Micro-Ramp Flow Control of Normal Shock/Boundary Layer Interactions

Transcription

1 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5-8 January 2009, Orlando, Florida AIAA Micro-Ramp Flow Control of Normal Shock/Boundary Layer Interactions Thomas Herges, * Erik Kroeker, Greg Elliott, and Craig Dutton University of Illinois at Urbana-Champaign, Urbana, Illinois, Boundary layer bleed has conventionally been used to control separation due to shock wave / boundary layer interactions (SBLIs) within supersonic engine inlets. However, bleed systems result in a loss of captured mass flow, incurring higher drag and ultimately lower propulsion system efficiency. Micro-ramp sub-boundary layer vortex generators (SBVGs) arranged in a spanwise array have been proposed in the past as a form of flow control methodology for shock wave/boundary layer interactions. Experiments have been conducted at Mach 1.4 to characterize flow details of such devices and obtain quantitative measurements of their ability to control the interaction of a normal shock and a turbulent boundary layer. The flow field was analyzed using Schlieren photography, surface oil flow visualization, and particle image velocimetry. An array of three micro-ramps, whose height was scaled to 40% of the incoming boundary layer thickness, was placed ahead of the shock interaction. It was demonstrated that the micro-ramps did entrain higher momentum fluid into the boundary layer which could improve boundary layer health. Specifically, the incompressible displacement thickness, momentum thickness and shape factor were decreased, and the skin friction coefficient was increased, for the SBLI with the micro-ramp array relative to the no-array case. Nomenclature Symbols A p = micro-ramp angle of incidence c = micro-ramp chord length C f = skin friction coefficient, τ w /[(1/2) ρ e u 2 e ] h = micro-ramp height H = incompressible boundary layer shape factor, δ * /θ H tr = transformed form factor M = Mach number PIV = particle image velocimetry s = spanwise micro-ramp spacing SBLI = shock/boundary layer interaction U = mean freestream velocity in streamwise direction u = mean velocity in streamwise direction u τ = wall-friction velocity, (τ w /ρ w ) 1/2 u + = mean velocity in streamwise direction in wall coordinates, u/u τ u = standard deviation of velocity in freestream direction u v = Reynolds shear stress v = standard deviation of velocity in transverse direction x = streamwise coordinate Xp = distance between normal shock and micro-ramp array y = tranverse coordinate * Graduate Research Assistant, Aerospace Engineering, 104 S. Wright St., AIAA Student Member. Graduate Research Assistant, Aerospace Engineering, 104 S. Wright St., AIAA Student Member. Professor, Aerospace Engineering, 104 S. Wright St., AIAA Associate Fellow. Professor and Head, Aerospace Engineering, 104 S. Wright St., AIAA Associate Fellow. 1 Copyright 2009 by Thomas Herges, Erik Kroeker, Greg Elliott, and Craig Dutton. Published by the, Inc., with permission.

2 y + z δ δ * θ ν Π ρ τ = transverse wall coordinate, yu τ /ν w = spanwise coordinate = boundary layer thickness = boundary layer incompressible displacement thickness = boundary layer incompressible momentum thickness = kinematic viscosity = coefficient of wake function = density = shear stress Subscripts e = conditions at the edge of the boundary layer w = conditions at the wall I. Introduction critical issue with the design of any supersonic inlet is the shock wave/boundary layer interactions (SBLIs) A that occur. In a supersonic inlet, air is decelerated by a series of shock structures usually terminating in a normal shock. As a result, the growing boundary layer along the wall of the inlet will experience adverse pressure gradients, possibly resulting in boundary layer separation and even engine un-start. Bleed systems, which extract low-momentum fluid from the boundary layer, have been demonstrated to reduce both boundary layer thickness and the severity of separation. 1 However, bleed systems result in a loss of captured mass flow. 2 The reduction in captured mass flow results in the necessity for larger inlets, incurring higher drag and ultimately lower propulsion system efficiency. In order to control SBLIs, several flow-control methods have been proposed in addition to boundary layer bleed systems. Early investigation into SBLI control focused on two-dimensional surface features that aimed to spread out the bifurcated lambda foot of the normal shock. A lambda shock decelerates the flow through a pair of oblique shocks, thus having a smaller total pressure loss than a single normal shock with the same static pressure rise. In addition, by spreading the lambda shock, the boundary layer will experience a smaller adverse pressure gradient and will be less likely to separate. This approach to SBLI control was investigated using a variety of methodologies including porous surfaces 3 and two-dimensional bumps. 4 While two-dimensional surface features like bumps proved effectual at spreading the lambda foot of the normal shock, the large surface features increase drag. Further investigation into SBLI control applied arrays of discrete three-dimensional surface features. Investigations of arrays of streamwise slots demonstrated that they were able to create the same bifurcated lambda structure as two-dimensional features when placed under an SBLI. 5 Of particular interest is that the lambda shock structure extended between the slots as well. 6 Thus, a series of three-dimensional features was demonstrated to be able to control the SBLI over a two-dimensional region. 7 With respect to the control efficacy of two-dimensional features like bumps, this suggested that the flow-control could be broken up into discrete arrays of three-dimensional features. Therefore, the flow-control benefit of a two-dimensional bump could be achieved with a smaller drag penalty. 8 Upon further investigation into arrays of three-dimensional geometries for SBLI control, sub-boundary layer vortex generators (SBVGs) demonstrated promise for reducing boundary layer growth and eliminating or reducing separation when placed upstream of the shock wave/boundary layer interaction By contrast to previously discussed control methods, SBVGs aim to control SBLIs by energizing the boundary layer and making it less susceptible to shock-induced separation. Like traditional vortex generators, SBVGs entrain higher momentum fluid to energize the low momentum fluid near the wall to improve boundary layer health and suppress or delay separation. Due to their smaller size, SBVGs have been shown to have significantly reduced device drag compared to conventional vortex generators. 11 One SBVG geometry that has been of particular interest is the micro-ramp. The micro-ramp has demonstrated the capability to reduce separation region length and reduce boundary layer thickness while being physically robust and easy to machine While micro-ramps did not completely eliminate boundary layer separation in the previous experiments, they could break up separation regions in the vicinity directly behind the micro-ramp. 13 Therefore, like the three-dimensional bump, an array of micro-ramps would be needed in order to control the SBLI for an entire supersonic inlet. The spacing of such an array has been previously proposed. 10 2

3 The micro-ramp geometry has been optimized in earlier investigations to minimize the transformed form factor (H tr ) and separately to maximize the total pressure difference downstream of the shock wave/boundary layer interaction. 10 It was found that, when the micro-ramp geometry was optimized for one criterion, the other criterion suffered. Three optimized geometries scaled by micro-ramp height were derived, one for each criterion separately and one for which each criterion was equally weighted. 10 These optimized geometries have been the focus of several recent investigations. 1,12-14 In the present study, the normal shock wave/boundary layer interaction downstream from a micro-ramp array geometry optimized for transformed form factor has been characterized. The array was investigated in a Mach 1.4 flow, for which the SBLI is incipiently separated. The flow field is analyzed using Schlieren photography, surface flow visualization, and particle image velocimetry. II. Experimental Setup A supersonic blowdown wind tunnel designed for Mach 1.4 was used to study the flow over and around a microramp array as well as the array s effect on a normal shock/boundary layer interaction. The cross-sectional area of the test section of the wind tunnel without the micro-ramp array measures 63.5 mm in height and width. The test section has a length of 416 mm. The tunnel has large windows in each side wall providing optical access for Schlieren photography and PIV and a smaller window in the top wall for surface flow visualization, as well as a small window in the bottom wall for PIV laser sheet access (see Fig.1; bottom wall window not shown). The air supply for the wind tunnel is an Ingersoll-Rand compressor with a 34 m 3 /min flow rate at 1 MPa pressure. The wind tunnel is capable of running longer than 20 minutes. The tunnel is controlled by both a pneumatic valve, with a Fisher TL 101 Process Controller, and a manual gate valve. The stagnation pressure and total temperature of the wind tunnel at the operating conditions of these experiments are kpa and 301 K, respectively. The incoming boundary layer is 4.25 mm thick as determined by PIV, and the unit Reynolds number is 30.4x10 6 m -1. The pressure measurements are made with Ashcroft K1 transducers with 1% full-scale accuracy. There are three pressure transducers, one for the supply tank, one for the tunnel stagnation pressure, and one for the static pressure in the test section. A thermocouple mounted in the contraction section of the tunnel measures the stagnation temperature. A schematic of the wind tunnel along with the position of the micro-ramp array is shown in Fig. 1. The dimensions used for the micro-ramp array examined were based on the optimized geometries from Ref. 10 and are listed in Table 1, as well as shown in Fig. 1a. These dimensions were obtained by minimizing the transformed form factor (H tr ) as explained in Ref. 10. The micro-ramp array was machined into an insert that could be replaced with a blank for measurements of the normal shock/boundary layer interaction without the micro-ramp array. Table 1: Micro-ramp dimensions Quantity Value δ 4.25 mm A p 24.0 h/δ 0.40 c/h 7.20 s/h 7.50 Xp/δ The normal shock was held in place with a 5 degree expansion of the upper wind tunnel wall that continued for mm in the x direction before ending with a lip; this expansion is referred to as the shock holder. The shock holder location with respect to the wind tunnel is shown in Fig. 1b. The shock holder held the normal shock at an average Xp/δ value of 14.4 (dimensionally, 61.2 mm) from half the chord length of the micro-ramp array to the normal shock with a standard deviation of 3.5 mm as compared to the target Xp/δ value of This is equivalent to the normal shock lying at a distance of 66.6 mm from the front of the micro-ramp array. 3

4 (a) Top Window Shock Holder Y Normal Shock X, Flow Direction Z Micro-Ramp Array Figure 1. Experimental schematics: (a) micro-ramp array and wind tunnel. Instantaneous Schlieren images and surface flow visualizations were obtained of the micro-ramp flow, as well as particle image velocimetry measurements. A top view of the experimental setup for Schlieren photography can be seen in Fig. 2a. Instantaneous Schlieren photography was conducted using a Newport Corp. flashlamp Model LM-1 pulsed at 10 Hz for a duration of 20 ns using a Quantum Components Model 9514 Pulse Generator and a Xenon Corporation Nanopulser Model 437B. The pulsed light was reflected through the test section using the optical components seen in Fig. 2a. Both collimating mirrors have a focal length of m. The image was cut horizontally from below with the knife edge before passing into the PCO.1600 CCD camera manufactured by Cooke Inc. 4

5 (a) Flash Lamp Mirror Free Stream Image Micro-ramp Array Knife Edge CCD Camera CCD Camera Free Stream Micro-ramp Array Normal Shock Figure 2. Schematic of flow visualization setups: (a) Schlieren photography and surface flow. The setup for the surface flow visualization is shown in Fig. 2b as a side-view schematic. The surface oil used for the surface flow visualization is one part oleic acid, five parts titanium dioxide and ten parts silicone oil. Images of the micro-ramp and surface oil flow were obtained through the window in the top of the wind tunnel while the tunnel was running at a stagnation pressure of kpa. The same PCO.1600 CCD camera used for Schlieren photography was used to obtain the surface flow visualization images. A schematic of the experimental setup used for obtaining the PIV images in this investigation is shown in Fig. 3a. A Laskin Nozzle was use to seed the main flow with Di-Ethyl-Hexyl Sebacate (DEHS), which generated particles with a diameter less than 1 mm. The seeding was introduced approximately 3.5 m upstream of the test section, which provided an adequate dispersion of the particles into the freestream flow. The particles were illuminated by a 0.5 mm thick light sheet that spanned the distance of each streamwise position as indicated in Fig. 3b. The light sheet was produced by a dual-head New Wave Nd:YAG laser in conjunction with cylindrical and spherical lenses. The laser was operated at 532 nm with each pulse delivering approximately 40 mj of energy. The time separation between laser pulses to illuminate the DEHS particles was ns. The PIV images recorded in the study were obtained with the same CCD camera as described above for the Schlieren photography setup. The resulting image pairs were then processed by the dpiv 2.1 software developed by Innovative Science Solutions, Inc. The PIV images were obtained at three streamwise and five spanwise positions as displayed in Fig. 3b for the experimental setup with the micro-ramp array. The diagram in Fig. 3b is a plan view of the xz plane, but the images were obtained in the xy plane at the three streamwise positions for five equally spaced spanwise locations of one symmetry unit of the micro-ramp array from the centerline of the center ramp (span 1) to the plane bisecting the gap to the adjacent ramp (span 5). PIV data for the experimental setup without the micro-ramps were only obtained at spanwise positions 1 and 5 for all three streamwise positions since the flow is nominally two-dimensional, and it was felt unnecessary to obtain measurements at all five spanwise locations. The normal shock is located between streamwise positions 1 and 2, so that streamwise position 1 is downstream of the micro-ramp array while being 5

6 upstream of the normal shock. Streamwise positions 2 and 3 help to show the effects of the micro-ramp array on the SBLI directly behind the normal shock as well as further downstream, respectively. (a) Mirror Streamwise Position 2 View Streamwise Position 1 View Streamwise Position 3 View PIV Pulse Spherical Lens Cylindrical Lens Normal Shock CCD Camera Laser Span 1 Span 2 Span 3 Span 4 Span 5 Average Normal Shock Position x=66.6 mm X=0 Position 1 x=37.1 mm to x=65.6 mm Position 2 x=67.6 mm to x=96.6 mm - x position measured from front of micro-ramp array Figure 3. (a) Schematic of PIV setup. Locations of PIV measurements. Position 3 x=122.0 mm to x=159.3 mm III. Results and Discussion A. Incoming Boundary Layer PIV measurements of the incoming boundary layer were conducted in order to accurately determine the incoming boundary layer parameters of the wind tunnel test section and to determine the correct micro-ramp sizing. The incoming boundary layer is characterized by the values shown in Table 2. The boundary layer thickness of the incoming flow was determined by the wall-normal distance at 99% of the mean freestream velocity. Table 2: Incoming Boundary Layer Properties Quantity Value δ 4.25 mm δ * mm θ mm H 1.31 C f Π 0.61 A modified wall wake velocity profile for turbulent compressible boundary layers, as discussed in Ref. 15, was fit to the measurements of the incoming boundary layer, as well as, to the boundary layer at streamwise position 3, both with and without the micro-ramp array. The comparison of the modified wall wake velocity profile for the 6

7 incoming boundary layer is shown in Fig. 4. The method of least squares was used to fit the wall-wake profile to the experimental velocity profiles. From the fit of the modified wall wake velocity profile to the experimental data, C f and the corresponding δ were calculated, as well as the wake strength Π value. The boundary layer incompressible displacement thickness and momentum thickness were then calculated from Eqs. (1) and (2) respectively. u dy (1) U δ * δ = 1 0 θ = u e δ 1 dy (2) 0 U e u U e The resulting velocity profile fit in normalized outer coordinates (y/δ) is shown in Fig. 4a. Figure 4b shows that the incoming boundary layer profile in wall coordinates is what would be expected for a fully-developed compressible turbulent boundary layer as shown in Ref. 16 for comparable Reynolds numbers. The wake strength parameter for the incoming boundary layer is slightly higher, but comparable to Π 0.55 ± 0.05 for a compressible turbulent boundary layer with Re θ > 2000 (Ref. 16). The skin friction coefficient for the incoming boundary layer is also quite similar to that seen using the modified wall wake velocity profile for turbulent compressible boundary layers as described in Ref. 15, and the incompressible shape factor compares well with that for a fully developed turbulent boundary layer at the Reynolds number of the wind tunnel test section. 17 (a) Figure 4. Measured incoming boundary layer velocity profile compared to the fit for a modified wall wake velocity profile: (a) in normalized outer coordinates and in wall coordinates. B. Schlieren Photography Instantaneous Schlieren photographs of the flow without a micro-ramp array in the Mach 1.4 tunnel are shown in Fig. 5. Close up view Fig. 5b shows that there is no clear evidence of separation due to the normal shock/boundary layer interaction, but that there is an increase in boundary layer thickness as compared with the incoming boundary layer. The flow is likely incipiently separated, meaning that the flow is just on the edge of separation. A Mach 1.4 SBLI is usually incipiently separated because the shock strength is not quite high enough to cause full separation. 18 A weak secondary shock downstream is also present in Fig. 5 showing the transonic nature of the flow field. 7

8 (a) Normal Shock Figure 5. Instantaneous Schlieren photography of normal shock without micro-ramp array: (a) wide view and zoomed-in view of normal shock/boundary layer interaction. Figure 6 displays instantaneous Schlieren photographs of the flow with the micro-ramp array. The boundary layer immediately behind the micro-ramp array apparently thickens in comparison to the incoming boundary layer, and it also produces periodic large-scale structures showing the turbulence created by the vortices generated by the micro-ramp array. There is an oblique shock produced by the leading edge of the micro-ramp as well as one produced at the trailing edge. The latter shock is most likely due to the increase in boundary layer thickness after the micro-ramp array. The increase in the boundary layer thickness will affect the necessary geometry of a supersonic inlet when compared to traditional inlet designs using a bleed system for boundary layer control. (a) Normal Shock (c) Micro-ramp Array Figure 6. Instantaneous Schlieren photography of normal shock with micro-ramp array: (a) wide view, zoomed-in view of normal shock/boundary layer interaction, and (c) zoomed-in view of micro-ramp array. Comparing Figs. 5 and 6, it appears that the boundary layer is thicker after the normal shock with the microramp array in the flow than without it in the flow field. There also does not appear to be any clear evidence of separation of the flow, and it is likely incipiently separated with the micro-ramp array as well as without the microramp array. C. Surface Flow Visualization A surface flow visualization photograph of the micro-ramp array is shown in Fig. 7. The streaklines past the trailing edges of each micro-ramp show how the micro-ramp creates two large counter-rotating vortices, one on each 8

9 side. The darker areas are indicative of the high-momentum flow of these vortices along the surface of the wind tunnel. The surface flow visualization also shows how the flow curves over the edges of the front face of the microramp creating the vortices as this flow separates from the ramp. The two large vortices along the trailing edges of the micro-ramp are shown by the small amount of oil left just behind the two trailing edges. This oil also shows that there might be smaller secondary counter-rotating vortices created along with the larger main vortices. At the very tip of the trailing edge there is a deposit of oil indicating that the flow has separated there, but a little downstream of this, the large vortices come together showing another region of high momentum along the wall surface. The flow to either side of each micro-ramp appears to be relatively unaffected, indicating that an array of micro-ramps is necessary to have a substantial effect on the flow in a supersonic inlet. Each micro-ramp in the array has similar surface flow characteristics showing that the flow at the micro-ramps is unaffected by neighboring micro-ramps, and the flow appears to be symmetric over each micro-ramp. The prominent features of the surface flow are marked in Fig. 7 (as also shown in Ref. 13). The high-momentum regions show that the flow near the surface is energized by the micro-ramp, indicating that it may indeed help with separation after a shock/boundary layer interaction. A potential problem is that the Schlieren images seem to indicate an increase in the boundary layer thickness downstream of the micro-ramp array, demonstrating that these high-momentum vortices start to lift off the surface the further downstream they get from the array. (a) Figure 7. (a) Surface flow visualization of micro-ramp array and with features marked. The surface flow visualization of the normal shock/boundary layer interaction is displayed in Fig. 8 both with and without the micro-ramp array. Figure 8 confirms what was seen by Schlieren photography in that the flow is apparently incipiently separated due to the normal shock/boundary layer interaction both with and without the micro-ramp array. In Fig. 8b the effects of the micro-ramp array (particularly the counter-rotating vortices) can be seen leading into the normal shock, but the vortices do not appear to have much of an effect on the surface flow indicating that they have likely started to lift off the surface the further they travel from the micro-ramp array, as also seen with the Schlieren photography. 9

10 (a) Normal Shock Figure 8. Surface flow visualization of normal shock wave: (a) without micro-ramp array and with micro-ramp array. D. Particle Image Velocimetry Figure 9 presents the mean velocity in the x direction for all three streamwise positions, with column one displaying spanwise position 1 (centerline) without the micro-ramp array, and columns two and three with the micro-ramp array for spanwise positions 1 (centerline of center ramp) and 5 (centerline of the adjacent ramp gap), respectively. The normal shock lies between streamwise positions 1 and 2. The effects of the shock can be seen at the downstream end of streamwise position 1 and at the upstream end of streamwise position 2. The spanwise position 5 data without the micro-ramp array is not presented here, since the flow is nominally two-dimensional. Figures 10, 11, and 12 present u, v, and u v, respectively, for the flow field in a similar format to Fig. 9 in order help present the data clearly. The first row in Fig. 9 shows how the micro-ramp array increases the boundary layer thickness directly behind the center span of the micro-ramp array (spanwise position 1) compared to the flow without the micro-ramp array. However, it appears that the boundary layer thickness has decreased for the span in-between micro-ramps of the array (spanwise position 5) with the micro-ramp array as compared to without it. The PIV data in Fig. 9 are also consistent with the results seen from Schlieren photography and surface flow visualization in that there is no clear evidence of flow separation and that the boundary layer is likely incipiently separated due to the normal shock/boundary layer interaction both with and without the micro-ramp array. The flow fields displayed in row two (streamwise position 2) show how the boundary layer thickness increases due to the normal shock, but there are still the same relations between the columns as seen for row one, i.e., a thicker boundary layer directly downstream of the ramp, but thinner between ramps, as compared to the no-array case. The boundary layer is clearly re-developing as it moves downstream to streamwise position 3 as displayed by Fig. 9g, 9h, and 9i, since these figures reveal that higher momentum flow is moving closer to the wall as it moves further downstream from the normal shock. 10

11 (a) (c) 11 (d) (g) (e) (h) (f) (i) Figure 9. Average u velocity at: (a) without micro-ramp array streamwise position 1/spanwise position 1, with micro-ramp array streamwise position 1/spanwise position 1, (c) with micro-ramp array streamwise position 1/ spanwise position 5, (d) without micro-ramp array streamwise position 2/spanwise position 1, (e) with micro-ramp array streamwise position 2/spanwise position 1, (f) with micro-ramp array streamwise position 2/ spanwise position 5, (g) without microramp array streamwise position 3/spanwise position 1, (h) with micro-ramp array streamwise position 3/spanwise position 1, and (i) with micro-ramp array streamwise position 3/ spanwise position 5. 11

12 (a) (c) 12 (d) (g) (e) (h) (f) (i) Figure 10. u velocity at: (a) without micro-ramp array streamwise position 1/spanwise position 1, with micro-ramp array streamwise position 1/spanwise position 1, (c) with micro-ramp array streamwise position 1/ spanwise position 5, (d) without micro-ramp array streamwise position 2/spanwise position 1, (e) with micro-ramp array streamwise position 2/spanwise position 1, (f) with micro-ramp array streamwise position 2/ spanwise position 5, (g) without microramp array streamwise position 3/spanwise position 1, (h) with micro-ramp array streamwise position 3/spanwise position 1, and (i) with micro-ramp array streamwise position 3/ spanwise position 5. 12

13 (a) (c) 13 (d) (g) (e) (h) (f) (i) Figure 11. v velocity at: (a) without micro-ramp array streamwise position 1/spanwise position 1, with micro-ramp array streamwise position 1/spanwise position 1, (c) with micro-ramp array streamwise position 1/ spanwise position 5, (d) without micro-ramp array streamwise position 2/spanwise position 1, (e) with micro-ramp array streamwise position 2/spanwise position 1, (f) with micro-ramp array streamwise position 2/ spanwise position 5, (g) without microramp array streamwise position 3/spanwise position 1, (h) with micro-ramp array streamwise position 3/spanwise position 1, and (i) with micro-ramp array streamwise position 3/ spanwise position 5. 13

14 (a) (c) 14 (d) (g) (e) (h) (f) (i) Figure 12. Reynolds shear stress at: (a) without micro-ramp array streamwise position 1/spanwise position 1, with micro-ramp array streamwise position 1/spanwise position 1, (c) with micro-ramp array streamwise position 1/ spanwise position 5, (d) without micro-ramp array streamwise position 2/spanwise position 1, (e) with micro-ramp array streamwise position 2/spanwise position 1, (f) with micro-ramp array streamwise position 2/ spanwise position 5, (g) without micro-ramp array streamwise position 3/spanwise position 1, (h) with micro-ramp array streamwise position 3/spanwise position 1, and (i) with micro-ramp array streamwise position 3/ spanwise position 5. 14

15 (a) (c) Figure 13. Average u velocity yz end views of flow field for all three streamwise positions with the micro-ramp array: (a) x = 50 mm, x = 88 mm, and (c) x = 153 mm. Figure 13 shows yz end views of the average u velocity with the micro-ramp array for streamwise position 1 at x = 50 mm, position 2 at x = 88 mm, and position 3 at x = 153 mm to help display the 3D effects of the micro-ramps. Since there are only five spanwise positions, or five z positions, the resulting contour plots rely heavily on interpolation and sometimes have sharp peaks, as can be seen. For clarity in the plot, the data for the five spanwise positions were reflected across the z = 0 axis in the plot since this is a symmetric flow. The outline of the center micro-ramp is also sketched in each figure. Figure 13 helps to further show the results seen in Fig. 9. At streamwise position 1 (Fig. 13a), there is a region of low-momentum flow directly above the ramp, but higher momentum flow near the edges of the micro-ramp. The height of this low momentum flow reveals how the generated vortices lift off the surface the further downstream they move from the micro-ramp. The effects of the vortices are seen in Figs. 13b and 13c as well, but the effects are less prominent due to the re-developing boundary layer approaching equilibrium after its interaction with the normal shock. At the edges of Fig. 13c there is an area of lower momentum flow further from the surface as seen in the middle of the flow where the effects of the vortices are greatest. This area of lower momentum fluid is likely due to the movement of the vortices from the other micro-ramps in the area moving towards the center of the wind tunnel as they move downstream due to the slight wall effects of the tunnel as seen in Fig. 8. Figure 10 shows the u turbulence characteristics of the flow field in the same arrangement shown in Fig. 9. There appears to be a high u shear layer created by the primary vortices of the micro-ramp array as seen in Fig. 10b. This shear layer is generated at the center span of the array directly behind the micro-ramp and is not present at the span in-between micro-ramps. The normal shock also increases u at each span with and without the micro-ramp array as expected. The u turbulence is greatest for a further distance from the surface of the tunnel at spanwise position 1 with the micro-ramp array, again indicating that it has a larger boundary layer thickness. At streamwise position 3 the u turbulence is more uniform along all spans both with and without the micro-ramp array. At this downstream-most position, the boundary layer appears to be thinner and less turbulent on the plane between ramps (Fig. 10i) than for the case with no array (Fig. 10g). (a) (c) Figure 14. u velocity yz end views of flow field for all three streamwise positions with the micro-ramp array: (a) x = 50 mm, x = 88 mm, and (c) x = 153 mm. 15

16 The yz end views of u in Fig. 14 show how the vortices generated by the micro-ramp start to merge and lift off the surface the further they move downstream. The turbulence generated by the micro-ramps is still localized after the normal shock as displayed in Fig. 14b, but has increased in uniformity across the z-span further downstream of the normal shock with a decrease in magnitude, as demonstrated in Fig. 14c. Figures 11 and 15 display the v characteristics of the flow field in streamwise and spanwise views, respectively. The trends seen in v are quite similar to the trends seen for u. The shear layer generated by the primary vortices of the center micro-ramp is still present after the normal shock as represented by the increased magnitude of v near the centerline of the micro-ramp as compared to the surrounding flow field in Fig. 15b. Figure 15c shows that v has become more uniform across the z-span further downstream of the normal shock as seen with u in Fig. 14c, indicating that the boundary layer is re-developing and that the effects of the micro-ramp array have spread across all of the spanwise positions downstream of the normal shock. (a) (c) Figure 15. v velocity yz end views of flow field for all three streamwise positions with the micro-ramp array: (a) x = 50 mm, x = 88 mm, and (c) x = 153 mm. The Reynolds shear stress (u v ) of the flow field is displayed in Figs. 12 and 16. The shear layer generated along the micro-ramp centerline is shown quite clearly in Fig. 12b, and Fig. 12e shows that this shear layer does continue through the normal shock, but is reduced in strength (i.e., peak shear stress) and appears quite weak at streamwise position 3 as shown by Figs. 12h and 16c. The Reynolds shear stress of spanwise position 1 without the micro-ramp array at a given streamwise position is very similar to that at spanwise position 5 with the micro-ramp array. The largest difference is seen at streamwise position 3 where there is a larger Reynolds shear stress in the boundary layer closer to the surface for the case without the micro-ramp array (Fig. 12g). (a) (c) Figure 16. Reynolds shear stress yz end views of flow field for all three streamwise positions with the micro-ramp array: (a) x = 50 mm, x = 88 mm, and (c) x = 153 mm. Figure 17 displays the boundary layer profiles of the average u velocity, u, v and Reynolds shear stress at spanwise position 1 both with and without the micro-ramp array. These boundary layer profiles are the profiles measured at x = 50 mm for position 1, x = 88 mm for position 2 and x = 153 mm for position 3. Figure 17 shows 16

17 quantitatively how the boundary layer is thicker with the micro-ramp on the micro-ramp centerline, as seen with earlier results. Figure 18 shows similar boundary layer profiles for spanwise position 5 on the symmetry plane between microramps. For this spanwise position, the boundary layer thicknesses for the cases with and without micro-ramps are nearer each other than for span 1 on the micro-ramp centerline. (a) (c) (d) Figure 17. Boundary layer profiles at spanwise position 1 for streamwise position 1, x = 50 mm, streamwise position 2, x = 88 mm, streamwise position 3, x = 153 mm both with and without micro-ramp array for: (a) average u velocity, u, (c) v, and (d) Reynolds shear stress (u v ). Figures 17a and 18a show that there is a small effect of increased mean velocity/momentum near the wall due to the micro-ramp array. The shear layer generated by the micro-ramp array vortices on the micro-ramp centerline can be seen in each of the flow characteristics in Fig. 17, but it is also shown how its effects decrease as the flow moves through the normal shock and further downstream. It does not appear that the micro-ramps have a significant effect further downstream of the normal shock and that their effect is mainly present near the micro-ramp array. Again in Figs. 17 and 18 it can be seen, as in the contour plots, that the boundary layer thickness at streamwise position 1/spanwise position 1 is thicker with micro-ramps than without, but at streamwise position 1/spanwise position 5 the boundary layer is thicker without micro-ramps than with. Figure 17d shows how the shear layer 17

18 generated by the primary vortices of the micro-ramp does lift off the surface the further the flow moves downstream. This is quite clear when comparing streamwise positions 1 and 2. The effects of the shear layer can be seen at streamwise position 3 (see Figs. 14c, 15c, and 16c), at a location further from the wall than at position 2, but its effects are substantially less prominent. Figure 17d also shows how the maximum Reynolds shear stress without the micro-ramp array is usually closer to the wall than that for the case with the array at spanwise position 1, while Fig. 18d shows that the Reynolds shear stress profile is very similar between the cases with and without the array at spanwise position 5. The main differences in the Reynolds shear stress profile between the case with and without the array at spanwise position 5, is that the maximum Reynolds shear stress is slightly further from the wall without the array than with at streamwise positions 1 and 2 unlike at streamwise position 3. (a) (c) (d) Figure 18. Boundary layer profiles at spanwise position 5 for streamwise position 1, x = 50 mm, streamwise position 2, x = 88 mm, streamwise position 3, x = 153 mm both with and without micro-ramp array for: (a) average u velocity, u, (c) v, and (d) Reynolds shear stress (u v ). The results of the modified wall wake velocity profiles described earlier for the incoming boundary layer are shown in Fig. 19 for streamwise position 3/spanwise position 1 both with and without the micro-ramp array as well as for the incoming boundary layer for comparison. When comparing the fitted boundary layer thicknesses to the experimental results, the largest percent difference is 21%, which means that there is a reasonable correlation 18

19 between the fitted wall wake velocity profile and the experimental data. We also note that the boundary layer thickness determined directly from the experimental data is the 99% velocity thickness while that determined from the Sun and Childs 15 curve fit corresponds to approximately the 99.5% velocity thickness. The skin friction coefficient for the incoming boundary layer profile from the modified wall wake profile is 2.01*10-3. The skin friction coefficient decreases as the flow moves through the normal shock wave, as expected, but the flow with the micro-ramp array has a higher skin friction coefficient with a value of C f = 1.52*10-3 compared to 1.37*10-3 without the micro-ramp array. This latter result shows the ability of the micro-ramp array to energize the near-wall region of the boundary layer. Table 3 lists the spanwise-averaged boundary layer properties at streamwise position 3 both with and without the micro-ramp array. Since the flow is nominally two-dimensional without the micro-ramp array, the values for only spanwise position 1 are presented. Figure 20 presents these same boundary layer properties at streamwise position 3 for all five spanwise positions with the array and spanwise position 1 without. Comparing Table 3 and Fig. 20a it can be seen that the boundary layer thickness is greater at spanwise positions 1 and 2 with the micro-ramp array than without, while only at spanwise position 1 on the micro-ramp centerline are the displacement thickness and momentum thickness greater with the micro-ramps than without. (a) (c) Figure 19. Experimental boundary layer velocity profile fitted with the modified wall wake velocity profile described above at: (a) the incoming boundary layer, streamwise position 3/spanwise position 1 with micro-ramp array, and (c) streamwise position 3/spanwise position 1 without micro-ramp array. 19

20 Table 3: Boundary layer properties at streamwise position 3 (x = 153mm) Quantity Average Spanwise Spanwise Value Value With Array Without Array δ 8.80 mm 8.47 mm δ * 1.44 mm 1.67 mm θ 1.07 mm 1.16 mm H C f Figure 20b and Table 3 show that the boundary layer at streamwise position 3 is closer to separation without the micro-ramp array based both on the incompressible shape factor and skin friction coefficient at all five spanwise positions. This is shown by the fact that the incompressible shape factor with the array is less than without the array, while the skin friction coefficient with the array is larger than without the micro-ramp array. These results show that the micro-ramp array does indeed improve the boundary layer health downstream of the normal shock/boundary layer interaction and can help resist boundary layer separation in stronger SBLIs. (a) Figure 20. (a) Boundary layer thickness, incompressible displacement thickness, and incompressible momentum thickness incompressible shape factor and skin friction coefficient all at streamwise position 3 (x = 153 mm) for all spanwise positions with and without the micro-ramp array. IV. Conclusion A micro-ramp array has been examined at Mach 1.4 and its effects on normal SBLIs have been investigated. The flow over the array has been described in detail. At the trailing edge of the micro-ramps, separation occurs forming a counter-rotating primary vortex pair. The primary vortex pair lifts off the surface as it moves downstream, entraining higher momentum fluid into the boundary layer. A shear layer is also produced by the micro-ramps on the micro-ramp centerline. The effects of the micro-ramps are most obvious in the region directly downstream of the micro-ramps. The shear layer generated by these primary vortices does persist through the normal shock, but is substantially reduced in strength. The shear layer is all but dissipated by the most downstream observation location examined here. The shear layer appears to be spanwise-localized to the region directly behind the micro-ramps and is not apparent in the regions between the micro-ramps in the array. This necessitates the use of an array of microramps for large-scale inlet flow control. The normal shock was apparently not strong enough to induce large-scale boundary layer separation in the current experiments. It was therefore not possible to determine the effectiveness of the micro-ramp array in resisting separation in these experiments. The micro-ramp array did increase the spanwiseaveraged boundary layer thickness downstream of the SBLI. However, the micro-ramp array increases flow 20

21 momentum near the surface as shown by a decrease in the spanwise-averaged values of δ *, θ, and H and an increase in C f relative to the case with no array. This indicates that micro-ramps can definitely help with improving the health of the boundary layer and could resist separation in stronger SBLIs. Micro-ramps may thus be employed to augment or possibly replace bleed in the design of future supersonic inlets, thereby reducing drag and improving aircraft performance. Acknowledgments The authors would like to thank Rolls Royce and Gulfstream for funding this work on small scale 2D microramp effects. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of Rolls Royce and Gulfstream. Additionally we would like to thank our colleagues, Prof. Eric Loth at the University of Illinois, Tim Conners, Robbie Cowart, and Tom Wayman at Gulfstream, and Rod Chima, Jim Debonis, and Stefanie Hirt at NASA for their discussions and input regarding this work. References 1 Bodner, J.P., Davis, D.O., Gerber, I., Hingst, W.R., Experimental Investigation of the Effect of a Single Bleed Hole on a Supersonic Turbulent Boundary-Layer, AIAA Paper , July Aktinson, M.D., Numerical Investigation of a Super-Sonic Inlet Using Bleed and Micro-Ramps to Control Shock- Wave/Boundary Layer Interactions, AIAA Chokani, N., and Squire, L. C., Transonic Shockwave/Turbulent Boundary Layer Interactions on a Porous Surface, Aeronautical Journal, Vol. 97, May 1993, pp Stanewsky, E., Aerodynamic Benefits of Adaptive Wing Technology, Aerospace Science and Technology, Vol. 4, No. 7, 2000, pp Smith, A., and Babinsky, H., Fulker, J., and Ashill, P., Experimental Investigation of Transonic Aerofoil Shock/Boundary Layer Interaction Control Using Streamwise Slots, Proceedings of Fluid Mechanics and Its Applications, IUTAM Symposium Transsonicum IV, edited by H. Sobieczky, Kluwer, Dordrecht, The Netherlands, 2002, pp Smith, A., Babinsky, H., Fulker, J., and Ashill, P., Control of Normal Shock Wave/Turbulent Boundary-Layer Interaction Using Streamwise Slots, AIAA Paper , Jan Holden, H.A., Babinsky H., Separated Shock Boundary-Layer Interaction Control Using Streamwise Slots, AIAA Journal, Vol. 42, No. 1, January February 2005, pp Babinsky, H., Ogawa, H., Three-Dimensional SBLI Control for Transonic Airfoils, AIAA , 3rd AIAA Flow Control Conference, 5-8 June 2006, San Francisco, California. 9 Ashill, P.R., Fulker, J.L., Hackett, K.C., Research at DERA on Sub Boundary Layer Vortex Generators (SBVGs), AIAA Anderson, B., Tinapple, J. and Surber, L., Optimal Control of Shock Wave Turbulent Boundary Layer Interactions Using Micro-Array Actuation, AIAA , AIAA Fluids Engineering Conference, June 2006, San Francisco. 11 Lee, S., Loth, E., and Wang, C., LES of Supersonic Turbulent Boundary Layers with µvg s, AIAA Holden, H., and Babinsky, H., Effect of Microvortex Generators on Separated Normal Shock/Boundary Layer Interactions, Journal of Aircraft, Vol. 44, No. 1, January-February 2007, pp Pitt Ford, C.W., Babinsky, H., Micro-Ramp Control for Oblique Shock Wave / Boundary Layer Interactions, AIAA Shinn, A.F., Vanka, S.P., Mani, M., Dorgan, A., Michal, T., Application of BCFD Unstructured Grid Solver to Simulation of Micro-Ramp Control of Shock/Boundary Layer Interactions, AIAA , 25th AIAA Applied Aerodynamics Conference, Jun , Miami. 21

22 15 Sun, C. C. and Childs, M. E., A Modified Wall Wake Velocity Profile for Turbulent Compressible Boundary Layers, Journal of Aircraft, Vol. 10, pp , June Fernholz, H.H. and Finley, P.J. A Critical Commentary on Mean Flow Data for Two-Dimensional Compressible Turbulent Boundary Layers, AGARDograph 223, Fernholz, H.H. and Finley, P.J. Incompressible Zero-Pressure-Gradient Turbulent Boundary Layers: An Assessment of the Data, Progress in Aerospace Science, Vol. 32, pp , Carroll, B.F., A Numerical and Experimental Investigation of Multiple Shock Wave/Turbulent Boundary Layer Interactions in a Rectangular Duct, Ph. D. Dissertation, Mechanical and Industrial Engineering Dept., University of Illinois at Urbana-Champaign, Urbana, IL,