Planar,laser,scattering,visualization,of,streamwise,vortex,pairs,in,a,Mach,6,flow

Yinkai MA, Zhufei LI, Jiming YANG

Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China

KEYWORDS Counterrotating vortex pair;Hypersonic flow;Planar laser scattering;Scaling law;Shock tunnel

Abstract A series of cross-sectional flow fields of Counterrotating Vortex Pairs (CVPs) generated by a large-scale ramp vortex generator is observed using an ice-cluster-based Planar Laser Scattering (PLS) method in a shock tunnel with a nominal flow Mach number of 6. Combined with a numerical simulation, two streamwise CVPs with opposite rotating directions are identified in the wake flow of the vortex generator with an absence of a boundary layer, namely, a Primary CVP(PCVP)and a Secondary CVP(SCVP).The wake flow is divided into two stages with different features of the PCVP and SCVP. In Stage I, the PCVP and SCVP gradually mature, and the flow is relatively stable. In Stage Ⅱ, the PCVP and SCVP depart from each other, and the flow becomes unstable. The profiles of the transverse velocity in the spanwise symmetry plane induced by the PCVP and SCVP do not obey the scaling law of CVPs immersed in the boundary layer.A new scaling law is proposed, in which the transverse distances between adjacent saddle points in the crosssectional flow field are used as the characteristic lengths for the PCVP and SCVP. After this new scaling procedure, the profiles of transverse velocity induced by the PCVP and SCVP at different streamwise locations collapse well. Moreover, the PLS images show that the mixing between the CVPs and the outside high-momentum flow becomes evident at approximately 5.5 times the height of the vortex generator, which is earlier than that immersed in the boundary layer. These findings enrich the knowledge of CVPs in the hypersonic regime, especially in the absence of the boundary layer.

CVPs are ubiquitous phenomena in which streamlines converge and acquire angular momentum.1,2The entrainment effect induced by CVPs has shown great potential to energize the boundary layer and thus has been used to control shock wave/boundary-layer interactions3-5in the supersonic regime.Moreover, CVPs have been observed to accumulate lowmomentum streams in the internal flow of hypersonic inward-turning inlets,6,7resulting in an uneven distribution of flow parameters and a reduction in inlet performance.8Thus, knowledge of CVPs is of great significance in supersonic/hypersonic flows.

The Microramp Vortex Generator (MVG),9also known as the subboundary-layer vortex generator,10has been successfully used to generate CVPs inside the supersonic boundary layer for flow controls. For instance, Babinsky11-13and Zhang14et al.investigated the effectiveness of an MVG in mitigating the flow separation induced by shock wave/boundarylayer interactions. To achieve a better control performance,Anderson et al.15proposed an optimized MVG configuration with good structural robustness, which has been widely adopted in the literature. The optimized MVG was used in the subsequent experiments by Babinsky et al.12to reduce the size of separation. Giepman16and Ghosh17et al. found that the MVG was more effective in reducing the separation on the symmetry plane.To reveal the flow mechanisms,a number of experiments and numerical simulations were carried out,focusing on the vortical structures in the wake flow of the MVG. Babinsky et al.12identified a PCVP and multiple secondary vortices dominating the wake flow using surface oilflow visualization. Similar vortical structures were observed in the flow field by Wang et al.18with the help of the nanoparticle-based planar laser scattering technique. The upwash and downwash streams induced by the PCVP were characterized by Nolan and Babinsky19using laser Doppler anemometry. Li and Liu20demonstrated that arc-like vortices in the wake flow of the MVG were caused by a Kelvin-Helmholtz (K-H) instability using implicit large eddy simulation. Combined experiments and numerical simulations were performed by Sun et al.21who found that the PCVP becomes asymmetric at 10 times the height of the MVG due to downstream flow unsteadiness. For more details on the MVG,reviews are available by Lin22, Lu23,24et al., and recently by Huang et al.25

Compared with supersonic applications,studies of CVPs in the hypersonic regime are still limited,26and most of them are associated with the hypersonic boundary layer. For instance,the effects of CVPs on hypersonic shock wave/boundarylayer interactions were reported by Schreyer,27Gao,28and Sun29et al. Interestingly, a recent study by Sun et al.26found that the scaling law proposed by Sun et al.30for transverse velocity induced by the PCVP in the supersonic boundary layer was valid for the wake flow of the MVG immersed in the hypersonic boundary layer. In reality, CVPs are usually encountered in regions far away from the boundary layer,including the flow field downstream of a sonic jet in a supersonic/hypersonic cross-flow31and the internal/external flow of a hypersonic inward-turning inlet.32These CVPs naturally avoid the influence of the low-momentum fluids near the wall,which therefore, creates an obvious motivation to reveal the flow physics of the CVPs with an absence of the boundary layer, including knowing whether the scaling law proposed by Sun et al.30can be applied in the hypersonic wake flow and whether the entrainment of high-momentum fluids rather than low-momentum fluids by the CVPs can change the vortical structures and stability of the hypersonic wake flow.In the present work,CVPs without a boundary layer are generated in hypersonic flow, and the features of the CVPs are examined thoroughly using a combination of shock tunnel experiments and numerical simulation.

A large-scale ramp vortex generator based on the configuration proposed by Anderson et al.15is adopted to observe CVPs.As shown in Fig.1(a),the height of the vortex generator is h = 20 mm, the half-span angle α = 24°, and the chord length c = 7.2h. The origin of the coordinate system is set at the apex of the vortex generator trailing edge. The x, y, and z axes denote the streamwise, transverse, and spanwise directions, respectively. To avoid the effects of the boundary layer on the CVPs,the vortex generator is supported by two trestles with a triangular cross-section,as shown by the top view of the model in Fig. 1(b).

The experiments were conducted in the KDJB330 shock tunnel33of the University of Science and Technology of China with a nominal Mach number of 6, a total pressure of 1.45 MPa (a static pressure of 0.9 kPa), a total temperature of 900 K(a static temperature of 110 K),and a unit Reynolds number of 4.8×10-6m-1.As shown in Fig.2,the flow comes from the left,the outlet diameter of the nozzle is 330 mm,and the distance between the nozzle outlet and the leading edge of the vortex generator is 5 mm. The effective test time was approximately 20 ms, and a schlieren photographic system33was adopted to visualize the general features of the flow field.Recently,condensate-enhanced PLS has been successfully used to observe the hypersonic flow by Zhang,34Huang35and Zhu36,37et al. In the present study, an ice-cluster-based PLS technique38was used to acquire high spatiotemporal resolution images of the flow field, avoiding the integral effect of schlieren. Preceding the experiments, water vapor was added into the air in the driven tube with a volume fraction of approximately 2%. As the flow expanded through the tunnel nozzle, the water vapor in the incoming flow condensed into tiny tracer particles with an average diameter of approximately 67 nm.32The influence of water vapor is ignored because its volume fraction is minor.39

The PLS system was comprised of a continuous-wave laser(Millennia eV,Spectra-Physics CO.,Ltd)with a wavelength of 532 nm and power of 25 W, a set of lenses to transform the laser into a laser sheet,a camera(Phantom v611)with an exposure time of 99 μs,and a computer to record the time-averaged PLS images of the flow field. Moreover, to obtain the instantaneous flow field, a double-pulse Nd:YAG laser (Vlite-500,Beamtech Optronics Co., Ltd) with a wavelength of 532 nm was employed. The duration of each pulse was 10 ns with an energy of 500 mJ, effectively freezing the flow. A Charge-Coupled Device (CCD) camera (Bobcat-B6620, Imperx, Inc.)with a resolution of 4400 pixel × 6600 pixel was synchronized with the pulsed laser to record the PLS images.The spatial resolution of the PLS image is 39 μm/pixel.

As shown in Fig. 3(a), when the laser sheet illuminates a cross-section downstream of the vortex generator, the flow field is captured by the camera with the help of a flat mirror.Seven Cross-sections C1-C7 were obtained with a streamwise interval of h, in which the initial slice C1 was located at x/h = 0.5. Moreover, the flow field in the spanwise symmetry plane (z/h = 0) was observed using the imaging arrangement shown in Fig. 3(b).

Fig. 1 Schematics of ramp vortex generator and top view of model.

Fig. 2 Experimental model.

To better understand the flow field,a numerical simulation was performed using a three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solver based on the finite volume method. The Roe’s flux difference splitting scheme was used for the inviscid fluxes.40The convective terms and viscous terms were discretized by a second-order upwind scheme and a second-order central difference scheme, respectively. Since the k-ω Shear Stress Transport (SST) turbulence model has shown good performance on the evolution of vortex pairs17,32,41,42and has better numerical stability,43this turbulence model was employed to model the turbulence flow. The equation of state for an ideal gas was used, and Sutherland’s law was adopted to calculate the molecular viscosity of the gas. The numerical solution was considered to be convergent when the residuals were steady after falling by more than three orders of magnitude.

The computational domain and boundary conditions are shown in Fig. 4, in which the computational domain had the dimensions of 17.8h, 3h, and 6.5h in the streamwise x, transverse y,and spanwise z directions,respectively.At the pressure far field boundary,the parameters of the freestream were consistent with the experiments. No-slip and isothermal conditions were used on the solid wall with a fixed temperature of 300 K. The computational domain was discretized by structured hexahedron grids. As shown in Table 1, three sets of grids were tested for the grid independence study, where Nx,Ny, and Nzrepresent the number of grid points along the streamwise, transverse, and spanwise directions, respectively.The refinements were mainly performed in the regions near the spanwise symmetry plane (see Fig. 4). The minimum grid sizes along the spanwise direction near the symmetry plane for the three sets of grids (Mesh 1, Mesh 2, and Mesh 3) were 1 × 10-4m, 5 × 10-5m, and 2 × 10-5m, respectively. At x/h=2.5,the nondimensionalized pressure P/P∞(P∞is the static pressure of the freestream)distributions along the spanwise direction near the symmetry plane for the three sets of grids are compared in Fig.5.The P/P∞obtained by Mesh 2 and Mesh 3 were similar, indicating a reasonable convergence of the grid resolutions.Therefore,Mesh 2 is used in Section 3.Moreover,the numerical method is validated against the experimental results in Section 3.1.

3.1. Mean flow field

3.1.1. General features

Fig. 3 Schematics of arrangement of PLS imaging system (not to scale).

Fig. 4 Schematic of the computational domain.

Table 1 Three sets of grids used in grid convergence study.

Fig. 5 Comparison of P/P∞ along spanwise direction near symmetry plane obtained by various grid resolutions.

The experimental schlieren image and numerical contour of the transverse density gradient in the spanwise symmetry plane of the vortex generator are compared in Figs. 6(a)-6(b). The leading-edge shock angle of the vortex generator obtained by the numerical simulation is 16.9°, showing good agreement with the experimental value of 16.7°. To yield a first glance of the features in the wake flow of the vortex generator, the time-averaged PLS images of Cross-sections C1-C6 are presented in Fig. 7(a), whereas contours of Mach number and nondimensionalized static temperature T/T∞(T∞is the static temperature of the freestream) on the same cross-sections are illustrated in Fig. 7(b). Generally, the scattered light is strong in the region containing a large number of tracers,resulting in a bright region in the PLS images. As shown in Fig. 7(a),apparent dark regions are observed in the center of the flow field, although the rear silhouette of the vortex generator slightly blurs the PLS images of C1-C3 due to the diffuse reflection of light on the lateral surfaces of the vortex generator. Interestingly, the central dark regions in Fig. 7(a) nearly coincide with the low Mach number regions in Fig. 7(b)because the sufficiently high temperature of the local flow vaporizes the tracers.44-46Thus, the central dark region is surrounded by a shear layer Σ.Actually,the central dark region in the PLS image is dominated by CVPs, which is shown in Section 3.1.3.When compared with the images of C1-C3 in Fig.7(a),an evident increment in the transverse height of the central dark region is found in the images of C4-C6, suggesting the stretching of the CVPs in the downstream flow. Moreover,an Arch-Shaped shock(AS)and streamwise vortical structures(Vortex A and Vortex B)are also identified in the wake flow of the vortex generator (see Fig. 7(a)). Therefore, comprehensive comparisons and discussions on the flow physics are given in appropriate locations throughout Section 3.1.

As shown in Fig.8,the numerical results are compared with the experimental data in terms of the transverse height Δh of the central dark region, in which the experimental data are obtained by ten time-averaged PLS images and the numerical data are calculated by the distance between the upper and lower edges of the shear layer Σ.It is obvious that the numerical results are in good agreement with the experimental data.Note that Δh changes slightly at the beginning of the wake flow, whereas an evident increment appears near the location of x/h = 2.5. Thus, the evolution of the wake is divided into two stages: Stage Ⅰand Stage Ⅱin the following discussion.

Fig. 6 Comparison between experimental schlieren and present simulation.

Fig. 7 Overview of mean flow field.

3.1.2. Vortical structures

Fig. 8 Comparison between experimental and numerical data.

It is of great importance to reveal vortical structures because they significantly affect the wake flow of the vortex generator.Major vortices in the wake flow of the vortex generator are identified using contours of streamwise vorticity (ωx) with the help of numerical simulation. As illustrated by the threedimensional streamlines in Fig. 9(a), the streams from the top surface and the swept lateral surfaces of the vortex generator converge near the spanwise symmetry plane, which entrain the nearby fluids to form the PCVP at the beginning of Stage Ⅰ.Simultaneously,a Secondary CVP(SCVP)is generated underneath the PCVP by the streams from the bottom surface of the vortex generator, as shown in Fig. 9(b). For a more detailed generation mechanism of the CVPs induced by the ramp vortex generator, see Ref. 9. Note that both the strength and size of the PCVP are greater than those of the SCVP,and the rotating directions of these two CVPs are opposite. Generally, streamwise developments of the PCVP and SCVP dominate the wake flow of the vortex generator.

As shown in Fig. 9, two small Vortices A and B are also identified in the cross-section of the flow field. The formation of these vortices is revealed in Fig. 10. As shown in Fig. 10(a),Vortex A is produced by the interaction between the swept shock generated from the leading edge of the trestles and the boundary layer on the bottom surface of the vortex generator,which is similar to the main separation vortex observed in the flow field of the shock wave/boundary-layer interactions initiated by a single fin mounted on a flat plate.47Moreover, the wake of the trestle interacts with the streams from the top surface of the vortex generator and rolls up the downstream flow to form Vortex B(see Fig.10(b)).As Vortex A is far from the PCVP and SCVP,its influence on the PCVP and SCVP can be neglected.However,Vortex B may interact with the PCVP and SCVP due to its proximity to these CVPs.It is therefore necessary to examine the evolution of these CVPs in the following discussion.

Fig. 9 Three-dimensional streamlines colored by streamwise vorticity highlighting PCVP and SCVP.

Fig. 10 Three-dimensional streamlines colored by streamwise vorticity highlighting Vortex A and Vortex B.

3.1.3. CVP-induced velocity

To examine the evolution of these CVPs in the flow field, the transverse velocity(Uy)and the spanwise velocity(Uz)induced by the PCVP and SCVP are analyzed.The time-averaged PLS image of C4 and the corresponding numerical result are illustrated in Fig.11.It is obvious that the PCVP and SCVP dominate the local central dark region in the PLS image.As shown in Fig.11(a),the central dark region narrows near the middle,where the nondimensionalized spanwise velocity Uz/U∞induced by the PCVP and SCVP reaches a peak (see the red arrow in Fig. 11(b), and U∞is the freestream velocity). The streamlines in Fig. 11(b) indicate that the PCVP and SCVP rotate in opposite directions and entrain a large quantity of high-momentum fluids into the central dark region. These fluids collide in the interior of the central dark region and then move along opposite transverse directions to feed the PCVP and SCVP. Simultaneously, the lifting-up of the central dark region induced by the PCVP pushes the shock upwards and thus forms the bulged shock AS.

Fig. 11 Flow field on C4.

Fig. 12 Transverse positions of Uy,max, Uy,min, and SP0 at various streamwise locations.

As shown in Fig.11(b),the positions of the maximum(Uy,-max) and minimum (Uy,min) transverse velocities induced by CVPs are identified to distinguish the transverse movements of the PCVP and SCVP. Due to opposite rotating directions of the PCVP and SCVP,a saddle point SP0is formed between the transverse positions of Uy,maxand Uy,min, as illustrated by the streamlines in Fig. 11(b). Another two saddle points, SP1and SP2, are identified above the PCVP and beneath the SCVP,respectively.The transverse positions of Uy,max,Uy,min,and SP0at different streamwise locations are extracted from the numerical results and compared in Fig. 12. At the beginning of Stage I, the transverse position of Uy,maxdescends slightly, whereas those of Uy,minand SP0ascend slightly, suggesting that the immature PCVP and SCVP get close to each other. However, this trend is turned over in Stage II, in which the transverse positions of Uy,maxand Uy,minmove upwards and downwards, respectively. In other words, the PCVP and SCVP depart from each other,which is responsible for the distinct increment of Δh in Stage II(see Fig.8).Note that SP0also moves downwards and gradually catches up with the transverse position of Uy,min, suggesting shrinkage of the SCVP in Stage II. Thus, the PCVP dominates the wake flow further downstream of Stage II.

To reveal the velocity features of the CVPs in the spanwise symmetry plane, the profiles of Uy/U∞induced by the PCVP and SCVP at typical streamwise locations in Stages I and II are extracted and shown in Fig. 13. For comparison, the numerical results of an MVG immersed in a hypersonic boundary layer with a freestream Mach number of 5 conducted by Sun et al.26are presented in Fig. 13. Sun et al.26reported that Uy,maxdecays heavily and that Uy,minchanges slightly with streamwise locations in the hypersonic boundary layer, as shown in Fig. 13(a). In contrast, Uy,maxchanges slightly and Uy,minincreases obviously with streamwise locations in the present work. It is of great importance to reveal the reasons for these differences because they significantly affect the evolution of CVPs. When the PCVP entrains the low-momentum fluids in the boundary layer outwards, it produces a significant shear stress to reduce Uy,maxin return. The location of Uy,minremains close to the wall and immerses in the low-momentum fluids, resulting in a slight change in the magnitude. However, when CVPs entrain nearby high-momentum fluids outwards with the absence of a boundary layer(the present work), they can mitigate the decreasing trend of Uy,maxand enhance the value of Uy,min.

As shown in Fig.13(a),the profiles of Uydisplay some similar variation characteristics at different streamwise locations.Sun et al.30proposed a scaling law for the profiles of Uybased on the experiments of an MVG immersed in a supersonic boundary layer. In a subsequent numerical study, Sun et al.26demonstrated that this scaling law works well for an MVG immersed in a hypersonic boundary layer. However, it is still an open issue whether this scaling law is suitable for hypersonic flow in the absence of a boundary layer. Following the procedures proposed by Sun et al.30the scaling law is written as Eq. (1) and Eq. (2).

Fig. 13 Profiles of transverse velocity at spanwise symmetry plane and typical streamwise locations.

where ymaxdenotes the transverse location of Uy,max. After these scaling procedures, the present scaled profiles of Uyin Fig. 13(b) still change wildly with streamwise locations rather than collapsing together in the results obtained by Sun et al.26In other words, the present profiles of Uydo not follow Sun’s scaling law.30Sun’s scaling law does not take into account the influence of the SCVP. Thus, additional characteristics from the present CVPs should be sought to establish a new scaling law.

Considering opposite motions of the PCVP and SCVP in the present work (see Fig. 11(b)), it is necessary to analyze the induced profiles of Uyseparately. As shown in Fig. 13,SP0, SP1, and SP2vary with streamwise locations, which have a great impact on the shapes of Uyprofiles.In other words,the original Yscalecannot take into account these variations.Because the profile segments of Uybetween two adjacent saddle points are dominated by the PCVP and SCVP,the distance between SP0and SP1(h1) and that between SP0and SP2(h2)are employed as the characteristic heights to scale (y - ymax)and(y-ymin)for the PCVP and SCVP,respectively.Here ymindenotes the transverse location of Uy,min.A new scaling law for CVPs without the boundary layer in the hypersonic flow is written as Eq. (3) and Eq. (4). As shown in Figs. 14(a)-14(b),the scaled profiles of Uyat different streamwise locations using Eqs. (3) and (4) collapse much better than those using Sun’s scaling law(see Fig.13(b)).These results indicate that the profile segments of Uyinduced by the PCVP and SCVP obey a similar form of scaling law.Due to the shrinkage of the SCVP,SP0and SP2converge gradually downstream of x/h=6,which makes it difficult to identify h1and h2accurately. Thus, the scaled profile segments of Uyinduced by the PCVP and SCVP downstream of x/h = 6 are not shown in Fig. 14.

To quantitatively evaluate the entrainment effects induced by the PCVP and SCVP from the experiments, the position of Vortex B is used as an index because Vortex B is close to CVPs and sensitive to the entrainment of CVPs (see Fig. 11).As Vortex B is much weaker in strength and size,the influence of Vortex B on CVPs is minor. The geometric center spacing Δd of Vortex B in Cross-sections C2-C6 is extracted and plotted in Fig. 15, where Δd in each Cross-section is calculated by ten time-averaged PLS images. The decrease in Δd along the streamwise direction indicates that Vortex B is gradually driven to the spanwise symmetry plane. Interestingly, compared with Δd in Cross-sections C2-C3, Δd in Cross-sections C4-C6 decreases sharply and fluctuates violently, indicating that the flow state in Stage II may be different from that in Stage I.Thus,instantaneous PLS images with a higher spatial and temporal resolution are discussed in Section 3.2.

3.2. Instantaneous flow field

Fig.14 Profiles of transverse velocity scaled by present modified scaling law.

Fig. 15 Geometric center spacing (Δd) of Vortex B.

3.2.1. Instantaneous flow features in spanwise symmetry plane Fig. 16 presents an instantaneous PLS image pair captured with a time delay of 1.5 μs in the spanwise symmetry plane(z/h = 0) of the flow field. As shown in the image of time t in Fig.16,a relatively stable region in Stage I,close to the trailing edge of the vortex generator, is observed as a low luminance stripe, which shows a tendency to shrink. However,this relatively stable region can only be sustained for a short distance, after which it is overtaken by Stage II, where the gradual wriggling of the local shear layer (Σ) occurs.

Fig. 16 Instantaneous flow field.

Thanks to the high spatial and temporal resolution visualization technique, the undulating shear layer (Σ) is obviously identified, and some arc-shaped shocklets (marked by white dashed curves in Fig. 16)are clearly visible on the shear layer,which are similar to the shocklets reported by Wang et al.48using an MVG immersed in a supersonic boundary layer. The undulating shear layer (Σ) penetrates into the upper hypersonic flow, resulting in large disturbances that act like bluff bodies. Hence, arc-shaped shocklets form near local humps of the shear layer and interact with the original shock AS.As a result, the shock AS is elevated far downstream.

Note that a train of small-scale structures marked by white dotted squares in Fig. 16 appear downstream of C6 (x/h = 5.5), which are similar to the K-H vortices induced by shear from the upper hypersonic flow. Based on the instantaneous PLS image pair in Fig. 16, the streamwise velocity of the small-scale structures is calculated to be approximately 1.3 km/s,which is close to the velocity of the mainstream outside. As shown in Fig. 16, the much smaller features further downstream of the wake flow indicate that the flow in Stage II is unstable.

3.2.2. Instantaneous flow features in cross-sections

A series of instantaneous PLS images at various cross-sections are presented in Fig. 17 to give a first glance of the instantaneous flow field.As expected,the instantaneous flow topology presents more small-scale structures than that of the timeaveraged PLS images(see Fig.7(a)).In Stage I(C1-C3),vortex A and vortex B gradually mature,and the central dark regions are relatively stable and smooth.In Stage II(C4-C7),the central dark regions become more irregular at C4-C5,and Vortex B is observed to be entrained into the interior of the central dark regions at C6-C7, whereas the locations of Vortex A remain stable. This phenomenon indicates that the flow becomes unstable and the mixing process is enhanced in Stage II. Thus, much emphasis is placed on the instantaneous flow features of C4-C7 in the following discussion.

Fig. 17 Overview of instantaneous flow field.

Fig. 18 Instantaneous PLS images of C4-C5.

The close-up views of C4 and C5 are presented in Fig. 18.Compared with C4, the central dark region of C5 becomes longer,suggesting that the PCVP and SCVP depart from each other. Meanwhile, the central dark region of C5 becomes narrower, which is consistent with the sharp reduction of Δd in Stage II (see Fig. 15), indicating that much nearby highmomentum fluids are entrained into the interior of the PCVP and SCVP (see Fig. 11(b)). Hence, enhanced mixing between CVPs and outside high-momentum fluids is expected to occur in Stage II.

As shown in Fig.19,the instantaneous cross-sectional flow field of C6 captures the mixing between Vortex B and the central dark region,which confirms that the enhanced mixing process occurs at approximately x/h = 5.5. Furthermore, the image of C7 records the collision of Vortex B in the spanwise symmetry plane of the central dark region,showing the significant influence of the entrainment effect. Although the SCVP shrinks and the mixing process is dominated by the PCVP far downstream of Stage II (see Fig. 12), the temperature of the streams forming the SCVP is sufficiently high to vaporize the tracers (see Fig. 7(b)). As a result, these high-temperature streams are still shown as a dark region in C7. The enhanced mixing between the PCVP and outside high-momentum fluids eventually results in the unstable flow state far downstream of Stage II.

Fig. 19 Instantaneous PLS images of C6-C7.

The distance from the trailing edge of the MVG to where enhanced mixing occurs is an important parameter for flow control. Pickles and Narayanaswamy49reported that the mixing between the low-momentum fluids near the wall and the outside high-momentum fluids becomes sufficient downstream of the MVG in a range of 8h-13h. The supersonic boundary layer velocity profile becomes fuller at this range, and thus,the capability of resisting flow separation is improved.According to Sun et al.29the wake structures generated by the MVG inside a hypersonic boundary layer become unstable at approximately 12h downstream of the MVG. It seems that the development distance needed for the mixing process to become evident in the hypersonic boundary layer is longer than that of the supersonic regime. However, it is found that the mixing between CVPs and outside high-momentum fluids becomes evident at 5.5h downstream of the vortex generator in the present work, which is earlier than that immersed in the boundary layer. This result enriches the knowledge of CVPs with an absence of a boundary layer in the hypersonic regime.

CVPs generated by a large-scale ramp vortex generator with an absence of a boundary layer are investigated using the icecluster-based PLS method and numerical simulation at a nominal flow Mach number of 6. A series of cross-sectional PLS images of the CVPs are achieved. A PCVP and a SCVP with opposite rotating directions are identified in the flow field.Three saddle points are distinguished in the cross-sectional flow field, including SP0between the PCVP and SCVP, SP1above the PCVP, and SP2beneath the SCVP. According to the different features of the PCVP and SCVP, the wake flow is divided into two stages. In Stage I, the PCVP and SCVP gradually mature with the streamwise locations, and the wake flow is relatively stable. In Stage II, the PCVP and SCVP depart from each other. As the SCVP shrinks further downstream of Stage II, the PCVP gradually dominates the wake flow,and the wake flow becomes unstable with the generation of many small-scale structures. The scaling law for transverse velocity(Uy)in the spanwise symmetry plane induced by CVPs immersed in the boundary layer is not suitable for CVPs in the present study.Thus,a new scaling law is proposed and demonstrated to work well, in which the transverse distance between SP0and SP1, and that between SP0and SP2are adopted to scale the profiles of Uyinduced by the PCVP and SCVP separately. Moreover, the PLS images show that the mixing between CVPs and outside high-momentum fluids becomes evident at approximately 5.5h downstream of the vortex generator, which is earlier than that immersed in the boundary layer.These results deepen the understanding of CVPs encountered in the regions far away from the boundary layer in the hypersonic regime.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Nos. 11772325 and 11621202).

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