# Investigation of large-scale structures in supersonic planar non-reactive shear layer with a base flow region

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### Abstract

Large-scale structures in supersonic planar non-reactive shear layer with a base flow region are experimentally investigated. By utilizing the recently developed nanoparticle-based planar laser scattering (NPLS) method, the fine transient streamwise and spanwise flow fields are acquired, and the large-scale structures in the reattachment region, initial turbulent shear region, and developing turbulent shear region are analyzed. The predominant instability is convective for the two separated shear layer, whereas the instability in the base flow zone is still absolute according to the linear instability analysis. From the initial to developing turbulent shear layer region, the predominant instability transited gradually from absolute to convective instability, and the corresponding scales of the large-scale structures turn from about half to whole of the shear layer thickness. The entire streamwise mean flow topology and the streamwise and transverse velocity fluctuations are compared with different pressure ratios and with incompressible blunt trailing-edge shear layer. Linear instability analysis shows further evidence to the instability evolution of the supersonic shear layer with a base flow along the streamwise. It implied that instability induced by unmatched pressure in the wake zone can increase the absolute instability and improve the receptivity to inflow perturbations. The reattachment points are approximated with the intersection points of the reattachment shock pairs, which can be obtained from the transient NPLS images. The distribution of the reattachment points suggests that: the principal axis of the reattachment point distribution is dominated by the high-speed flow, and unmatched pressure increases the perturbation in the wake zone, result in a high absolute instability.

### Graphical abstract

## Keywords

Supersonic planar shear layer Large-scale structure Base flow Nanoparticle-based planar laser scattering## 1 Introduction

Supersonic non-reactive shear layer widely exists in chemical lasers, supersonic exhaust nozzles, and supersonic combustors. Recently, supersonic reactive and non-reactive shear layers have regain considerable research effort, primarily because of their importance in propulsion systems for air-breathing supersonic and hypersonic aircraft (Zhang et al. 2014; Ferrero et al. 2013).

The importance of trailing edge for the supersonic shear layer has transpired in very few studies and only recently has there been a regained interest in studying the early development of turbulent and transitional mixing layers (Braud et al. 2004). The flow structure in the supersonic planar non-reactive shear layer base flow region is primarily influenced by the geometry of the splitter plate and can deeply affect the streamwise evolution of the flow. Research has found that the vortices thickness for the blunt trailing-edge (BTE) case increases significantly compared to the thin trailing-edge (TTE) case (Laizet et al. 2010; Zhao et al. 2010a, b).

However, in a supersonic compressible base flow, the approaching boundary layers separate from the base corners and undergo a vigorous expansion to form free shear layers. The resulting free shear layer that develops after separation isolates the high-speed outer inviscid flow from the lower speed recirculation region. Its high turbulence and compressibility makes it a key component contribution to the near-wake flow (Reedy et al. 2012). These newly formed shear layers initially encounter a region of zero pressure gradient mixing and followed by a region of adverse pressure gradient mixing. As the shear layer approaches the reattachment point, a recompression process occurs. The entrainment characteristics of the shear layer essentially set the base pressure by determining the fraction of shear layer fluid that is unable to negotiate the adverse pressure gradient imposed by the recompression waves near the rear stagnation point and is, therefore, returned toward the base. The two shear layers eventually impinge at the reattachment point and subsequently form reattachment shock.

These inherent complexities, namely large flow gradients in thin shear layers, expansion waves, reattachment shock waves, reflection shock waves, large streamline curvature, compressibility, shear layer impingement, and the effects of turbulence, together with the interactions among the base flow, the mixing layer and the reattachment shock, have settled unprecedented obstacles on in-depth understanding of the supersonic shear layer with a base flow region, and persist it as a formidable research challenge.

The spatial and temporal development of turbulent wakes and mixing layers is strongly influenced by the dynamics of large-scale structures (von Terzi et al. 2009); therefore, the large-scale structures are of the most important research subject in BTE supersonic shear layer. Smith and Dutton (1996) have done the first investigation on the near–wake interaction of two dissimilar supersonic streams separated by a finite-thickness splitter plate with the application of planar imaging techniques. They described the large-scale structures in a compressible planar base flow, whereas Bourdon and Dutton (2001) described the large-scale structures in an axisymmetric blunt base flow at *M* = 2.46 with the planar Mie scattering imaging. These studies found that the large-scale structures were on average elliptical and inclined to the freestream flow in side-view images in both cases, matching the results from planar mixing-layer studies. Because of the high convective Mach number of the shear layers, the structures were not regularly spaced and often had a jagged appearance in instantaneous images. In side-view images, the structures grew markedly and became more elongated during recompression and reattachment, whereas the structures became more disorganized in appearance in the instantaneous images. In end-view images, both studies found mushroom-shaped large-scale structures, which match the results for incompressible mixing layers. Scarano and van Oudheusden (2003), as part of a particle image velocimetry study of a planar base flow at *M* = 2.0, found large-scale coherent structures in vorticity data for the trailing wake, with the structure sizes ranging from 17 to 50% of the local half width of the wake.

In an incompressible wake flow, the alternating large vortices (von Kármán vortices) are initially created through a vortex shedding mechanism occurring immediately behind the splitter plate. The BTE shear layer exhibits different dynamic behaviors, presenting simultaneously two types of global instability, including an absolute instability due to the splitter plate wake influence and a convective instability, and the characteristic of the mixing-layer behavior (Koch 1985). Researchers have found that the supersonic shear layers with a base flow are of highly three-dimensional (Zhang et al. 2014). The structural degeneration observed at high compressibility can be attributed to the dominance of three-dimensional instability modes (Chen et al. 1990). Therefore, does the two types of global instability still true for the compressible BTE supersonic shear layer?

Similar to the interaction between shock wave and turbulent boundary layer (Délery and Dussauge 2009), the mean velocities are essentially the same for the reattachment shock foot and the reattachment point. They move at a slow speed in the laboratory frame of reference, but it is of course supersonic with respect to the free stream flow (Clemens and Narayanaswamy 2014). Whether the driving mechanisms of low-frequency unsteadiness of the reattachment point and shock result from the propagation of the upstream turbulent perturbation and/or the intrinsic instability of the base flow in the wake?

In the present study, following those previous studies, the supersonic shear layers with a base flow were investigated with the recently developed nanoparticle-based planar laser scattering method; the main purpose of this work is to investigate large-scale structures, the instability of the reattachment point, and its influence on the evolution of the following supersonic shear layer.

The organization of the present paper is as follows. First, Sect. 2 presents the physical configuration. And then, Sect. 3 deals with the flow dynamics where instantaneous visualizations, statistical characteristics, and linear stability analyses are presented. Finally, the discussions of the main results are presented in Sect. 4.

## 2 Apparatus and experimental technique

In the present study, a test section with a BTE double Mach number nozzle is designed to produce a supersonic planar shear layer with a base flow region.

^{4}to 4 × 10

^{5}m

^{−1}.

The model consisted of a double Mach number nozzle terminated with a blunt trailing edge (BTE). The double Mach number nozzle is located at the centerline instead of apart at the upper and under walls, that is, the two converging and diverging Laval nozzle walls lean to each other back-to-back. The breathed air are accelerated to two independent supersonic Mach numbers in the two converging and diverging fluid fields surrounded by the double Mach number nozzle walls with the upper and under walls, respectively. The air streams at the nozzle exit are parallel to each other by elaborately designing the nozzle profiles. By this means, the influence of the boundary layer extended from the upstream to the mixing layer can be diminished furthest; therefore, a laminar boundary layer can be expected before the thick trailing edge.

However, since the double Mach number nozzle locates at the center, the nanoparticles accompanying with airstream are elbowed to the upper side and under side by the contracted throat; after that, the nanoparticles should follow well with the rapid expansion, shearing, reattaching, and mixing that experienced successively in the nozzle and after the thick trailing edge. Therefore, only very fine nanoparticles should be applied to ensure the following ability of particles, while the light intensity are proportional to the mean diameter of the nanoparticles, which means that it is more difficult to maintain instantaneous images with high signal-to-noise ratio. Meanwhile, a higher pulse energy output laser and the high signal-to-noise ratio NPLS (Zhao et al. 2009) flow visualization technique are both applied to enhance the instantaneous image qualification as much as possible. In this work, the mean size of the seeding particles is 18 nm for NPLS experiments, and the mean size of the seeding particles is 50 nm for velocity measurements.

The NPLS system is mainly composed of computer, synchronizer, CCD camera, pulse laser, and nanoparticle generator, the structure of which is schematically shown in Fig. 1b. In NPLS, the computer controls the collaboration of the components and receives the experimental images. The input and output parameters of the synchronizer are controlled by software, collaboration of other components is controlled by signal of the synchronizer. The timing diagrams of exposure of CCD and laser output of pulse laser can be adjusted according to the purpose of measurement. The laser beam is transformed to a sheet with cylindrical lens. The nanoparticle generator is driven by high-pressure gas, and the output particle concentration can be adjusted precisely by the driving pressure. While measuring the flow field with NPLS, the nanoparticles are injected into and mixed with the inflow of the flow field, while the flow is established in observing widow, the synchronizer controls the laser pulse and CCD to ensure synchronization of the emission of scattering laser by nanoparticles and the exposure of CCD (Zhao et al. 2009). Particle image velocimetry (PIV), which shares the same control system with NPLS, is also employed in the experiments to acquire instantaneous velocity field.

A higher energy output Q-switched Nd:YAG pulsed laser is used as light source to enhance the signal-to-noise ratio of the images, and the pulse energy output to the test section is 500 mJ for a pulse width of 6 ns and wavelength of 532 nm. The laser beam is oriented by an articulated arm and focused as a uniform sheet by cylindrical lens. The images are recorded by an interline transfer CCD camera, which has an array of 4000 × 4000 pixels with 4096 grayscales grades. The synchronizer, which has an accuracy of 250 ps, can adjust the time interval between the lasers emits and the CCD takes exposures according to the signals from the computer. By this way, the double-pulsed laser beams are insured to expose in the dual-exposure frames.

In the present study, the design Mach numbers of the double stream are *M*_{1} = 1.5 and *M*_{2} = 2.5, respectively. By measuring the pitot pressure gauge, the corresponding Mach numbers are *M*_{1} = 1.40 and *M*_{2} = 2.57, and the convective Mach number is *M*_{c} = 0.33. There are some intricate lights sparkling at the nozzle exit, which is owing to the reflection of laser sheet by the surface of the thick trailing edge. The Reynolds number *Re*_{ML} based on the velocity difference *U*_{2} − *U*_{1} (where *U*_{1} is the low-speed velocity and *U*_{2} is the high-speed one) and thick splitter plate thickness *h* = 10 mm is *Re*_{ML} = 4.6 × 10^{4}. The Reynolds number *Re*_{w} based on the mean convective velocity *U*_{c} = (*U*_{1} + *U*_{2})/2 and *h* is *Re*_{w} = 1.3 × 10^{5}. The velocity ratio *r* = *U*_{1}/*U*_{2} = 0.7 and the modified velocity ratio *λ* = (*U*_{2} − *U*_{1})/(*U*_{1} + *U*_{2}) = 0.35.

We conducted the test and calibration of the mixing-layer wind tunnel, and the accuracy of velocity measurements is ± 1%.

## 3 Results and analysis

### 3.1 The transient flow field

*p*= 1, where pressure ratio

*p*is the ratio of the low-speed flow pressure to the high-speed one. The transient flow field distinctly reveals the flow structures and its evolution in streamwise. Different from the large-scale structure with TTE (Zhao et al. 2010a, b), the current BTE case large-scale structures are much more complicated and turbulent due to the intensive interactions among the wake flow, the reattachment shock, and the shear layers.

As shown in Fig. 2, the flow field can be divided into four typical regions, which are the base flow region, reattachment region, initial turbulent shear region, and developing turbulent shear region, respectively.

However, separated shear layer with higher convective Mach number tends to translate to turbulent flow earlier. Since the flow change into turbulent immediately, the edge of the recirculation region shows itself turbulent, as shown in Fig. 3. There are two reattachment shocks at the end of the recirculation zone because of the recompression. With the spreading of the shock waves, the mixing layer becomes thicker and the large-scale structures come up. At the same time, the shocklets appear at the near shear layer zone due to the large-scale structures. Turbulent mixing makes the large-scale structures roll up faster than that of TTE.

*x*/

*h*= 1.7. The vortex shedding mechanism are more likely to be alternating large vortices (von Kármán vortices), which means that the absolute instability predominates to the convective instability. The large-scale structures are relatively smaller; the scales are about half of the shear layer thickness. The engulfed fluids in each side are largely come from its own side; the mixing efficient of the two incoming flow is quite limited.

With the evolution of the mixing layer, the velocity deficit descends rapidly; K-H vortex begins to roll up at about *x*/*h* = 4, see Fig. 2, which means that the convective instability predominates to the absolute instability. The large-scale structures are relatively larger; the scales are about the whole shear layer thickness.

### 3.2 The mean flow pattern

*p*= 1, 2, and 0.5. The wake zone, reattachment shock, and the reflected shock can be easily distinguished. Figure 7 shows the extracted mean streamwise velocity, streamwise and transverse velocity fluctuations at six different streamwise positions (0.05 h and every 4 h from 4 h) in the BTE mixing layer near to far trailing-edge zone.

For the *p* = 1 case, the end of the base flow behind the BTE is nearly parallel to the inlet flow, whereas for the *p* = 2 or *p* = 0.5 case, there is a declination to the lower pressure side, and the corresponding reattachment shock is also declined a small angle. The easily distinguishable reattachment shocks and their reflection shocks, interact with the shear layer, bend the shear layer upward and downward, and highly complicate the vortices dynamics.

Specially for the *p* = 0.5 case, the low-speed flow is to some extent chocked by the high-speed flow and the reattachment shock, which causes an curved shock, as shown in Fig. 6c, and leads the streamwise velocity to subsonic in some area at *x*/*h* = 3.0. After that, the high-speed flow acts as an ejector, accelerated the low-speed one to about *M*_{1} = 1.2 at about *x*/*h* = 12.0 and even *M*_{1} = 1.5 at about *x*/*h* = 16.0. And then, the low-speed flow is compressed by the reflect shock and decelerate to about *M*_{1} = 1.2 at *x*/*h* = 20.0. Whereas the streamwise velocity of the high-speed flow accelerates to about *M*_{2} = 2.9 due to its expansion to the opposite side. The whole flow field vibrates more violent in this case as respect to that of the other two.

As shown in Fig. 7a on the mean streamwise velocity, the wake influence on the BTE mixing layer diminishes very quickly for three pressure ratio cases of *p* = 1, 2, and 0.5. This can also be found in the streamwise and transverse velocity fluctuations in Fig. 7b, c.

The streamwise velocity fluctuations are of the same order of magnitude at the very BTE of *x*/*h* = 0.05 for three pressure ratio cases; each has double peaks: one on the high-speed side and one on the low-speed side. The double peaks blend rapidly with the evolution of the mixing layer, which can be hardly distinguished after the position of *x*/*h* = 4. The maximum streamwise velocity fluctuations are located on the high-speed velocity side, which is in good agreement (for the BTE case) with the numerical result from Laizet et al. (2010) and experiment results from Braud et al. (2004).

In particular, the streamwise velocity fluctuations are much higher than that of the transverse ones, as shown in Fig. 7b, c, which is diametrically opposite to that of lower Reynolds number case (*Re*_{ML} = 400) presented in Laizet et al. (2010). The streamwise velocity fluctuations are about an order of magnitude higher than that of transverse ones in near trailing-edge zone, whereas are three to four times higher in the far trailing-edge zone.

As shown in Fig. 7c, there is more than an order of magnitude lower transverse velocity fluctuations for the case *p* = 1 than that of *p* = 2 and 0.5 just behind the BTE. This implies that at the very exit of the BTE, transverse velocity fluctuations are mainly caused by pressures difference between the two inflows. With the evolution of the mixing, the transverse velocity fluctuations develop into the same order of magnitude.

Notice that there are more peaks on the transverse velocity fluctuations at *x*/*h* = 4 for the cases of *p* = 1 (*y*/*h* = 1.37 and − 1.38), 2 (*y*/*h* = 1.10 and − 1.53), and 0.5 (*y*/*h* = − 0.58), respectively. This phenomenon results from the reattachment shock. For the cases *p* = 1 and 2, there are two reattachment shocks. With the increasing of the low-speed flow pressure, the flow will bend to the opposite side, which leads to the reattachment shock incline to the high-speed side respected to the pressure matching case. As previously mentioned, the low-speed flow is to some extent chocked for the case *p* = 0.5, so that the reattachment shock at the low-speed side diminished. The remained reattachment shock in the high-speed side bends quite a lot to the low-speed side.

Note finally that both the streamwise and the transverse velocity fluctuations decrease sharply from within the near trailing-edge zone (*x*/*h* = 0 to 4) and then decline very slowly to about 0.01 and 0.002 (*x*/*h* = 20), respectively, which is not in agreement with the low Reynolds number case presented in Laizet et al. (2010). This is in good agreement with the common view: in high Reynolds number case, the compressibility is higher, which suppresses the development of instability (Chen et al. 1990).

### 3.3 The linear instability properties

*p*= 1, 2, and 0.5. Wallace and Redekopp (1992) suggested that the hybrid wake-/mixing-layer profile as follows:

*f*is the wake deficit parameter, i.e., the velocity deficit divided by the mean convection velocity, and

*λ*is the modified velocity ratio of the mixing layer. According to Laizet et al. (2010), this generic profile is a good approximation of the mean streamwise velocity profile of

*U*, and

*f*can be estimated as follows:

*f*(

*x*) > 0.95, the corresponding flow becomes absolutely unstable; Laizet also noted that an absolutely unstable region must be expected for each mixing layer due to the boundary condition on the trailing edge which implies

*f*(

*x*) = 0.

*f*for each situation, and the DNS result for BTE (Laizet et al. 2010) is also plotted in the figure. The Reynolds numbers considered in the present study are quite higher than that of DNS result of Laizet et al. (2010), where

*Re*

_{ML}= 400 and

*Re*

_{w}= 1000. There are no areas where

*f*(

*x*) > 1, which is obviously difference between the present experiment work and the DNS result. It should be resulted from low signal-to-noise ratio in the recirculation zone just behind the blunt trailing edge. For the situation of

*p*= 1, the area where

*f*(

*x*) > 0.95 is significantly less important than that of Laizet’s DNS result, where the flow is absolutely unstable for 0 <

*x*/

*h*< 0.85 and 0 <

*x*/

*h*< 1.44, respectively. Therefore, a reasonable conclusion can be drawn that higher Reynolds number tends to have less absolute instability and relatively poor receptivity to inflow perturbations. For the situation of

*p*= 2 and 0.5, the area where

*f*(

*x*) > 0.95 is more important than that of

*p*= 1, where the flow is absolutely unstable for 0 <

*x*/

*h*< 1.03 and 0 <

*x*/

*h*< 1.40, respectively. It implied that instability induced by unbalanced pressure in the wake just behind the BTE can increase the absolute instability and improve the receptivity to inflow perturbations. Moreover, the situation of

*p*= 0.5 has much more obviously improvement in the receptivity, that is to say, a low-speed flow with lower static pressure tends to have less resistance to the oppression of high-speed flow, which increase the instability of the flow.

Figure 8b shows the streamwise evolution of the modified velocity ratio *λ*. At the end of near trailing-edge zone, there is a peak for each case, located at *x*/*h* = 4.2, 5.0, and 2.4. Increasing the low-speed flow pressure will increase the expansion of the low-speed flow and compress the high-speed flow behind the BTE, both of the two effects will increase the modified velocity ratio and decrease the convective Mach number, which will increase the growth rate of mixing layer. The highest pressure ratio corresponds to the highest velocity ratio, and will have the highest growth rate, which is in agreement with the momentum thickness results from Zhang et al. (2014).

Furthermore, in the near to far trailing-edge zone (*x*/*h* = 1 or 2 to 12), the wake deficit parameters of the present high Reynolds number cases tend to drop more sharply to about 10% than that of 40% for the low Reynolds number one in Laizet et al. (2010), which means that the wake effect diminished much more faster for the high Reynolds number case.

Finally, in the far trailing-edge zone (*x*/*h* > 12), the convective instability predominates the developing of the BTE mixing layer, since the wake deficit parameters are about or less than 10%.

### 3.4 Reattachment point

As previously mentioned, the reattachment point is an important character of the supersonic BTE mixing layer. The position of the reattachment point can illustrate the area of recirculation region. The latter the position of the reattachment point, the larger the area of the recirculation zone is, and the larger the area where *f* (*x*) > 0.95 is, which indicate a better receptivity to inflow perturbation.

However, the reattachment point is not easy to acquire, because of the instability of the BTE wake flow. In the fine transient flow field image, the reattachment shock pair is closely related to the reattachment point, and each transient flow filed image can give one intersection point. Therefore, it is reasonable to use the intersection point of the reattachment shock pair as an approximation of it.

*p*= 1 and 2. Where the blue lines are the linear fitted reattachment shocks and the green circus are the intersection points of each reattachment shock pairs. The mean reattachment point of each saturations is marked with red star, and the coordination are (0.93, − 0.17) and (1.02, − 0.24), respectively.

The mean reattachment points of the both cases locate at the side of the high-speed flow, which, because the high-speed flow has lower expansion ability. It is obviously that, with the decreasing of *λ*, the expansion ability ratio of high-speed flow to low-speed one decreases, and the mean reattachment points inclines more to the side of high-speed flow. With the increasing of static pressure of the low-speed flow, the mean reattachment point tends to bend down to the high-speed flow, which results a lower transverse coordination. Meanwhile, the mean reattachment point also moves downstream with the increasing of low-speed flow pressure, which forms a larger area where *f* (*x*) > 0.95, which implies a higher absolute instability.

The distribution of the reattachment points is replotted in polar coordinate system, as shown in Fig. 9c, d, where the blue line is the linear fitted line of the intersection points for each case. The linear fitted line of the intersection points represents the principal axis of the turbulent distribution. The inclination angle of the principal axis for the situation of *p* = 1 is 20.0°. In addition, the inclination angles of the reattachment point (0.93, − 0.17) with the lips of the low/high-speed flow exits (0, ± 0.5) are − 35.8° and 19.5°, respectively. This suggested that high-speed flow has much more important influence on the reattachment point’s dynamic behavior for the pressure matching case. The lower the modified velocity ratio *λ*, the more important the high-speed flow is on the reattachment points dynamic behavior. The instability of the reattachment point results from the perturbation of the recirculation zone of the wake, it can be concluded that with the increasing of the recirculation zone pressure, the reattachment point moves downstream and inclines to the side of low-speed flow. It suggested that high-speed flow should be paying more attention in regard to the influence on BTE mixing-layer dynamic behavior.

In the case of *p* = 2, the inclination angle of the principal axis decreases to 13.5°, it indicated that low-speed flow has more influence on the reattachment points dynamic behavior. It suggested that low-speed flow should have higher pressure to increase its influence on BTE mixing-layer dynamic behavior.

The standard deviations of the reattachment points are 0.21 and 0.23 in the cases of *p* = 1 and 2, respectively. The higher standard deviations are consistent with the higher absolute instability in the case *p* = 2.

## 4 Conclusion

Large-scale structures in supersonic planar non-reactive shear layer with a base flow region are experimentally investigated. Experiments were performed in the low-noise supersonic mixing-layer wind tunnel, which runs in an indraft mode. A test section with a BTE double Mach number nozzle is designed to produce a supersonic planar shear layer with a base flow region

By utilizing the recently developed nanoparticle-based planar laser scattering (NPLS) method, the fine transient streamwise and spanwise flow fields are acquired. However, since the double Mach number nozzle locates at the center, the nanoparticles accompanying with airstream are elbowed to the upper and under side by the contracted throat; therefore, the concentration of the nanoparticle in the wake zone is relatively less than that of nozzle located at wall, which leads to a lower signal-to-noise ratio. The inner field of the wake zone cannot be well understood.

The large-scale structures acquired from the NPLS fine structures showed that K-H vortices on the two separated shear layer at the BTE wake zone, which suggested that the predominant instability is convective. However, the instability in the inner base flow zone is still absolutely unstable according to the linear instability analysis. Therefore, further efforts, either by improved experiment method or numerical simulation, are very necessary to understand how the recirculation flow affects the instability of the reattachment point and reattachment shocks.

From the initial to developing turbulent shear layer region, the predominant instability transited gradually from absolute to convective instability, and the corresponding scales of the large-scale structures turn from about half to whole of the shear layer thickness. Linear instability analysis provides further evidence to the instability evolution of the BTE supersonic shear layer along the streamwise. It implied that instability induced by unmatched pressure in the wake zone can increase the absolute instability and improve the receptivity to inflow perturbations. The transient spanwise flow field suggested that the supersonic shear layer with a base flow is of highly three-dimensional, but the scales that roll up in the spanwise vary in a large range. To achieve a better or predictable mixing, active or passive control is preferred. Central slopped blunt trailing edge may have excellent effect on introducing unmatched pressure to the base zone, providing an enforcement to roll up in the spanwise.

Using the intersection points of the reattachment shock pairs as the approximation of reattachment points works very well on the investigation of its distribution. The distribution of the reattachment points suggests that the principal axis of the reattachment point distribution is dominated by the high-speed flow and unmatched pressure increases the perturbation in the wake zone, result in a higher instability.

However, the location of the mean reattachment point and the distribution of the reattachment points obtained from the experiment results still have limitation on illustrating the temporal evolution process and spectral-domain distribution, which is due to that there is no temporal correlation between two pairs of PIV data. It can be further investigated with CFD simulated data in the future.

## Notes

### Acknowledgements

The financial support of the National Natural Science Foundation of China (No. 11172324) is gratefully acknowledged.

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