experimental studies of transitional boundary layer...

American Institute of Aeronautics and Astronautics1

Experimental Studies of Transitional Boundary Layer ShockWave Interactions

Z.R. Murphree*, J. Jagodzinski,* E.S. Hood, Jr., * N.T. Clemens,+ and D.S. Dolling†

Center for Aeromechanics ResearchDepartment of Aerospace Engineering and Engineering Mechanics,

University of Texas at AustinAustin, Texas 78712-1085

Shock wave boundary layer interactions generated by a cylinder on a flat plate werevisualized with a particular emphasis on transitional interactions. Surface-streakline(kerosene-lampblack), schlieren, and low-repetition rate planar laser scattering were used tovisualize the flowfield. Furthermore, high-speed (10 kHz) planar laser scattering in astreamwise-spanwise plane (plan view) was used to visualize the time-varying structure ofthe separated flow. The shapes and scales of the transitional interactions are compared tothose of laminar and turbulent interactions. It was observed that transitional interactionsare highly variable in their structure, but they appear to be a composite of the other twotypes with laminar scaling along the plate centerline and turbulent scaling in the outboardregion. The plan view planar imaging shows that even the most laminar interactions exhibitseparated flow regions that are transitional or turbulent. Furthermore, the fluctuations inthe size of the separated flow for more laminar-like transitional interactions weresignificantly larger than for turbulent interactions.

Nomenclatured = cylinder diameterXcyl = distance from plate leading edge to cylinder leading edgeXsep = distance from plate leading edge to primary separation line along plate centerlineXtrans = distance from plate leading edge to transition along plate centerlineλsep = distance from cylinder leading edge to primary separation line along plate centerline

I. Introductionhock wave/boundary layer interactions (SWBLI), often accompanied by separation, are a ubiquitousphenomenon in high-speed flight. Most of the work done in this field over the past 50 years has been in fully-

developed turbulent flows because most practical applications were at transonic and low supersonic speeds ataltitudes where Reynolds numbers are large and turbulent flow the norm. An understanding of these turbulentinteractions is very important for vehicle design because the interactions result in very high unsteady thermal andacoustic loads that can result in diminished component performance and material failure. In contrast, transitionalshock wave/boundary layer interactions, in which the incoming boundary layer is in a transitional state, or in whichtransition is induced within the interaction itself, appear to be even more unsteady and could have greater adverseeffects, and yet have received little attention. This lack of attention has stemmed from both the lack of criticalapplications and from the formidable challenges that the study of such flows poses to both experiment andcomputation. However, high Mach number air-breathing propulsion systems are of increasing interest to the U S AirForce, and the inlets of such systems will have extremely complex shock/boundary layer interactions withsignificant regions of transitional flow. These transitional interactions will have a powerful influence on the localinlet flow properties and on the uniformity, the quality, and the steadiness of the flow entering the combustor. It isfair to say that our current understanding of transitional interactions is extremely poor. The capabilities of modern

* Graduate Research Assistant, Member+ Professor, Associate Fellow† Professor, Fellow

S

44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-326

Copyright © 2006 by Z.R. Murphree, J. Jagodzinski, E.S. Hood, Jr., N.T. Clemens, and D.S. Dolling. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


non-intrusive instrumentation, especially particle image velocimetry (PIV) and planar laser scattering (PLS), nowoffer an opportunity to initiate studies of transitional interactions and build the knowledge base.

II. Experimental Program and TechniquesThe experimental program was carried out in the high-Reynolds-number Mach 5 blow-down wind tunnel located

at the Wind Tunnel Laboratories at the Pickle Research Campus of the University of Texas at Austin. The facilityuses a bottle field of eight tanks that has a combined storage volume of 140 ft3 and can be pressurized to a maximumof 2550 psia. The stagnation temperature and pressure were 653º R and 363 psia. Downstream of the 2-D Mach 5nozzle, the flow enters a 27 in long constant-area test section which is 7 in high and 6 in wide.

The interactions for this study were generated by a circular cylinder on a flat plate. The cylinder could betranslated streamwise along the plate, and the state of the boundary layer at a given position would dictate the typeof interaction (laminar, transitional, or turbulent). Three different plates were used, all with smooth surface finishesand tapered leading and trailing edges. The first, used for kerosene-lampblack surface flow visualization, was an 18inch long flat brass plate that was bolted to the tunnel walls. The second surface was a 10 inch long brass platedesigned to provide optical access to study the interactions. This plate was mounted in the tunnel with a supportingstrut, but the strut presented so much blockage to the flow that the cylinder had to be very small in order for thetunnel to start. The third surface was also a 10 inch long plate, but was mounted without a supporting strut in orderto reduce the blockage so that larger cylinders (up to a half inch in diameter) could be used to generate largerinteractions. The third plate also did away with the threaded holes for attaching the cylinder in order to reduce flowdisturbances. In this case the cylinder was held in place with the compressive force of a screw-jack.

Experimental techniques employed to date have included: a) surface-streakline visualization using a kerosene-lampblack mixture, used to determine quantitatively the mean separation line, b) schlieren imaging, and c) PLS. Theschlieren setup consisted of a high-speed camera, neutral density filters, a razor blade for a knife-edge and either aHelium-Neon laser (Spectra-Physics Model 102-1 controlled by a Spectra-Physics Laser Exciter Model 212-1) or aflash-lamp (EG&G Electro Optics model LS-1130-4 flash-lamp, 2-microsecond duration). The choice dependedwhether overall flow characteristics or local image quality were of primary concern. Figure 1 shows the arrangement.Images were acquired using a KODAK EKTAPRO HS Motion Analyzer, Model 4540 mx or a Cohu 4990. Thecameras were fitted with either a Computar MC Zoom Macro 1:3.5~5.3 lens for the laser schlieren or a Nikon EDAF Micro Nikkor 200 mm 1:4D lens paired with the flash-lamp. The EKTAPRO camera processor could record fullframes at 30, 60, 125, 250, 500, 750, 1,125, 2,250 and 4,500 frames per second, whereas the Cohu operated at 30frames per second.

PLS images were taken using twodifferent setups enabling plan views (i.e.streamwise-spanwise view) of the flow. Theflow was seeded with a finely atomizedethanol fog, which was then illuminated withlaser light. The scattering from the condensedfog was then captured by a high-speed 1kx1kCMOS array (Photron FASTCAM-ultimaAPX) with a 50 mm 1:1.4 lens. In both setupsthe laser sheet was brought in parallel to thesurface of the flat plate through a sidewindow. In the first setup the camera wasimaging the sheet through the opposite sidewindow and was therefore positioned at anoblique angle as shown in Fig. 2. Due to theviewing angle, these images exhibit some geometric distortion and blurring at the edges. The light was provided bya flashlamp-pumped frequency-doubled Nd:YAG laser (Spectra-Physics PIV 400) operating at 10 Hz and around150 millijoules per pulse. In the second setup the camera was positioned normal to the plate surface. For these teststhe light was provided by a diode-pumped Nd:YLF laser (Coherent Evolution 90) operating at 10 kHz and 9millijoules per pulse. At this high framing rate the maximum resolution of the camera was 512x256.

Figure 1. Schematic diagram of flash-lamp schlieren setup.


III. ResultsIn the first phase of the study, surface streak line visualizations were obtained for several cylinder locations

relative to the plate leading edge. Three examples, which highlight three flow regimes, are shown in Fig. 3. At eachof these stations, and others, results were repeatable. The pattern shown in Fig 3a is the classic image seen innumerous studies in which the incoming boundary layer is fully turbulent. The separation line is symmetric aboutthe plate-cylinder center line, with separation on center line occurring about two cylinder diameters upstream of thecylinder leading edge. In Fig 3b, with the cylinder shifted 1 in further upstream (4 in downstream of the plateleading edge) the flow structure and scales change significantly. The separation scale is significantly larger (oncenter line the primary separation line now is about 5 cylinder diameters upstream of the cylinder leading edge) andthe flow structure is no longer symmetric about the cylinder center line. There is some indication of multipleseparation lines. The significant variation in spanwise structure is also evident in the plan view PLS images and inthe conventional side-view schlieren images which will be shown later. At this stage it is not clear if the incomingboundary layer is transitional, if transition occurs in the separated shear layer, elsewhere in the interaction, or somecombination of the latter. Which ever it is, it is probable that the location and process will not be symmetric acrossthe span and will result in an asymmetric flow structure. It is possible that disturbances originating at the plateleading edge trigger early transition, or waves from the tunnel floor or sidewalls hasten or delay transition at somelocations but not at others. In any event, the global behavior is repeatable, since the essential features of the imageremain the same from run to run.

CMOScamera

cylinder

flat plate

laser sheet

M∞=5

(a) (b)Figure 2. Schematic diagram of PLS setup. (a) Overall assembly and (b) inside the test section

(a) (b) (c)Figure 3. Surface streakline visualization (kerosene-lampblack) of cylinder-induced interactions in a Mach5 flow. (a) “Fully turbulent”: Xcyl = 5 in, (b) “transitional”: Xcyl = 4 in, and (c) “laminar”: Xcyl = 2.75 in.


When the cylinder is shifted 1.25 in further upstream (Xcyl = 2.75 in) the interaction becomes larger still, andnominally symmetric about the cylinder center line, indicative of a “laminar-like” interaction. The maximumprimary separation distance is slightly larger than in Fig. 3b. Again, it is difficult to characterize the flowfield asbeing laminar or transitional since it may well be a mix of these two flows. With respect to primary separationlocation, Young et al. (1968) reported that in laminar flow at Mach 3 the center line separation distance varied from4.1 diameters to 6.8 diameters as the flow Reynolds number was increased by a factor of about 20, indicating aReynolds number dependence.1 Smaller values were observed at Mach 5. At Mach 5.5, Hung and Clauss (1980)reported values of 9 to 12 diameters for laminar flow.2 However, as was pointed out by Özcan and Holt, theyassumed that separation occurred where the surface temperature or static pressure first begins to rise above theundisturbed value and this assumption will overpredict the separated flow scale significantly since the distance fromthe initial rise in pressure to the separation location can be several cylinder diameters.3 The Özcan and Holt studynoted that for laminar cases with a height to diameter ratio greater than about 4 (essentially a semi-infinite cylinder)the maximum primary separation distance was typically between about 6.6 and 7.6 diameters upstream of thecylinder. In Fig. 3c it is likely that the incoming undisturbed boundary layer is on the verge of transition, or isperhaps laminar, and transition occurs early in the separated shear layer. Considering that the location of primaryseparation on center line decreases from about 6-8 diameters to about two diameters as the flow goes from entirelylaminar to fully turbulent, a large range of scales are possible depending on where and how transition occurs in thedisturbed flowfield.

The normalized separation distances, l sep/d, from the surface flow visualization of the current study agree wellwith the results of Kaufman et al., as shown in Fig. 4. 4 In the figure, Xsep and Xtrans are the locations of separationand the end of transition, respectively, measured from the plate leading edge. The aforementioned large change inmean interaction scale as it changesfrom laminar to transitional toturbulent is evident. The reduction ofl sep/d from the laminar/transitionalvalues to the fully turbulent valuesoccurred at the same positions relativeto transition even though the largestlaminar/transitional extent ofseparation was about 10% higher thanin Kaufman et al.4 Comparisons withthe data of Özcan and Holt3 andYoung et al.1 suggest that thisdifference in l sep/d is reasonable. Inorder to make the comparison shownin Fig. 4 it was necessary to employ acorrelation function developed byRamesh and Tannehill5. Thiscorrelation predicts the Reynoldsnumber for the onset and end oftransition (between which is the“transition band”). The value for theend of transition, which was calculatedto be 4.1 in, was used to normalize thex-axis of Fig. 4.

Planar laser scattering images for similar cases to those discussed above are consistent with surface streaklineimages and bring out more details of these complex flows. Figure 5a shows the case that presumably corresponds toa laminar interaction similar to Fig. 3c. In this case the cylinder diameter is slightly smaller (0.375 in compared to0.5 in and is positioned about 0.7 in closer to the plate leading edge). Recall that the light sheet is parallel to and 0.1in above the plate surface and the camera views the scattering from an oblique angle and so some distortion andblurriness are present at the edges of the images. Light and dark regions correspond to regions of high and low fogdensity, respectively. Low velocity regions are rendered as black owing to droplet evaporation in the relativelywarm fluid. Figure 5a reveals a separation shock that stands off from the cylinder by about 3.6 diameters. Note thatthe laser sheet is elevated off the plate and so the origin of the shock is farther upstream. We should emphasize thatalthough we assume this shock is a separation shock, we see no evidence of separated flow immediately downstream

Figure 4. Comparison of data from current study with that ofKaufman et al. 4


of it. It is possible that separated flow is not observed because the laser sheet location was too high to see it. Thisissue will be explored in future work. We observe that the separation shock is relatively steady and its shape alongthe centerline of the plate is almost straight. The latter observation is consistent with many of the surface streaklinepatterns that we have taken in “laminar” interactions. In Fig. 5b the cylinder is at the same location relative to theplate leading edge but a “trip strip” (a strip of tape) has been attached to the plate surface just downstream of theleading edge. The interaction now has a mixed structure with the flow upstream and to the left of the cylinder(looking upstream) exhibiting a laminar-like character whereas the flow on the right exhibits a turbulent-likecharacter with separation much closer to the cylinder. On the left hand side, downstream of the laminar-likeseparation location dark turbulent streaks/spots are evident in the image. We believe that a turbulent separationshock may exist on the left side that is similar to that on the right, but it cannot be seen due to the blur in the image.We note that this flow is much more unsteady than the previous case as the “laminar” shock is highly variable in itsshape and the region of turbulent flow exhibits large variations in its overall scale.

M∞= 5

plateleading

edge

"laminar"separationshock

2.1"

cylinder

(a)

"laminar"separation shock

"turbulent"separation

shock

M∞ = 5

boundary layertrip strip

(b)

Figure 5. Planar laser fog scattering images of cylinder-induced interactions. The 0.375 in cylinder is 2.1 infrom the leading edge. The view shown is a plan view that exhibits some distortion because it was taken at anoblique angle. (a) untripped boundary layer, (b) tripped boundary layer.


Figure 6 shows the case when the cylinder is moved about 1.9 in further downstream. The image now becomesessentially symmetric with respect to the centerline of the plate (consistent with the surface streakline visualizations).The dark streaks in the image are associated with increased temperatures associated with what is presumably theseparated flow. On center line these dark streaks first appear about 2 cylinder diameters upstream of the cylinder,consistent with the location of turbulent separation as inferred from other techniques. Interestingly, there is noseparation shock that can be identified in the turbulent cases. It may be that the laser sheet is too close to the wall toeffectively see the separation shock. Note that the same flow structure is observed in Fig. 6 whether the trip strip isin place or not.

When the flow was imaged at a higher rate (10 kHz vs. 10 Hz), some very interesting phenomena were observed.The problem with imaging the separation shock again presented itself, so the state of the boundary layer could notbe inferred from λsep. However, the location of transition could be found by imaging the boundary layerdevelopment of the tripped flow with the cylinder removed. Figure 7 shows representative images of the boundarylayer development on the plate. The laser sheet is 0.04 in from the plate surface, and the flow is left to right. ThisPLS technique seems to be very effective for imaging this development; laminar, transitional, and turbulent flowsare clearly distinguishable and the cylinder could be placed accordingly to generate a certain type of interaction.

M ∞ = 5

t u r b u l e n ts e p a r a t e d f l o w

Figure 6. Planar laser for scattering images for a case where the cylinder is farther downstream, thusgenerating a turbulent interaction. Xcyl = 3.95 in.

(a) (b) (c)

Figure 7. Development of boundary layer on flat plate without interaction. (a) laminar, (b) transitional, and(c) turbulent. Flow is from left to right.


The changes in scale of the separated flow in both the streamwise and spanwise directions in a “transitional”interaction are quite substantial. The shape of the interaction is also highly variable and very sensitive to the state ofthe incoming boundary layer. Figure 8 shows four non-sequential images of such an interaction taken at 10 kHz.These particular images were chosen to illustrate the unsteadiness of the interaction. This particular interaction isoccurring towards the laminar edge of the transition band. The bulge a quarter of the way up the frame remainsfairly constant and looks to be caused by a roughness element upstream either on the plate surface or leading edge. Itis also interesting that the transitional interactions do not seem to be time resolved at 10 kHz, but the fully turbulentinteractions do. This interaction extends farther upstream for a given spanwise location than in the more turbulentcases.

When the interaction occurs farther into the transitional band, the separated flow begins to look more like thecombined laminar/turbulent interaction, with laminar scaling close to the centerline and turbulent scaling off-center,as seen in Fig. 9. The interactions are more swept and become more steady, relatively speaking.

A fully turbulent interaction is shown in Fig. 10. The scales of this interaction are smaller in both dimensionsthan those previous, and both the scales and the shape remain relatively constant from frame to frame. While theturbulent case is much more unsteady than a purely laminar interaction is, the data would suggest that the

Figure 8. Non-sequential images of a more laminar “transitional” interaction. Flow is from left to right. Cylinderand dark area to right of white line added in processing.

Figure 9. Non-sequential images of turbulent “transitional” interaction. Flow is from left to right. Cylinderand dark area to right of white line added in processing.


unsteadiness is at a maximum near the laminar end of transition. This may seem counter-intuitive, but another flowfeature was observed that might be offer some insight into this trend.

When the cylinder was placed in tripped flow that appeared essentially laminar there were intermittent bursts ofturbulence extending up to 4.5 diameters upstream and occurring as much as 3.5 diameters off of the centerline, asshown in Fig. 8. These bursts tend to have a consistent general shape, that of a “V” pointing downstream, and bear astriking resemblance to Emmons turbulent spots that appear in the transition process6. The light band immediatelyupstream of these structures is characteristic of a shock. These spots were found to occur in intermittent groupings ofthree or four spots, but within each grouping the spots were temporally very close together, with as little as 200microseconds separating them. While no definitive conclusions can be drawn yet, it is possible that the highlyunsteady nature of the transitional interaction could be closely related to the formation of these spots.

Figure 9 shows sample side-view schlieren images of a transitional interaction. Since these images are the resultof integration of the light beam across the width of the test section care is needed in their interpretation. The blurredinclined wave in the upper half of the image and the clearly defined vertical wave immediately upstream of the

Figure 8. Turbulent spot formation in interaction region. Flow is from left to right. Cylinder and dark area toright of white line added in processing. d = 0.375 in, Xcyl = 5.9. Images are not sequential.

Figure 10. Sequential images of turbulent interaction imaged at 10 kHz. Flow is from left to right.Cylinder and dark area to right of white line added in processing.


cylinder are easily identified as the rippling plate leading edge shock wave and the steady cylinder bow shock,respectively. There appear to be several shock waves that coalesce near the triple point, with the upstream waveappearing weaker. The upstream wave is likely the laminar separation shock, whereas the downstream waves arelikely turbulent separation shocks. The plan-view PLS images and surface streakline images show that the flowstructure is highly non-uniform in the spanwise direction and so these waves are probably generated at differentspanwise locations.

IV. ConclusionThe plan view PLS images have proven to be very effective in visualizing the global flowfield structure of

laminar, transitional and turbulent interactions. The laminar interactions are characterized by a single, relativelysteady, separation shock, which exhibits a large radius of curvature. The turbulent case is more symmetricallydistributed and more three-dimensional. The transitional interactions exhibit a “laminar” separation shock near thecylinder centerline but turbulent separation shocks in the outboard regions. This dual-shock behavior leads to aseparation shock structure that exhibits an inflection point. The PLS images demonstrate that the flow structure ofthe transitional interactions is highly spanwise non-uniform and therefore care should be taken when interpretingspatially integrated techniques such as schlieren or shadowgraphs. A significant piece of the explanation for thehighly unsteady nature of the transitional interaction may well lie in the formation of turbulent spots and theirbehavior within the interaction itself. Future work should focus on these spots both independently and incombination with the SWBLI. Additionally, future work will have to address the PLS imaging of the primaryseparation shock.

AcknowledgmentsThis work was sponsored (in part) by the Air Force Office of Scientific Research, USAF, under grant/contract

number FA9550-04-1-0112. The views and conclusions contained herein are those of the authors and should not be

Cylinder

Plateleading-edge

shock

(a)

Leading-edgeshock

laminar separationshock

Cylinderbow shock

Flow

turbulentseparation

shocks

(a) (b)

Figure 9. Spark schlieren photographs of a transitional interaction. (a) Schematic showing field of view, (b) and(c) are sample images.


interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AirForce Office of Scientific Research or the U.S. Government.

The authors would like to thank Dr. Bharath Ganipathisubramani and Pablo Bueno for their help with theexperimental setup and execution and Edward J. Zihlman and Frank Wise for their technical expertise. The authorswould also like to thank machinists Travis Crooks, David Gray and Joe Edgar

References1Young, F.L., Kaufman, L.G., and Korkegi, R.H., “Experimental Investigation of the Interactions Between Blunt Fin Shock

Waves and Adjacent Boundary Layers at Mach Numbers 3 and 5,” ARL 68-0214, Dec 1968.2Hung, F.T. and Clauss J.M., “Three-Dimensional Protuberance Interference Heating in High-Speed Flow,” AIAA-80-0289,

AIAA 18th Aerospace Sciences Meeting, Jan 1980.3Özcan O. and Holt M. (1984), “Supersonic Separated Flow past a Cylindrical Obstacle on a Flat Plate,” AIAA Journal, Vol.

22 No. 5, pp. 611-617.4Kaufman, L. G., II, Korkegi R. H. and Morton, L. C., “Shock Impingement Caused By Boundary Layer Separation Ahead of

Blunt Fins,” ARL 72-0118, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio, Aug 1972.5Ramesh, M. D. and Tannehill J. C., “Correlations To Predict Transition In Two-Dimensional Supersonic Flows,” 33rd AIAA

Fluid Dynamics Conference and Exhibit, June 23-26.6Cantwell, B.J., Coles, D. and Dimotakis, P., “Structure and entrainment in the plane of symmetry of a turbulent spot,”

Journal of Fluid Mechanics, Vol. 87, 641-672.

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