent with the relative time-averaged velocity, and so, the phase-averaged velocity becomes high, and a high-speed region is formed. In a similar way, the direction of the perturbation velocity is opposite to the relative time-averaged velocity at the upper left of the turbulent hot spot, and so, the phase-averaged velocity becomes low, and a low-speed region is formed. In addition, it is observed that the centers of the high-speed and low-speed regions are at the edge of the turbulent hot spot. As mentioned earlier, the magnitude of the perturbation velocity is greatest at the edge of the turbulent hot spot. Therefore, the maximum velocity in the high-speed region and the minimum velocity in the low-speed region are also at the edge of the turbulent hot spot. It is clear that the formation of the high-speed and low-speed regions is closely related to the existence of the turbulent hot spot, and these flow structures will have a significant impact on the passage flow.

The turbulent hot spot moves downstream with the first-stage stator wake. We draw the turbulent hot spot at several phases in Fig. 5, which can be viewed as showing the trajectory of the turbulent hot spot with time. The turbulent hot spot is the result of the interaction between the first-stage rotor and stator wakes, and thus is the point of the intersection of these two wakes. This means that the turbulent hot spot is located not only in the first-stage stator wake but also in the first-stage rotor wake. In the rotating coordinate system, it is assumed that the rotor blade does not move, while the stator blade rotates relative to it. At this time, the first-stage stator wake sweeps the entire second-stage rotor blade, while the position of the first-stage rotor wake is fixed relative to the second-stage rotor blade. So, the tracked motion of the turbulent hot spot should show it to be in the first-stage rotor wake region. As the wake convects downstream, its strength decays. In our experiments, the first-stage rotor wake cannot be distinguished in the second-stage rotor blade passage. This means that the first-stage rotor wake dissipates greatly in the first-stage stator blades passage and gaps. With the dissipation of this wake as it moves downstream, the interaction between the two wakes becomes weak. Therefore, the turbulent hot spot diffuses as it moves downstream. The turbulent hot spot is identified by the contour of vorticity, ω = 2. It is observed that the region of the turbulent hot spot increases in size as it moves downstream. It is clear that the strength of the turbulent hot spot decreases, but its area becomes larger as it moves downstream. More importantly, the turbulent hot spot decays more slower than the wake itself. Even when the wake is very weak, the turbulent hot spot still has a strong effect.

Let us make a brief summary of the properties and effects of the turbulent hot spot. A high-speed region and a low-speed region are formed owing to the influence of the turbulent hot spot. These flow structures move downstream with the wake. The turbulent hot spot diffuses as it moves downstream, but it decays more slower than the wake, and it increases in size. In addition, compared with the phase-averaged results at multiple phases, the turbulent hot spot has a much higher turbulence level, turbulent kinetic energy, and concentrated vorticity than the wake. Therefore, the turbulent hot spot is more unstable and active than the wake. Thus, the turbulent hot spot plays a potentially important role in the passage flow.

It is difficult to acquire near-wall data from traditional PIV measurements in a turbomachine because of light pollution and strong shear. In our experiments, near-wall PIV methods are used to acquire boundary layer information. The optimal synthetic particles (OSP) and adaptive meshing and stretching of the image (AMSI) methods improve the accuracy of PIV calculation in the near-wall region.^39,40 To present the results in a clear way, we use an orthogonal coordinate system based on the rotor blade surface in this subsection.

We mentioned briefly earlier that there is a thickened boundary layer region when the upstream wake is impinging on the boundary layer. In Fig. 3, this thickened region is observed at phase P13, labeled as A. Its development can be seen from the distributions of phase-averaged results in the orthogonal coordinate system based on the rotor blade surface, as shown in Fig. 6, where the thickened boundary layer region is again labeled as A, and the black line is the edge of the wake.

It is much easier to identify the shape of the thickened boundary layer region from the phase-averaged vorticity distributions. At phases P13 and P14, the whole of the thickened region is observed. This region has a large front and a flat tail. The leading edge is located at the wake centerline and changes steeply. In contrast, the trailing edge is flat, changes slowly, and is outside the wake zone. The maximum height of the thickened boundary layer region lies between the centerline and the trailing edge of the wake. It is worth noting that the trailing edge of the wake lies at the center of the thickened boundary layer region. From the phase-averaged velocity distribution results, it can be observed that the thickened boundary layer region is a low-momentum zone. The maximum thickness is about twice that of the boundary layer in the absence of the wake. Wheeler et al.³² observed a thickened laminar boundary layer on a compressor stator blade that was due to the wake–leading-edge interaction. They observed that this thickened laminar boundary layer lay behind the wake and moved downstream with it. On the thickened boundary layer, there exists a high-speed region that is formed by the turbulent hot spot. The high-speed region is not seen to increase the low momentum of the thickened boundary layer region.

On comparing the averaged vorticity distributions from phase P12 to phase P15, the evolution of the shape of the thickened boundary layer region can be observed. At phase P12, there is a small package at the outer edge of the boundary, near s/S = 0.55. The scales in the flow direction and normal direction of the thickened boundary layer region are small. This means that this region is in its early stages of formation at phase P12. When the thickened boundary layer region moves downstream with the wake, it expands. At phase P13, the leading and trailing edges are located at s/S = 0.82 and s/S = 0.65, respectively. At phase P14, the leading edge is near the trailing edge of the blade, and the trailing edge is located at s/S = 0.78. From a comparison of the results at phases P13 and P14, it is evident that the thickened boundary layer region becomes longer and higher. Furthermore, the propagation velocity of the leading edge of the thickened boundary layer region is equal to the speed of the wake, but the propagation velocity of the trailing edge is less than of the speed of the wake. At phase P15, the wake impinges on the trailing edge of the blade. The thickened boundary layer region moves to the trailing edge of the blade, and the leading edge merges into the rotor wake.

The distributions of the turbulence level and turbulent kinetic energy are shown in Fig. 7. It is evident that the turbulence level and turbulent kinetic energy are both high in the thickened boundary layer region. Furthermore, the turbulent kinetic energy between the maximum height point and the trailing edge of the thickened boundary layer region is higher than that between the maximum height and the leading edge. The turbulence level has a similar pattern. Jia et al.³⁸ observed a zone of high turbulent kinetic energy when the inlet guide vane wake impinged on the rotor blade in a single-stage compressor. They found that the region with the highest turbulent kinetic energy was located at the trailing edge of the wake. The thickened boundary layer region that we observed in our experiments is an unstable zone that may be a turbulent spot. In the bypass transition with a wake, turbulent spots are formed after the wake impinges on the boundary layer. As the turbulent spots convect downstream with the wake at different speeds, they spread and eventually merge into turbulence.

In the wake-induced transition, the interaction of the wake and the boundary layer leads to formation of turbulent spots. There is a calmed region behind a turbulent spot, with higher shear stress and a fuller velocity profile. The calmed region is more stable than a laminar boundary layer, and its presence can suppress separation and transition. A plot of the velocity profile along the suction surface at phase P13 is shown in Fig. 8. The lines with solid dots are the phase-averaged results at phase P13, and the lines with stars are the time-averaged results at the same locations. The wake does not arrive at the trailing edge of the suction surface, and the phase-averaged results are similar to the time-averaged results. At s/S = 0.7 to s/S = 0.9, the upstream wake impinges on the boundary layer, and the latter thickens owing to the presence of the negative jet. The thickened boundary layer is located at s/S = 0.65 to s/S = 0.8, and the boundary layer displacement of the phase-averaged results is much higher than that of the time-averaged results. In addition, the mainstream velocity of the phase-averaged results is larger than that of the time-averaged results because the high-speed region is near the boundary layer. At s/S = 0.6, the profile of the phase-averaged results is fuller than that of the time-averaged results because of the calmed region.

When the upstream wake impinges on the boundary layer, the profile of the latter will change. The boundary layer development is substantially affected by the interaction with the impinging wake, as shown in Fig. 9. The color lines with solid dots are the phase-averaged velocities at different phases, and the black lines with asterisks are the time-averaged results. We choose four positions at which we present the boundary layer development in a wake passing cycle. Taking s/S = 0.85, the boundary layer is separated without the wake (see phase P10, for example). The boundary layer profile thickens and becomes a thickened shear layer. From phase P10 to phase P14, the upstream wake impinges on the boundary layer. At this moment, the trailing edge of the wake is located at s/S = 0.85 at phase P14. It is clear that the boundary layer thickens owing to the negative jet effect of the wake. This is different from the result of Uzol et al.,³⁵ who observed a thinning of the boundary layer when the wake impinged. The thickened boundary layer region is caused by the high turbulence intensity in the wake. The mainstream velocity increases greatly owing to the influence of the high-speed region. From phase P18 to phase P02, the boundary layer gradually becomes thinner because of the calmed region. The boundary layer profile is much fuller, and separation is suppressed. From phase P06 to phase P10, the boundary layer gradually thickens and recovers to separation. It is observed clearly that the boundary layer thickens, thins, and recovers to separation when the upstream wake impinges. Therefore, boundary layer development is periodic in a wake passing cycle.

The t–n diagrams of the velocity and RMS of the unsteady boundary layer at s/S = 0.75 and s/S = 0.97 are presented in Fig. 10. The abscissa corresponds to the wake passing period T, and the ordinate is the normal distance n above the blade suction surface. Both the unsteady velocity and RMS are normalized by the inlet velocity of the second-stage rotor blades. The wake center, which convects over the blade surface at the local freestream velocity, is indicated by line C. The leading and trailing edges of the wake are represented by lines L and T, respectively. The highest turbulence intensity in the wake occurs at the center of the wake along line C. In addition, what is different from past results is that the velocity is high in the wake region near the boundary layer because of the presence of the high-speed region. As the upstream wake impinges on the blade, the boundary layer thickness first increases owing to the presence of the negative jet, and a thickened boundary layer region in the form of a turbulent spot is formed because of the high turbulence intensity in the wake. The boundary layer then gradually becomes thinner owing to the presence of the calmed region that follows the turbulent spot. Finally, the boundary layer thickens and recovers to separation. It is possible that the wake itself cannot suppress separation and makes the boundary layer thicker. However, the calmed region caused by the interaction between the wake and the boundary layer can suppress separation and make the boundary layer thinner.

The boundary layer thickness δ₉₅ and momentum thickness θ at the trailing edge s/S = 0.97 are presented in Fig. 11. It is clear that the thickness of the boundary layer increases very rapidly from the leading edge to the center of the wake. It also increases from the center to the trailing edge, but the change is slow. The maximum thickness of the boundary layer is located at the trailing edge of the wake. After the trailing edge of the wake, the boundary layer thickness decreases slowly for a short time because the trailing edge of the thickened boundary layer region is behind the trailing edge of the wake. Then, the boundary layer rapidly becomes thinner owing to the presence of the calmed region. Finally, it slowly becomes thicker again and recovers to separation.

The boundary layer thickness δ₉₅ and momentum thickness θ are shown in Fig. 12. The integral parameters of the unsteady boundary layer are calculated from the phase-averaged PIV measurements along the suction surface. The black dashed lines are the leading and trailing edges of the wake, labeled as LE and TE. The black dashed-dotted line is the center of the wake, labeled as C. The slope of a line is the propagation velocity in a space–time diagram. The propagation velocity of the wake is equal to the freestream velocity U_m. The red dashed line is the leading edge of the calmed region, and the red solid line is the trailing edge, labeled as CL and CT, respectively. The slope of line CL is half of the freestream velocity, which means that the propagation velocity of the leading edge of the calmed region U_CL = 0.5U_m. Similarly, the propagation velocity of the trailing edge of the calmed region U_CT = 0.3U_m. These results are similar to those of Halstead et al.² The thickened boundary layer region lies between lines C and CL. The effect of the unsteady wake on boundary layer development can be seen from the space–time diagrams of the boundary layer thickness and momentum thickness. It is obvious that the integral parameters are periodic in a wake passing period.

The blade–wake and wake–wake interactions in a multistage turbomachine are key issues from the physics perspective as well as for the engineering design. To the best of our knowledge, this is the first time that near-wall PIV measurements are performed successfully within the second-stage rotor of a two-stage compressor in air. On one hand, the effects of wake–wake interaction and multistage blade rows on downstream flow have not been extensively studied. Chow et al.³⁷ observed the turbulent hot spot in the rotor wake at the second stage rotor outlet and attributed it to the discontinuous velocity of the wake segments. His work mainly focused on the formation of the turbulent hot spot at the rotor outlet. In the present experiments, the evolution and impact on passage flow of the turbulent hot spot within the second-stage rotor are studied in detail. On the other hand, for an air multistage compressor, the dynamic evolution of the boundary layer caused by wake impingement over a rotating blade has not been thoroughly investigated before. Jia et al.³⁸ studied the effects of wake strengths and the reduced frequency on unsteady boundary layer development in a single-stage compressor. In the present study, experiments are conducted within a two-stage compressor to study in detail the boundary layer development resulting from the wake–blade interaction in a wake passing period. Therefore, this work, which focuses on turbulent hot spot and boundary layer development within the second-stage rotor, greatly broadens our understanding of complex flow in a multistage turbomachine.

The distributions of phase-averaged results at three representative phases during one wake passing cycle have been shown. At phase P04, the flow is quiet because there is no wake in the measurement areas, and separation is observed at the trailing edges of the rotor blades. The first-stage blade wake impinges on the second-stage rotor blades at phase P13. It is obvious that the stator wake is distorted and produces a kink structure. In addition, there is a high-speed region and a low-speed region around the turbulent hot spot. A thickened boundary layer region is observed, with a high turbulence level and high turbulent kinetic energy. The first-stage stator wake moves to the trailing edge and interacts with the second-stage rotor wakes at phase P16. It is observed that the second-stage rotor wake widens, and the velocity defect is aggravated. The turbulence level and turbulent kinetic energy in the rotor wake increase because of the interaction between the rotor wake and the upstream wake.

The kink, also called the turbulent hot spot, that results from the first-stage rotor and stator wakes is an unstable structure with a high turbulence level, high turbulent kinetic energy, and concentrated vorticity. From the perturbation velocity field, it is clear that the perturbation velocity is counterclockwise around the turbulent hot spot, and the magnitude of the perturbation velocity around the turbulent hot spot is much larger than that in the wake. The high perturbation velocity changes the passage flow, leading to the formation of a high-speed region and a low-speed region. The turbulent hot spot is the point of intersection of two wakes, and so tracking of the motion of the turbulent hot spot should show it to be in the first-stage rotor wake region in the relative coordinate system. In our experiments, it is difficult to identify the first-stage rotor wakes in the second-stage rotor blade passage because of their decay. In addition, a comparison of the phase-averaged results at multiple phases shows that the turbulent hot spot has a much higher turbulence level, turbulent kinetic energy, and concentrated vorticity than the wake. Therefore, the turbulent hot spot is more unstable and active than the wake. The turbulent hot spot possibly plays a significant role in the passage flow.

Boundary layer information is obtained by using near-wall PIV measurements. It is observed that the impingement of the upstream wake on a blade causes the formation of a thickened boundary layer region. The trailing edge of this region is outside the wake zone, and its leading edge is located at the wake centerline. The thickened region convects downstream with the wake, and its length and thickness increase. This region is an unstable zone with a high turbulence level and high turbulent kinetic energy, and it appears to be a turbulent spot. A calmed region that follows the thickened boundary layer region can suppress the separation and transition. The velocity profile is much fuller in the calmed region.

Thus, when the upstream wake impinges on the blade, the boundary layer thickness first increases owing to the presence of a negative jet. A thickened boundary layer region in the form of a turbulent spot is formed because of the high turbulence intensity in the wake. The boundary layer then becomes thinner owing to the presence of the calmed region. Finally, the boundary layer again thickens gradually and recovers to separation. Thus, the boundary layer thickness is periodic in a wake passing cycle. It is likely that the wake itself cannot suppress separation, but it does make the boundary layer thicker. However, the calmed region caused by the interaction between the wake and the boundary layer can suppress separation and make the boundary layer thinner.

This work was supported by the National Natural Science Funds of China (Grant Nos. 9175200, 109103010062, 10921202, 11372009, 11602005, and 11632002). We thank Dr. Lichao Jia for his help with the experimental techniques.