Hypersonic Shock-Wave/Boundary-Layer Interactions on a Cone/Flare Model

Transcription

1 AIAA AVIATION Forum June 25-29, 2018, Atlanta, Georgia 2018 Fluid Dynamics Conference / Hypersonic Shock-Wave/Boundary-Layer Interactions on a Cone/Flare Model Carson L. Running, Thomas J. Juliano, University of Notre Dame, Notre Dame, IN 46556, USA Joseph S. Jewell, Matthew P. Borg, Roger L. Kimmel Air Force Research Laboratory, th St., WPAFB, OH 45433, USA Time-resolved surface-temperature measurements have been carried out on a 7 halfangle circular cone/flare model in the AFRL Mach-6 Ludwieg tube using infrared thermography. Measurements were performed on a total of 16 different nosetip bluntness/flare angle geometries at two different freestream unit Reynolds numbers. Experimental measurements and computations were conducted on the upstream portion of the model to determine the state of the boundary layer entering the interaction region. Downstream Stanton-number contours and profiles were calculated and used to investigate the effect of nosetip bluntness, flare angle, and freestream unit Reynolds number on boundary-layer separation/reattachment locations and peak heating/heating slopes. The footprint of Görtler vortices was observed upon reattachment of the boundary layer on the flare and the nondimensionalized wavelength of these vortices was calculated. Wrapping the model with a thin, black, high-emissivity film successfully obtained high-quality infrared images on a low-emissivity model. Nomenclature c p specific heat capacity (J/kg K) k thermal conductivity (W/m K) L axial location of the cone/flare junction (mm) M Mach number p pressure (kpa) q heat flux (W/m 2 ) R local radius of curvature (mm) Re unit Reynolds number (/m) r nosetip radius (mm) St Stanton Number T temperature (K) u velocity (m/s) x streamwise distance (x = 0 at the model nosetip) (mm) y vertical distance (y = 0 on the model centerline) (mm) z spanwise distance (z = 0 on the model centerline) (mm) α thermal diffusivity (mm 2 /s) β camera angle with respect to x-axis ( ) y + local grid quality at the wall in the wall-normal direction ε emissivity θ camera viewing angle ( ) λ wavelength (mm) ρ density (kg/m 3 ) φ azimuth angle (φ = 0 along windward ray) ( ) Sub/superscripts n normal wall surface measurement 0 stagnation condition transformed coordinate intermediate coordinate freestream condition Graduate Research Assistant, Department of Aerospace and Mechanical Engineering. Student Member, AIAA. Assistant Professor, Department of Aerospace and Mechanical Engineering. Senior Member, AIAA. Research Scientist, AFRL/RQHF (Spectral Energies, LLC), Senior Member, AIAA. Aerospace Engineer, AFRL/RQHF, Senior Member, AIAA. Principal Aerospace Engineer, AFRL/RQHF, Associate Fellow, AIAA. Cleared for public release. Case Number 88ABW of 22

2 I. Introduction The aerothermodynamic loads on some hypersonic vehicles are strongly influenced by shock-wave/boundarylayer interactions. This phenomenon observed on an axisymmetric cone/flare geometry is illustrated in Fig. 1 and has been studied by a number of researchers As the boundary layer grows along the cone frustum, it faces an adverse pressure gradient due to the presence of the flare causing it to locally separate from the surface. Because the high pressure caused by the flare feeds upstream through the subsonic portion of the boundary layer, the separation takes place ahead of the cone/flare junction. 13 The separated boundary layer induces its own shock wave, identified in Fig. 1 as the separation shock. The separated boundary layer subsequently turns back toward the model flare reattaching at some downstream location causing a second shock wave called the reattachment shock. Upon reattachment, the boundary layer has become relatively thin and the pressure is high. Thus, this becomes a region of high local aerodynamic heating. In between the two shocks, a recirculation bubble is formed. Figure 1: Cone/flare shock-wave/boundary-layer interaction schematic. It is generally accepted that the separation location can be identified where the Stanton-number, St, slope increases for a turbulent boundary layer and decreases for a laminar boundary layer. 3 5, 14 It is also generally recognized that the peak heat flux observed on the flare occurs a small distance downstream of the physical 4, 15 reattachment point. Both of these heating phenomena can be measured with infrared thermography; therefore, locations of separation and reattachment can be determined. Although a number of previous studies have investigated this phenomenon, it is still a challenging problem for both experimentalists and computationalists alike. Knight et al. 12 addresses many of these challenges and discusses the need for more experimental data to validate computational models of shock-wave/boundarylayer interactions. Infrared-thermography measurements are especially valuable for computationalists because they provide global contours of the phenomenon. In addition, testing a diverse set of geometries and flow conditions is beneficial because it helps the research community gain insights to general trends affecting shock-wave/boundary-layer interactions. Because of these needs, the current study investigates the effect of nosetip bluntness, flare angle, and freestream unit Reynolds number on laminar and turbulent boundary-layer separation and reattachment. This geometry is applicable to hypersonic reentry vehicles and projectiles. II. Facility and Model A. Facility The results presented herein were collected in the Air Force Research Laboratory s (AFRL) Mach-6 Ludwieg tube wind tunnel. 16 The tunnel has a 30-inch-diameter, Mach-6 nozzle. Each test consists of two periods of steady flow, each of which is approximately 0.1 seconds long. Pitot pressure fluctuations are approximately 2 of 22

3 3%. 16 A custom plug-type fast valve is used to start the tunnel. The tunnel was run at two alternating stagnation-pressure conditions. All data for this work were collected during the first expansion period of steady flow for each of those two stagnation pressures. Table 1 summarizes the flow conditions for this first expansion period. Table 1: Flow conditions for the first expansion period. Test Condition M p 0 (kpa) T 0 (K) Re (/m) B. Model The model used in this work consisted of a 610-mm-long (with the sharp nosetip), 7 half-angle circular cone followed by a 76-mm-long flare section. The model has four interchangeable nosetips of varying radius r and four different flare angles, providing a total of 16 possible geometry combinations. The four nosetip radii are nominally sharp, 0.5 mm, 5.1 mm, and 10.2 mm. The four flare angles are 34, 37, 40, and 43. Figure 2 illustrates the model geometry for a given nosetip/flare combination. A laser-optical positioning device and digital protractor ensured that the model was positioned at 0 in both pitch and yaw directions relative to the tunnel nozzle. Figure 2: Model geometry (dimensions are in inches). r = 0.5 mm, 34 flare. The model is made of aluminum, which has low emissivity. In order to increase the emissivity for infrared measurements, the model s frusta and flares were wrapped in a matte-black film. The film was a 3M 1080 series film which has a thickness of 90 µm. Each section of the model was wrapped independently; however, the nosetip was not wrapped. Slight imperfections in the heating contours are observed where different sections of the model mate due to small gaps and overlaps in the film at those locations. It will be shown that these small forward- and backward-facing steps do not affect the measured heating rates in any significant way. A number of previous infrared-thermography studies have painted their models black in order to increase the emissivity. This is somewhat difficult to apply and even more difficult to remove if changes want to be made to the model s geometry and/or instrumentation. Painting the model creates a non-uniform 3 of 22

4 surface finish, which complicates calculating the heat flux because the paint-layer thickness is unknown and the emissivity is non-uniform. Painting the model creates surface roughness which can affect the model s boundary layer. Using a thin film provides a uniform surface thickness, less surface roughness, and easy removal and reapplication. Figure 3 shows the wrapped model in the wind-tunnel test section. Figure 3: Wrapped model in the wind-tunnel test section. The model was originally instrumented with four XCE A Kulite pressure transducers in the aft frustum. The pressure transducers were mounted flush with the aluminum surface along a ray of the cone that was not covered with the film nor imaged with the infrared camera. The pressure-transducer signal was collected at 2 MHz and conditioned with a custom signal-conditioning box. During the first test, the three downstream transducers were sucked into the model; two were broken. The most upstream transducer, located at x = 355 mm (as measured from the sharp nosetip), survived and provided pressure measurements for all the tests investigating the upstream boundary-layer state. III. A. Infrared Thermography Camera and Setup The surface temperature of the wrapped model was measured with an InfraTec 8300 hp infrared camera. The camera is a mid-wave, 14-bit camera with a spectral range of µm. The detector format is pixels. All images were acquired at 355 Hz, some with a telephoto lens having a focal length of 50 mm and others with a standard lens having a focal length of 25 mm. Each lens has its own factory calibration curve for the appropriate temperature range observed in this work. The camera viewed from a side port at the same height as the tunnel s centerline. The distance from the camera to the cone s midpoint was 840 mm. A 15-mm-thick calcium fluoride (CaF2 ) window was used for all of the tests because of its transmission range of µm. The window had an anti-reflective coating from µm. Surfacetemperature measurements were made accounting for the transmissivity, 0.94, of the window, the surrounding environmental temperature, and the emissivity of the film (discussed in the following subsection). B. Directional Emissivity Directional emissivity can be a source of significant error when measuring with an infrared-camera system. Infrared thermography is inherently a two-dimensional measurement technique and therefore one of its main limitations is accurately measuring a non-planar model. In the case of this work, the model being measured is three dimensional in nature. In addition, the process of radiation in general is highly dependent on the emissivity of the object emitting radiation. This combination of error sources illustrates the need for a correction technique that addresses the directional emissivity of the three-dimensional model if quantitative data along the edges of the model are desired. 4 of 22

5 The emissivity coefficient, ε, of the surface, depends on the angle, θ, between the direction normal to the emitting surface and the direction of the emitted radiation through the following relationship. ε(θ) = ε n cos(θ) a cos(θ)b (1) In this relationship, ε n represents the emissivity value when viewing normal to the surface, while a and b are the fitted constants. This dependence becomes strong at high viewing angles such as the edges of a conical model. See Ref. 17 for an example of this methodology. A rigorous study of the film s directional emissivity has not been conducted for this work; therefore, the values of a and b are unknown. The normal-viewing emissivity value, ε n, has been experimentally determined to be This bench-top experiment consisted of comparing surface thermocouple measurements to infrared measurements of the film and another material with known ε n. For most materials, the emissivity value is nearly constant for viewing angles that are less than 70. This trend can be seen in Fig. 4 (data taken from Ref. 17) for the material PEEK, which is a high performance plastic that is often used in infraredthermography studies. Because all quantitative data evaluated in this work come from the centerline of the model, it is reasonable to ignore directional-emissivity effects and calculate the surface temperature using ε n = To support this assumption of relatively low viewing angles, a global map of the local viewing angle of the model will be presented in the next section ) (deg) Figure 4: Directional emissivity, ε(θ), for PEEK (recreated from Ref. 17). C. Image-Mapping Technique As mentioned above, local viewing-angle values are needed in order to safely neglect directional-emissivity problems. In addition, image mapping can be used to generate precise coordinate transformations which are useful for an accurate representation of the data and especially useful when comparing infrared images to other optical measurements such as pressure-sensitive paint. Starting with the camera position and model geometry, the image-processing technique re-creates the image using a theoretical rendering of the model and an orthographic projection. The theoretical model is a useful construct because x and φ are known precisely at every point. The non-visible area of the model is cropped out based on the camera distance and position, while the visible part of the theoretical model is multiplied by a standard projection matrix to create a virtual 2-D image. An orthographic projection, as opposed to a perspective transformation, was used because the camera was sufficiently far away from the cone making depth-perception effects negligible. The orthogonal-projection-matrix relations are given by Equations 2 and 3 using homogeneous coordinates. 18 The angle θ represents the camera viewing angle in rotation about the models z-axis, and the angle β represents the camera position in rotation about the x-axis. x, y, and z are points on the model, x, z, and t are intermediate variables, and finally x and z are the coordinates of the transformed point. x z t = cos(θ) sin(θ) 0 0 sin(β) sin(θ) sin(β) cos(θ) cos(β) 0 cos(β) sin(θ) cos(β) cos(θ) sin(β) x y z 1 (2) 5 of 22

6 x = x t, z = z t (3) Because this projection is orthographic, t = 1. If this were a perspective transformation, t would be a depth-scaling parameter. After the projection, the actual image is scaled, aligned, and mapped onto the theoretically created image. The actual image then replaces the virtual image, and all the steps performed to create the virtual image are done inversely to the actual image. This step is where viewing distortion is corrected and the 3-D position of each pixel on the actual image is calculated. Once the 3-D position of each pixel is known, information about the image such as x-φ mappings or viewing angles, can be easily calculated. The image and 2-D projection of the model initially have different units, the image being in pixels and the 2-D projection in mm. A conversion factor is therefore needed to align the images. If registration points are visible then two or more registration points can be used to find this conversion. The 3-D position of the registration points can be put through the same 2-D projection as the virtual model, making the position of the registration points known in both the image frame and projection frame. If no registration points are visible, which is the case for this work, the corners of the model are used instead. The position of the corners, or tip, of the model are again found in both the actual and virtual images. Alignment to the theoretical model provide x, y, φ, and θ at every pixel on the model. Figure 5 provides example outputs from this code. It is important to point out that along the centerline of the model, the local viewing angle, θ, is always less than 70. This supports the earlier approximation of using a constant emissivity value, ε n = (a) x (b) y (c) φ (d) θ Figure 5: Sample outputs from image-mapping code. D. Heat-Flux Calculations The surface heat flux was calculated by inputting the infrared-temperature data into a subroutine based on QCALC 19 (later translated into MATLAB 20 ). This code calculates the surface heat flux as a function of time from the temperature history for each pixel. The code was extended to include every pixel on the model s surface, allowing for the generation of a global surface-heat-flux map at a particular instant in time. This code solves the transient 1-D heat equation in either Cartesian, cylindrical, or spherical coordinates by implementing a second-order Euler explicit finite difference approximation. By implementing cylindrical coordinates, the model s local curvature is taken into account. As a result of the 1-D nature of this analysis, all lateral conduction is neglected which is a reasonable assumption for the short test times (0.2 seconds). 6 of 22

7 Generally this code assumes constant and homogeneous material properties. This assumption is not valid in this work since heat is transferred through both the film and the aluminum model at any given pixel location. The code was adapted to account for the composite nature of the model by inputting the associated thermal properties and local thicknesses of each of the two materials. Thermal contact resistance between the two materials was neglected. An adiabatic back-face boundary condition is assumed on the inner portion of the aluminum wall which is a reasonable assumption for the short test times. The material properties of the film and aluminum used in the heat-flux calculations can be seen in Table 2. Table 2: Thermal properties of the film and aluminum used for heat-flux calculations. Material c p (J/kg K) k (W/m K) ρ (kg/m 3 ) α (mm 2 /s) 3M 1080 Series Film Aluminum 6061-T Because 3M does not provide thermal-property information for their films, the film values seen in Table 2 were chosen based on discussions with a materials expert at the University of Notre Dame, Prof. Tengfei Luo. Prof. Luo estimated that the thermal conductivity, k, and specific heat capacity, c p, of the film would be on the order of W/m K and J/kg K respectively. These estimated values were selected based on the material composition of the film (layers of pigmented cast Polyvinyl chloride (PVC) and a solvent based adhesive back). Tabulated data for general-purpose PVC indicate that k = 0.19 W/m K and c p = 949 J/kg K. The heat-flux rates calculated with these values were lower than the expected rates based on empirical trends. A k value on the upper limit (0.5 W/m K) and c p value on the lower limit (900 J/kg K) of the estimated ranges yielded results with much better agreement and were therefore chosen as the values used for all of the heat-flux calculations in this work. The density, ρ, of the film was experimentally measured. Measuring the thermal properties of the film is difficult because it is so thin; however, a new system is currently being tested and should be capable of producing experimental values for both k and c p in the near future. In addition to heat flux, St was calculated to provide a dimensionless measure of surface heating. St will be defined in this work as, St = q ρ u c p (T 0 T wall ), (4) where q, ρ, u, c p, T 0, and T wall are the heat flux, freestream density, freestream velocity, specific heat capacity, stagnation temperature, and measured wall temperature, respectively. IV. Computational Efforts The mean flow over the 7 conical forebody is computed from the reacting, axisymmetric Navier-Stokes equations with a structured grid, using a version of the NASA Data Parallel-Line Relaxation (DPLR) code 21 which is included as part of the STABL software suite, as described by Johnson 22 and Johnson et al., 23 and has previously been used for similar blunt-cone cases by Jewell and Kimmel 24 25, 26 and others. This flow solver is based on the finite-volume formulation. The use of an excluded volume equation of state is not necessary for the boundary-layer solver because the static pressure over the cone is sufficiently low that the gas can be treated as ideal. The mean flow is computed on a single-block, structured grid (see Fig. 6) with dimensions of 401 cells by 359 cells in the streamwise and wall-normal directions respectively. The inflow gas composition in each case is air with O 2 and N 2 mass fractions. While the computation includes chemistry, the impact of chemical reactions is negligible, as the local maximum temperature does not exceed 490 K for any case. The wall temperature is constant at 297 K for each case. Zero angle of attack is assumed for all computations. Grids for the 7 half-angle cone with each of the four nosetips (see Table 3) were generated using STABL s built-in grid generator, and mean-flow solutions were examined to ensure that at least 100 points were placed in the boundary layer for each of two stagnation-pressure conditions (see Table 1), for a total of eight separate cases. The boundary-layer profiles and edge properties are extracted from the mean-flow solutions during post-processing. The wall-normal span of the grid increases down the length of the cone to a maximum of up 7 of 22

8 Table 3: Summary of grids generated, each corresponding to a different nosetip radius used in the present study. r (mm) Maximum Grid Height (mm) [m] [m] Figure 6: Grid for the r = 0.5-mm case with 401 streamwise and 359 wall-normal cells. For clarity, every third wall-normal cell is shown. to 92 mm at the base, allowing for the shock to be fully contained within the grid for all cases tested. The grid is clustered at the wall as well as at the nose in order to capture the gradients in these locations. The y + value for the grid, extracted from the DPLR solution for each case, is everywhere less than 1, where y + is a measure of local grid quality at the wall in the wall-normal direction. Stability analyses are performed using the PSE-Chem solver, which is also part of the STABL software suite. PSE-Chem 27 solves the reacting, two-dimensional, axisymmetric, linear parabolized stability equations (PSE) to predict the amplification of disturbances as they interact with the boundary layer. The PSE-Chem solver includes finite-rate chemistry and translational-vibrational energy exchange. The parabolized stability equations predict the amplification of disturbances as they interact with the boundary layer. In the present study, the only definitively observed transition onset was detected during the second expansion period (p 0 = 1000 kpa) for Case 1 shown in Table 1 with the 0.5-mm-radius nosetip. This transition onset occurred at x = 280 mm (as measured from the 0.5-mm-radius nosetip) and was defined as the location where the slope of the St increased from the laminar heating rate. Only data from the first expansion period are presented in the current study due to tunnel unstart which occured when using the 43 flare; however, it is interesting to note this particular case during the second expansion period since transition onset was observed. This transition-onset location corresponds to a transition N-factor at onset of 4.6, which is consistent with transition N-factors observed in other noisy hypersonic facilities. 28 Table 4 summarizes computed N-factor limits for cases where transition onset was not observed on the forebody, but the flow was determined to be either laminar or turbulent at the nosetip/frustum junction. Figure 7 presents the mean-flow result for this transition-onset case, illustrating bluntness effects on the local unit Reynolds number for the second expansion period of Case 1 shown in Table 1 (p 0 = 1000 kpa) with r = 0.5 mm. The bluntness creates a stagnation region followed by a bubble of high-temperature, low-mach number gas, in which the local unit Reynolds number is low. 8 of 22

9 y [m] x [m] x local unit Re [1/m] Figure 7: Unit Reynolds number contours (detail, first 5 cm of the cone) for the second expansion period of Case 1 shown in Table 1 (p 0 = 1000 kpa) with r = 0.5 mm. A. Test Matrix Overview V. Results and Discussion A total of 40 wind-tunnel tests were conducted in this work. The first eight tests were conducted with all four nosetips, the 34 flare, and both Re. The infrared camera s field of view spanned from just downstream of the nosetip to just upstream of the cone/flare junction. These initial tests were conducted to determine the state of the boundary layer for all of the nosetip-re combinations. The computations and pressure-transducer data also aided in this effort. After the boundary-layer state was determined for each nosetip-re combination, the infrared camera was moved to view the interaction region for the remaining 32 tests which spanned all possible nosetip, flare, and Re combinations. All St data presented in this work were for a test time of 0.04 seconds after tunnel start-up. This time corresponds to the first period of steady flow and precedes the tunnel unstart that was observed during testing with the 43 flare. All pertinent flow conditions for this first expansion period can be seen in Table 1 above. All tests were conducted at nominally zero angle of attack; however, asymmetry is observed in the upstream St contours provided below. More discussion on this asymmetry can be found in subsection B. Thin bands of high and low heating rates are observed at the film junctions. In all of the centerline profiles provided, these slight imperfections have been corrected for by interpolating the data points over these areas using the data just upstream and downstream of the film junctions; however, these imperfections have not been corrected for in the St contours in order to illustrate the as-measured data. Small debris were found embedded in parts of the film throughout the tests. These debris show up as tiny hot spots in the St contours but do not affect any centerline St profiles. The surface-temperature data used to calculate the St contours and centerline profiles were temporally filtered by seconds. In addition to temporal filtering, the centerline St profiles have been spatially filtered by a 7 3 pixel rectangular kernel. B. Boundary-Layer State The state of the incoming boundary layer has a great effect on how it interacts with the flare and separates/reattaches; therefore, before one can start analyzing boundary-layer separation and reattachment, the state of the incoming boundary layer needs to be known. To do this, the infrared camera was rotated towards the nosetip to view upstream of the cone/flare junction. All four nosetips were tested at both Re for these upstream tests. The goal of these tests was to determine the boundary-layer state, so only one of the flares (34 ) was tested. Figure 8 shows upstream St contours mapped to x-y coordinates for the sharp, 0.5-mm-, and 10.2-mmradius nosetips. The x and y coordinates have both been non-dimensionalized by the distance from the respective nosetip of each cone to the cone/flare junction location, L. Since x = 0 at the nosetip of each respective nosetip configuration, the cone/flare junction will have the same x/l value (i.e. 1) regardless of which nosetip is used. Note that Fig. 8c begins at x/l = 0.2 as opposed to x/l = 0.3 seen in Figs. 8a and 8b. This difference comes from the fact that L is different for each nosetip case. The thin low-heating band at the most upstream portion of the image is where the unwrapped nosetip mated with the upstream frustum. 9 of 22

10 Because the nosetip was not wrapped, the low-emissivity aluminum provides low surface temperatures as measured by the infrared camera. This thin band is not included in the centerline profiles. In addition, the thin high-heating band near the middle of the contours is a consequence of a film junction where the two frusta meet. It is important to note that the heating is not affected upstream or downstream of this film junction within the infrared camera s field of view. It is unknown whether the junction affected boundarylayer transition farther downstream. (a) r = sharp, Re = /m (turbulent) (b) r = 0.5 mm, Re = /m (transitional) (c) r = 10.2 mm, Re = /m (laminar) Figure 8: Upstream St contours showing the boundary-layer state. 34 flare. These three test-conditions were chosen because their St contours show three distinct heating trends which correspond to turbulent, transitional, and laminar boundary layers respectively. Figure 8a shows a relatively constant high heating rate across the length of the two frusta which corresponds to a turbulent boundary layer. Figure 8b shows a gradual increase in heating until a maximum is reached at approximately x/l = 0.5. This heating trend is a classic example of a transitional boundary layer. By x/l = 0.6, the boundary layer is turbulent and shows similar heating to that of Fig. 8a. Asymmetric heating is clearly observed in the contour provided in Fig. 8b. Since the heating bands from the film junctions in Fig. 8b are straight vertical lines, i.e. not at an angle of attack, this asymmetry is likely due to slight flow angularity from the wake of the fast valve. This asymmetry is believed to be within the bounds of ± 1 in pitch and yaw based on Fig. 7 from Ref. 29 which shows the effect of angle of attack on boundary-layer transition location. Figure 8c shows a lower heating rate than either Fig. 8a or Fig. 8b, which is typical of a laminar boundary layer (note that the contour scale on Fig. 8c is different than Figs. 8a and 8b). Although a laminar boundary layer is believed to be present, a sharp dip in heating followed by a steep rise is observed on the downstream portion of the aft frustum. This heating bucket is a direct consequence of the presence of the flare; in fact, the deviation from the laminar heating identifies the boundary-layer separation location. It is interesting to note that although the flow angularity produces an asymmetric transitional front, separation (and reattachment shown later) shows a more axisymmetric nature. This observation is supported by previous works, which have shown that small non-zero pitch and/or yaw only slightly affect boundary-layer 3, 8, 9 separation and reattachment locations. These works have also indicated that the physical mechanisms governing the interaction region flow structures are similar within the range of pitch and/or yaw observed in the current study. Figure 9 shows upstream centerline St profiles for all four nosetips at both Re with the 34 flare in addition to empirical St trends from Ref. 30. At the lower Re, the r = sharp and r = 0.5-mm tests are already in a transitional state at the beginning of these profiles and are both past the end of transition as they 10 of 22

11 approach the cone/flare junction. For the higher Re tests, these same two nosetip configurations are both turbulent at the beginning of these profiles. This observation is expected since the Re is nearly doubled. It is clear that for the sharper of the two nosetip configurations, the boundary layer entering the interaction region is turbulent. A clearly different heating profile is observed in the r = 5.1-mm and r = 10.2-mm tests. This trend is consistent of a laminar boundary-layer profile because of its constant low heating. A clear drop in St is observed as the boundary layer moves closer to the cone/flare junction, which is an indication of boundary-layer separation. This general trend of increasing nosetip radius delaying transition is consistent with the findings of Jewell et al. 24 who observed a similar tendency within the same regime of nosetip radius Reynolds numbers. (a) Re = /m (b) Re = /m Figure 9: Upstream centerline St profiles with empirical trends showing the boundary-layer state. 34 flare. Figure 9 shows good qualitative agreement between the experimentally derived and empirically based St profiles, which was the reason the current film k and c p values were chosen. It is uncertain why the experimental St profiles are consistently lower than the turbulent empirical trends. It is also observed that the r = sharp and r = 0.5-mm cases do not converge to the same St value. The downstream 0.5-mm-radiusnosetip St profiles are 19% and 6% higher than the sharp-nosetip St profiles for the Re = /m and Re = /m cases respectively. This discrepancy is likely due to the different boundary-layer thicknesses produced by the different nosetip radii. Figure 10 shows the pressure traces measured at x/l = 0.6 (as measured from the sharp nosetip) for the four upstream tests conducted at Re = /m. 0.1 seconds of data were collected before the tunnel started. The two expansion periods are clearly present for the 34 -, 37 -, and 40 -flare tests. Tunnel unstart was observed around t = 0.05 seconds for all tests conducted with the 43 flare. Qualitatively, these traces are useful for confirming the boundary-layer state along the cone. Two distinct fluctuation levels are observed. The two sharper nosetip configurations show relatively high fluctuation levels for both periods of steady flow while the two blunter nosetip configurations yield relatively low fluctuation levels. These results support the observations found in the St data discussed above, namely, that a turbulent boundary layer is present for the two sharper nosetips and a laminar boundary layer is present for the two blunter nosetips. Table 4 summarizes the boundary-layer state entering the interaction region for all nosetip-re combinations. Values of the root-mean-squared pressure fluctuations (rms) calculated from the first 0.04 seconds of steady flow are also provided. These rms values were calculated by integrating under the power-spectraldensity curve for frequencies less than the sensor s resonant frequency to ensure that the values reflect aerodynamic effects. A difference in fluctuation level is observed between the turbulent and laminar tests which supports these conclusions. In addition, the N-factor (based on the first and second instability modes) computed at the nosetip/frustum junction is provided for every test case. This location was chosen because it reflects the most upstream data collected for the eight tests investigating the boundary-layer state. For all of the turbulent cases, the transition N-factor would be less than those provided in Table 4 since the boundary layer was already transitional or turbulent by the nosetip/frustum junction location. For all of the laminar cases, the critical N-factor would be greater than the ones provided in Table of 22

12 (a) r = sharp (turbulent) (b) r = 0.5 mm (turbulent) (c) r = 5.1 mm (laminar) (d) r = 10.2 mm (laminar) Figure 10: Pressure traces for upstream boundary-layer-state tests. 34 flare, Re = /m. Table 4: Boundary-layer state summary. r (mm) rms (kpa) N-Factor Boundary-Layer State Re ( 10 6 /m) Re ( 10 6 /m) Re ( 10 6 /m) sharp Turbulent Turbulent Turbulent Turbulent Laminar Laminar Laminar Laminar 12 of 22

13 C. Interaction Region Figures 11 and 12 show centerline St profiles for all tests conducted with the infrared camera viewing from just upstream of the cone/flare junction to the end of the flare. Figure 11 shows results collected at Re = /m while Fig. 12 provides data collected at Re = /m. The two tests conducted with the 10.2-mm-radius nosetip and 34 flare did not save correctly; therefore, there is no data presented for these two cases as seen by their absence in Figs. 11d and 12d. (a) r = sharp (turbulent) (b) r = 0.5 mm (turbulent) (c) r = 5.1 mm (laminar) (d) r = 10.2 mm (laminar) Figure 11: Downstream centerline St profiles. Re = /m. Figure 13 shows global St contours mapped to x-φ coordinates, where φ is the azimuthal angle (φ = 0 identifies the model s centerline normal to the camera since the model is not at an angle of attack for any of the tests conducted in this work). This mapping is convenient because the separation and reattachment locations are seen as straight, vertical lines at a constant x location. The flare portion tapers off on the top and bottom of these contours because not all of the flare was imaged with the infrared camera. Only 120 of these contours are shown because 30 on the top and bottom edges have been cropped. These three contours were chosen because they show the three distinct interaction-region phenomena observed throughout this test campaign; namely, a separated and reattached turbulent boundary layer (Fig. 13a), a separated and reattached laminar boundary layer (Fig. 13b), and a turbulent boundary layer that did not separate (Fig. 13c). In this work, separation location will be defined as the axial location where the centerline St slope abruptly increases for a turbulent boundary layer and decreases for a laminar boundary layer. This is consistent with 3 5, 14 other studies conducted on similar geometries. Figures 11a, 11b, 12a, 12b, and 13a all show a clear 13 of 22

14 (a) r = sharp (turbulent) (b) r = 0.5 mm (turbulent) (c) r = 5.1 mm (laminar) (d) r = 10.2 mm (laminar) Figure 12: Downstream centerline St profiles. Re = /m. increase in St upstream of x/l = 1 for tests conducted with the 40 and 43 flares. This increase in St is followed by a well-defined plateau region and marks the separation location for the incoming turbulent boundary layer. This result is consistent with Ref. 14. No clear rise in St is observed upstream of x/l = 1 for the turbulent boundary layers interacting with the 34 and 37 flares (Figs. 11a, 11b, 12a, 12b, and 13c). It is concluded that separation does not occur for these cases due to the turbulent boundary layer s ability to resist separation, especially for smaller flare angles. Turbulent computational results conducted by Olivier et al. corroborate this conclusion (see Fig. 10 from Ref. 11). It should also be noted here that the orange St profile seen in Fig. 11a exhibits a higher value than expected. It is clear that this particular trace does not follow the same trends as the others. The reason for this discrepancy is unknown and more tests for this particular case are needed to investigate this issue. Figures 11c, 11d, 12c, 12d, and 13b show a gradually increasing St profile entering x/l = 1 for all of the flares tested. A clear decrease in St (i.e. separation) for these laminar boundary-layer cases is not observed because separation occurs farther upstream than the infrared camera s field of view. In the current field of view, only the gradual increase from the heating bucket is captured. Figure 9 above shows the clear decrease in St for the 34 -flare tests well upstream of x/l = 1. Because of this, laminar boundary-layer separation was only measured for the 34 -flare tests since that is the only flare that was used during the upstream measurements. It is promising however that such a clear deviation from the laminar heating profile is observed indicating the separation location. 14 of 22

15 (a) r = sharp, 43 flare, Re = /m (turbulent (b) r = 5.1 mm, 40 flare, Re = /m (laminar separation and reattachment) separation and reattachment) (c) r = 0.5 mm, 34 flare, Re = /m (turbulent, no separation) Figure 13: Downstream St contours. It is generally agreed upon in literature that reattachment occurs some very small distance downstream of the maximum heat-flux location.4, 15 This maximum St is readily observed in all of the profiles shown in Figs. 11, 12, and 13 (other than the eight total tests where no separation occurred as discussed above). In this work, reattachment will be defined as the axial location where this maximum heat-flux value is reached; therefore, the vague small distance downstream of that value will be neglected. In addition to a clear St maximum, the presence of streamwise hot streaks upon reattachment is observed in all of the tests exhibiting boundary-layer separation and reattachment (see Figs. 13a and 13b). These hot streaks are suspected to arise from the mean-flow distortion of G ortler vortices. A more quantitative discussion regarding separation, reattachment, and the G ortler vortices is provided below. It should be noted that the small flow angularity will slightly affect the precise location of separation and reattachment; however, previous studies have shown that this effect is minimal when alignment is within ±1 in pitch and yaw which has been shown to be the case for this work.3, 8, 9 It should also be noted that any unsteadiness in the separation and reattachment regions was not measured at the 355 Hz frame rate used in this work. D. Boundary-Layer Separation and Reattachment Figure 14 plots the nosetip radius versus the separation and reattachment locations for every test where separation and/or reattachment was observed. The x-axis gives the distance, in mm, from the cone/flare junction (i.e. negative values identify locations upstream of the cone/flare junction). Open-circle markers identify tests conducted at the lower Re while cross markers identify tests conducted at the higher Re. Each of the four colors correspond to a particular flare angle. All markers at a negative distance identify a separation location while all markers at a positive distance identify a reattachment location. Figure 15 plots the nosetip radius versus the separation length, in mm, for every test where both separation and reattachment were observed. The uncertainty in the separation and reattachment locations has been calculated by finding the deviation in axial location when the St value is within ±5% of the upstream value for separation and of the peak value for reattachment. The maximum uncertainties for laminar and turbulent separation location are ±1.0% 15 of 22

16 and ±0.2%, of the reported values, respectively. The maximum uncertainties for laminar and turbulent reattachment are ±1.8% and ±0.8%, of the reported values, respectively. Figure 14: r vs. separation and reattachment locations. Figure 15: r vs. separation length. 1. Nosetip-Bluntness Effect For laminar boundary-layer separation, as the nosetip bluntness is increased, the separation location moves upstream. Although this observation is taken from only one flare angle, it is supported by previous works. 14 The difference between the sharp- and 0.5-mm-radius-nosetip cases does not appear to affect the separation location. For laminar boundary-layer reattachment, as the nosetip bluntness is increased, the reattachment location moves farther downstream on the flare which has also been observed in previous works. 14 This observation 16 of 22

17 means that the entire separation length increases with increasing nosetip bluntness for a laminar boundarylayer interaction region. Again, there is no noticeable difference between the reattachment location for the sharp- and 0.5-mm-radius-nosetip cases. In general, it is observed that boundary-layer separation moves upstream while boundary-layer reattachment shifts downstream as nosetip bluntness increases. This observation is seen clearly in the laminar boundary-layer tests although this might only be because of the larger difference in nosetip bluntness for those two cases. 2. Flare-Angle Effect Figure 14 shows how the flare angle (i.e. different colored markers) has an effect on the phenomena of boundary-layer separation and reattachment. Since laminar separation was only measured for the 34 flare, it is impossible to say anything regarding a flare-angle effect for laminar boundary-layer separation. However, for the two sharper-nosetip cases, it is observed that the separation location moves upstream with increasing flare angle. The opposite trend is observed regarding reattachment location. As flare angle increases, the reattachment location shifts farther downstream on the model. Therefore, a larger separation region is present for larger flare angles, as expected. This trend is also observed in Fig. 15. It uncertain why the 34 and 37 flares with r = 5.1 mm and Re = /m seen in Fig. 14 do not follow this trend. 3. Re Effect The Re effect can be seen in Fig. 14 by looking at the open-circle versus cross-marker locations. For the two nosetips yielding a laminar boundary layer, separation moves downstream with increasing Re which is supported by previous works. 5 It is difficult to find a clear trend with the two sharper-nosetip cases; however, the data seems to indicate that Re does not affect the separation location in any significant way. The same observation is made regarding the effect Re has on the reattachment location, since most of the cross markers fall very near the open-circle markers for both turbulent and laminar tests. E. Boundary-Layer Peak Heating and Heating Slopes In addition to identifying the location of boundary-layer separation and reattachment, measurements of peak heating and heating slopes are critical for designing flight vehicles and building accurate computational models. Figure 16 shows how the peak St achieved upon reattachment is affected by nosetip radius, flare angle, and Re. Figure 17 plots the slope of the St as measured from the cone/flare junction to the reattachment location versus the nosetip radius. Figure 16: Peak St vs. r. 17 of 22

18 Figure 17: St slope vs. r. 1. Nosetip-Bluntness Effect Figure 16 suggests that as the nosetip bluntness increases for a given turbulent or laminar boundary layer, peak heating will also increase. That is to say, as the nosetip radius increases from sharp to 0.5 mm, likecolored markers in Fig. 16 increase; likewise, as the nosetip radius increases from 5.1 to 10.2 mm, like-colored markers in Fig. 16 also increase. There is currently no explanation for the r = 10.2 mm, 37 flare, Re = /m case which has a lower peak St than the same case with the 5.1-mm-radius nosetip. It is uncertain what underlying physical mechanisms govern this general behavior and there are no previous works to support this finding. Figure 17 shows that for a given incoming boundary-layer state, flare angle, and Re, as nosetip bluntness increases, the St slope decreases. This finding is supported by Schrijer et al. 5 who showed that the St slope is higher for an incoming turbulent boundary layer than for its laminar counterpart. This observation also corroborates the boundary-layer-state findings discussed above. 2. Flare-Angle Effect A much clearer trend is observed in Fig. 16 regarding the effect flare angle has on peak St. For each nosetip radius, the green markers have the highest peak heating followed by the blue, red, and black markers meaning that the peak St increases with increasing flare angle, as expected. Figure 17 illustrates that as the flare angle increases, the heating slope decreases, meaning that the smallest flare angle produces the steepest heating slope. This trend is also clearly seen in the downstream St profiles shown in Figs. 11 and 12 above. 3. Re Effect Figure 16 also provides evidence for the effect Re has on peak heating. It is observed that the lower Re cases (open-circle markers) have higher peak values of St compared to the higher Re cases (cross markers); therefore, peak St increases as Re decreases. A similar trend is seen in Fig. 17; namely, the lower Re cases produce a steeper St slope than the higher Re cases. 18 of 22

19 F. Görtler Vortices Streamwise hot streaks are observed along the flare upon reattachment of the boundary layer. These hot streaks are suspected to arise from the mean-flow distortion of Görtler vortices. Figures 13a and 13b illustrate this streaky behavior. In order to quantify these vortices, spanwise St profiles were taken in the φ direction at a constant x location just downstream of reattachment. These profiles were then detrended with the use of a linear fit. To compute the dominant wavelength associated with the Görtler vortices, the Fast Fourier Transform (FFT) of each data set was computed. Figure 18 shows the detrended spanwise St profile and FFT at x/l = 1.05 for the test whose St contour is shown in Fig. 13b. The detrended St profile seen in Fig. 18a does not span the full azimuthal range of seen in Fig. 13 because the flare portion at x/l = 1.05 has already started to taper off due to the camera field of view (see Fig. 13b). The FFT yields the wavelength, λ, which can then be nondimensionalized by the local radius of curvature, R. This value of λ/r will be presented in terms of degrees for clarity when comparing with the global x-φ contours. A peak λ/r can be identified in Fig. 18b yielding the dominant λ/r associated with the Görtler vortices. This dominant λ/r was then confirmed by looking at the streaks seen in the global St contours. The uncertainty in calculating λ/r is defined by the sparsity of data points where the peak is observed. For the FFT shown in Fig. 18b, the peak λ/r = 5.88 and the nearest data points on either side are located at ±0.42 of this value. (a) Detrended St profile (b) FFT of detrended St profile Figure 18: λ/r analysis of Görtler vortices. r = 5.1 mm, 40 flare, Re = /m (laminar separation). This analysis was conducted for all of the tests where a clear reattachment was observed. Figure 19 shows these λ/r results plotted against the various nosetip radii r. It is difficult to determine any clear trends regarding the λ/r of the observed Görtler vortices in Fig. 19. More work needs to be done to further characterize the trends of the observed Görtler vortices. Future computational analysis could assist in this process. 19 of 22

20 Figure 19: λ/r of Görtler vortices vs. r. VI. Conclusions A series of wind-tunnel tests has been carried out in the AFRL Mach-6 Ludwieg tube wind tunnel on a 7 half-angle circular cone/flare model in order to investigate the effect of nosetip bluntness, flare angle, and freestream unit Reynolds number on boundary-layer separation and reattachment. Time-resolved surface-temperature measurements were made using an infrared camera and St profiles and contours were calculated and used to investigate the shock-wave/boundary-layer interaction. The boundary-layer state was determined to be turbulent for the two sharper nosetips and laminar for the two blunter nosetips at both Re. Measurements conducted in the interaction region yielded separation and reattachment locations as well as peak St values and St slopes. Global St contours showed signs of Görtler vortices in the flowfield along the flare portion of the model and the dominant λ/r of these vortices was calculated. Geometric effects were investigated and it was found that, in general, an increase in nosetip bluntness and/or flare angle increased the overall separation length while an increase in Re decreased the separation length. These observations were more apparent for the two laminar test cases. It was found that as nosetip bluntness and flare angle increased, the peak St increased but the St slope decreased. It was also observed that lower Re produced higher peak St and steeper St slopes. The flare angle and Re had a greater effect on peak heating and heating slope than the nosetip bluntness. Future Work There are a number of near-term next steps planned for this project. The authors would like to obtain separation-location measurements for all of the laminar cases by viewing farther upstream on the model. During those tests, the model will be instrumented with thermocouples and pressure transducers to collect data that will assist in heat-flux and boundary-layer-state calculations respectively. A thorough investigation of the thermal properties of the 3M 1080 series film is currently underway and will ensure accurate heatflux calculations. Computations of the interaction region have also already begun and will be used to validate the qualitative boundary-layer separation/reattachment observations. The authors would also like to obtain global unsteady-pressure measurements with a high-frequency-response anodized-aluminum pressuresensitive paint (AA-PSP) in the long-term future. 20 of 22