The experiments were performed in a supersonic low-noise wind tunnel at Mach number 3 (Fig. 1). The total temperature T₀ is 300 K and the total pressure P₀ is 101 kPa. The experimental parameters including Mach number Ma_∞, unit Reynolds number Re, and the flow velocity U_∞ are given in Table 1. The dimensions of the test section are 120 mm in height, 100 mm in width, and 250 mm in length. The testing model for the FFS is h_f = 10 mm in height (δ/h_f = 1.02, δ is the undisturbed turbulent boundary layer thickness), and 100 mm in width. Note that the width of the model is the same as that of the test section; therefore, the flow field at mid-span can be considered as two-dimensional (2D). The testing model is placed on a flat-plate. The micro-ramp in the present experiments has a height h = 4 mm (i.e., 39.2% δ), with a wedge half angle α = 24° and a chord length c = 7.2h. It is scaled to Anderson’s specification, as shown in Fig. 2. An array of three micro-ramps are placed ahead of the testing model, with the spanwise space (the distance between two micro-ramps’ center line) s = 7.5h, as shown in Fig. 3. The center line of the array is aligned with the center line of the flat-plate. The distance between the trailing edge of the micro-ramps and the leading edge of the FFS is 70 mm.

Fig. 1.

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	Fig. 1. Mach 3 low-noise wind tunnel.

Table 1.

Table 1.

Table 1. Experimental parameters. . Ma∞ T0/K P0/kPa Re/m−1 U∞/ms−1 3.0 300 101 7.5×106 620

Table 1. Experimental parameters. .

Fig. 2.

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	Fig. 2. Geometry of Anderson’s micro-ramp (h = 4 mm, c = 7.2h, α = 24°).

Fig. 3.

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	Fig. 3. Schematic of experimental setup.

The NPLS is an optical flow visualization technique based on Rayleigh scattering, which uses the nanoparticles as tracer particles.^[16] It has been used to investigate the supersonic mixing layer, boundary layer, compression ramp, aero-optics, and so forth.^[17–19] As shown in Fig. 4, the NPLS system is composed of a nano-particle generator, a dual-cavity Nd:YAG laser, an interline transfer double-exposure CCD camera, a synchronizer, and a computer. The laser with 500 mJ pulsed energy at the wavelength of 532 nm and 8 ns pulse duration is used as a light source. The laser beam is transformed into a uniform light sheet with the thickness less than 0.5 mm by a set of cylindrical lenses. The flow is imaged using an interline transfer CCD camera with the resolution of 2048×2048 pixels. The PIV system shares the same nano-particle generator with NPLS system. Planar PIV measurements are carried out to capture the instantaneous and average velocity fields.

Fig. 4.

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	Fig. 4. Schematic diagram of NPLS system.

Instantaneous images of Mach 3 turbulent flow over the FFS without and with micro-ramps are shown in Fig. 5. The coordinates’ origin x = 0 is located at the leading edge of the FFS and the coordinates of the trailing edge of the micro-ramps are x = −70 mm. In Fig. 5(a), the shock wave S₁ is the separation shock; the incoming boundary layer exhibits small hierarchy structures and has been already fully developed turbulence. In Fig. 5(b), the shock waves C₂ and C₃ are generated by the micro-ramps; the separation shock C₁ is distorted by the large-scale vortex structures. Compared with Fig. 5(a), the flow structures are greatly altered in Fig. 5(b). It can be seen that the typical boundary layer is replaced by the micro-ramp’s wake flow, which has a larger scale than that of the incoming boundary layer. Close to the micro-ramp’s trailing edge, the flow structures exhibit a fairly darker strip, which is a slice of the micro-ramp’s wake. The dark zones correspond to cross sections of the ramps’ wakes which maintain an approximate round shape. The wake’s interior displays a particular structure with lower luminance that appears to be the vortex cores of the primary counter-rotating vortex pair.^[17] However, after a length of about 4δ (at about x = −30), it is replaced by a new large-scale vortex, which is characteristic of intermittent large-scale structures and can survive downstream the FFS.

Fig. 5.

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	Fig. 5. Instantaneous images of Mach 3 flow over the FFS (a) without micro-ramps and (b) with micro-ramps.

Figures 6 and 7 show an instantaneous image pair with a 10 μs delay of Mach 3 flow over the forward facing step without and with the micro-ramps, respectively. In Fig. 6, after a time interval of 10 μs, the structure A in the outer part of the boundary layer only rotates clockwise for a small angle; the structure B close to the wall becomes larger and rotates anticlockwise for some angle; the structure C becomes longer in the streamwise direction. In Fig. 7, after a 10 μs delay, the structures A, B, and C have only a little change in spatial configuration but rotate clockwise for some angles. In summary, after a span of 10 μs, the large-scale structures keep most features and only move down streamwise for some distance; however, the small-scale structures have changed to some extent. The flow structures without and with the micro-ramps both have the characteristics of moving very fast and changing slowly in form.

Fig. 6.

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	Fig. 6. An image pair with a 10-μs delay of Mach 3 flow over the FFS. (a) t1, (b) t1 + 10 μs.

Fig. 7.

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	Fig. 7. An image pair with a 10-μs delay of Mach 3 flow over the FFS with the micro-ramps. (a) t2, (b) t2 + 10 μs.

Figure 8 reports a typical particle image recording of Mach 3 flow over the FFS. It can be seen that the particles are uniformly seeded. The total datasets of 500 image pairs were obtained. As a pre-processing step, the particle image was normalized using a min/max filter. The data analysis was performed using a correlation window of 32 × 16 pixels with a 50% overlap shifting, yielding a spatial resolution of 16 × 8 pixels (= 0.86 mm × 0.43 mm). Vectors’ validation was accomplished by deleting vectors whose cross-correlations did not meet a sufficient signal-to-noise ratio, and deleting those whose magnitudes and directions varied too much from their nearest neighbors.

Fig. 8.

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	Fig. 8. Particle image recording of Mach 3 flow over the FFS.

Figure 9 shows the velocity topology of Mach 3 flow over the FFS with and without micro-ramps. The average velocity profiles (u-component) are compared in Figs. 9(a) and 9(b), while the turbulent intensities are in Figs. 9(c) and 9(d). The U/U_∞ = 0 line distinguishes the reversal region from the outer flow. Without the micro-ramps, the range of the reversal flow zone in streamwise direction is 3.4δ, while it is 1.7δ with the control of micro-ramps. The reduction is 50%. The flow field contains a high-velocity outer layer (typically U/U_∞ > 0.5), and a low-velocity inner layer (typically U/U_∞ < 0.5).^[17] With the control of micro-ramps, the low speed region (0 < U/U_∞ < 0.5) is enlarged more than that without control. The cause is the reduction of reversal flow region and the intermittent large-scale structures induced by the micro-ramps. The reduction of reversal flow region makes the U/U_∞ = 0 line close to the wall. Meanwhile, the intermittent large-scale structures induced by the micro-ramps are larger than those without the micro-ramps, which make the U/U_∞ = 0.5 line far away from the wall. As a result, the velocity gradients in the low speed region are smaller than that without control. In addition, it results in lower turbulence level, as seen in Figs. 9(c) and 9(d). Herein, two-dimensional turbulence intensity is adopted. From Figs. 9(c) and 9(d), it can be seen that the region for the highest turbulence intensity values is almost the same as the zone between the zero-velocity line and U/U_∞ = 0.5 line.

Fig. 9.

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	Fig. 9. The average streamwise velocity profiles U/U∞ (a) without and (b) with micro-ramps. Turbulent intensity (c) without and (d) with micro-ramps. The solid black lines represent streamlines of U/U∞ = 0 and 0.5, respectively.

The unsteady behavior of the separation bubble is presented in Fig. 10, showing two instantaneous PIV images of Mach 3 flow over the FFS with micro-ramps. Figure 10(a) shows a small separation bubble of approximately 16 mm², while figure 10(b) presents a large separation bubble of about 102 mm². Here, the size of the separation bubble is approximately calculated by the flow reversal region within the zero-velocity line.

Fig. 10.

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	Fig. 10. Two uncorrelated instantaneous PIV images of the FFS flow field with micro-ramps. The solid black line shows the zero-velocity iso-line. (a) Small separation bubble. (b) Large separation bubble.

The local separation probability P_sep is defined as the percentage of the time reversed flow occurs at a certain point (x,y). Figure 11 compares the separation probability of the FFS flow field with and without micro-ramps, here, P_sep is calculated from an ensemble of 500 PIV images. From Fig. 10, it can be seen that the flow reversal region with the control of micro-ramps is only slightly reduced compared with no control. However, the probability of encountering reversed flow at a certain point is greatly reduced, i.e., the probability of encountering reversed flow is greatly reduced, especially at some regions close to the FFS, which can be seen from the grayness value of the Fig. 11. Mean flow separation can then be defined as the point where the flow is separated for 50% of the time, so the mean separated area A_sep is calculated by integrating the 50% separation probability domain. Without the control of micro-ramps, A_sep is 91.7 mm², while it is 48.5 mm² with the micro-ramps. The reduction is 47%.

Fig. 11.

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	Fig. 11. The separation probability Psep of the FFS flowfield (a) without a micro-ramp and (b) with micro-ramps.

Since the size of the separated bubble is correlated with the position of the separation shock,^[13,20] it is expected that when the size/unsteadiness of the separated bubble decreases, the unsteadiness of the separation shock also reduces. After the shock wave, there is a great velocity gradient. Therefore, the shock position can be determined by locating the biggest velocity gradient along the x direction at different wall-normal locations. In order to evaluate the unsteadiness of the separation shock, its location is calculated by finding the maximum of dV/dx along the horizontal line y = 3δ. The same procedure is repeated for the five rows of vectors above and below this line. After removing obvious edges, the separation shock locations are obtained in a least squares fitting procedure. This linear fit is employed to calculate the shock position at y = 3δ.^[13] The process is repeated for all 500 images, then the separation shock unsteadiness is represented by the standard deviation σ of shock locations x_s at y = 3δ. Without control of a micro-ramp, the standard deviation σ (x_s) is 1.71, while with micro-ramps it decreases to 1.26. The reduction in separation shock unsteadiness is 26% with the control of the micro-ramps.