AIAA 2006-3361 36th AIAA Fluid Dynamics Conference and Exhibit 5 - 8 June 2006, San Francisco, California Experimental Study of an Incident Shock Wave/Turbulent Boundary Layer Interaction Using PIV R.A. Humble,* F. Scarano,† and B.W van Oudheusden‡ Delft University of Technology, 2629 HS Delft, The Netherlands Particle Image Velocimetry is applied to the interaction between an incident shock wave and a flat plate turbulent boundary layer at Mach 2.1. The undisturbed boundary layer is characterized by its mean and turbulence properties. The interaction region is characterized by the mean velocity field, which shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. The unsteady flow properties are inspected by means of instantaneous velocity fields. Patches of reversed-flow are frequently observed at several locations. Although significant reversed-flow is measured instantaneously, on average no reversed-flow is observed. Turbulence properties show the highest turbulence intensity in the region behind the impingement of the incident shock wave. Turbulence anisotropy is found to be present, with the streamwise component dominating. A distinct streamwiseoriented region of relatively large Reynolds shear stress magnitude appears in the redeveloping boundary layer and persists downstream. The recovery of the boundary layer towards its initial equilibrium conditions therefore appears to be a gradual process. T I. Introduction HE interaction between a shock wave and a turbulent boundary layer remains one of the most outstanding problems of modern high-speed fluid dynamics. The interaction embodies all of the effects of compressibility, turbulence, and separation that present special challenges for both experimentalists and theoreticians alike. Since shock wave/turbulent boundary layer interactions are prevalent in a variety of high-speed applications, such as longhaul civil transportation systems, as well as other high-speed manoeuvring vehicles, a detailed understanding of this phenomenon is essential for efficient aerodynamic and propulsion design. Numerous experimental efforts over the decades have sought to gain a better understanding of the shock wave/turbulent boundary layer phenomenon. Early studies were intent on improving the understanding of the flow within the interaction region and therefore considered the simplest configurations for investigation. A series of planar interactions were studied1-6 which represent the internal interactions which typically occur within supersonic air intakes. These investigations demonstrated the importance of the incident shock wave on the mean flow and pressure distribution along the interaction zone, as well as in some cases the turbulence properties. Mean flow properties were mapped as functions of Mach number and Reynolds number, as well as the incident shock wave strength and state of the undisturbed boundary layer. Experimental studies of shock wave/turbulent boundary layer interactions have been generally frustrated however, by the limitations of the experimental techniques used.7 Whilst hot-wire measurements and laser Doppler velocimetry have provided detailed information on the nature of turbulence in these flows, without whole-field quantitative information a complete characterization of the dynamical aspects of the flowfield cannot be made. Furthermore, whilst numerical simulations of these flows have achieved some degree of success, they have been generally hampered by the recognized deficiencies of the available turbulence models. It is generally accepted that conventional turbulence models can predict the mean flow properties of the interaction region reasonably well, but the accurate prediction of the associated turbulence properties still remains problematic.8 * Research Assistant, Faculty of Aerospace Engineering, AIAA Member. Associate Professor, Faculty of Aerospace Engineering. ‡ Associate Professor, Faculty of Aerospace Engineering. † 1 American Institute of Aeronautics and Astronautics Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. With advances in laser and digital imaging technology, rapid developments in non-intrusive, planar flow diagnostic tools, such as Particle Image Velocimetry (PIV) in particular have been made. This technique is capable of performing direct instantaneous velocity flowfield measurements making it suitable to investigate large-scale unsteady flow phenomena. Although the interaction between an incident shock wave and a turbulent boundary layer has been widely researched for many decades, the application of non-intrusive measuring techniques to the phenomenon has been the subject of relatively few studies. In the 1970's turbulence measurements were made using hot-wire anemometry and laser velocimetry9,10 and provided a good basis for future turbulence studies. Later workers11 used laser velocimetry with the aim of providing experimental data to aid the validation of turbulence closure models. More recently, PIV in conjunction with pressure transducers has been used to better understand the physical phenomena taking place.12 The need for a better understanding of this type of flow, as well as the potential of non-intrusive measurement techniques provide the impetus for the present study. The objective of the following paper is to apply PIV to the interaction between an incident shock wave and a flat plate turbulent boundary layer. The undisturbed boundary layer is characterized by its mean and turbulence properties. Instantaneous whole-field velocity field measurements are obtained of the interaction region from which inferences about the turbulence properties are made. These results may be useful for analytical and computational modelling purposes. II. Apparatus and Experimental Techniques A. Flow Facility Experiments were performed in the blow-down transonic-supersonic wind tunnel (TST-27) of the High-Speed Aerodynamics Laboratories at Delft University of Technology. The facility generates flows in the Mach number range 0.5 to 4.2 in the test section. In the present study, tunnel operation is near Mach 2 in view of the interest in the low supersonic domain. The test section dimensions are 280mm×270mm. The Mach number was set by means of a continuous variation of the throat section and flexible nozzle walls. Small deviations in Mach number were corrected for by automatic fine adjustment of the choke. The tunnel operates at unit Reynolds numbers ranging from 30×106 to 130×106m-1, enabling a blow-down operating use of the tunnel of approximately 300s. Two experiments were conducted in the present study, namely; an experiment to characterize the undisturbed boundary layer and an experiment to characterize the interaction region. In both cases, the wind tunnel was operated at a nominal Mach number of 2.1 with a stagnation pressure of 280kPa and stagnation temperature of 284K. The test boundary layer developing along the top wall of the wind tunnel was chosen in both cases in order to realize the advantages of a thick boundary layer, namely; an increase in the scales of the mean and fluctuating flowfield, which improves the spatial resolution. After naturally transitioning upstream in the nozzle, the boundary layer developed along a smooth surface under nearly adiabatic flow conditions for a development length of approximately 2m along the divergent part of the wind tunnel nozzle. Upon entering the test section three boundary layer thicknesses upstream of the extrapolated wall impact point of the incident shock wave, the boundary layer was fully developed and exhibited smooth wall type behaviour. The undisturbed boundary layer properties are summarized in Table 1. Table 1. Undisturbed boundary layer properties Parameter Quantity M∞ 2.1 U∞, m/s 525 δ99, mm 20 δ*, mm 4.2 θ, mm 1.4 Re, 1×106 m-1 38.1 Reθ 5.29×104 uτ, m/s 19.5 cf 1.52×10-3 The displacement thickness δ* and momentum thickness θ are the compressible values. The density variation was deduced from the velocity distribution using the adiabatic Crocco-Busemann relation with a constant recovery factor r=0.89, with the assumption that the static pressure in the transverse direction remains constant. 2 American Institute of Aeronautics and Astronautics A 100mm long single-sided shock generator with deflection angle 100 was placed in the freestream flow to generate the incident shock wave. The generator was rigidly mounted in the centre of the test section on an 80cm long sting and spanned approximately 65% of the test section width. A schematic representation of the experimental apparatus and Schlieren image indicating the PIV field-of-view (FOV) is shown in Figs. 1a and 1b respectively. The origin of the reference coordinate system is located on the tunnel wall with x measured in the downstream flow direction from the extrapolated wall impact point of the incident shock wave and y normal to the wall. It can be seen that the shock generator is of sufficient length to prevent the expansion fan at its shoulder from influencing the interaction region. It is clear however, that the redeveloping boundary layer may well be affected by the expansion. M=2.1 y x a) b) Figure 1. Experimental arrangement. a) Experimental setup, b) Schlieren image (dashed rectangle indicates FOV2) B. PIV Technique Two-component PIV was employed in the present study. Flow seeding constitutes one of the most critical aspects of PIV in high-speed flows. A 2-D rake was used to seed a fraction of the flow in the settling chamber with titanium dioxide (TiO2) particles with a nominal median diameter of 50nm and bulk density of approximately 1000kg/m3. A particle response assessment across the incident shock wave enabled a particle relaxation time of τp=2.1µs to be determined, corresponding to a frequency response of fp=476kHz and Stokes number Sk=0.06 based upon a flow time scale δ/U∞. The seeded flow was illuminated by a Spectra-Physics Quanta Ray double-pulsed Nd:Yag laser with 400mJ pulsed energy and a 6ns pulse duration at wavelength 532nm. Laser light tunnel access was provided by a probe inserted into the flow downstream of the shock generator. The laser pulse separations in the boundary layer and interaction experiments were 0.6µs and 2µs respectively, producing particle displacements of approximately 0.3mm and 1mm respectively in the freestream flow. This corresponds to approximately 11 pixel maximum displacement in both cases. The light sheet was approximately 1.5mm thick. Particle images were recorded by a PCO Sensicam QE 12-bit Peltier-cooled CCD camera with frame-straddling architecture and a 1376×1040 pixel sized sensor. Only 432 pixels were used in the transverse direction given the large aspect ratio of the flow region investigated and at the same time to achieve an increased recording rate of 10Hz. The camera was equipped with a Nikon 60mm focal objective with a focal number f#=8 in combination with a narrow-band-pass 532nm filter. In the boundary layer experiment, the camera was rotated 900 to maximize the number of pixels normal to the wall. This flow was imaged over a FOV1 of 12mm×39mm resulting in a digital resolution of approximately 28µm/pixel. In the interaction experiment, FOV2 was 124mm×39mm resulting in a digital resolution of approximately 89µm/pixel. Both sets of recorded images were interrogated using the WIDIM algorithm.13 This method is based upon the deformation of correlation windows with an iterative multi-grid scheme, which is particularly suited for highly sheared flows. A dataset of 475 images was acquired in each case. The boundary layer and interaction experiments were interrogated using windows of size 61×7 and 21×21 pixels respectively with an overlap factor of 75%. This resulted in window sizes for FOV1 and FOV2 of 1.7×0.2mm2 and 1.9×1.9mm2 respectively. 3 American Institute of Aeronautics and Astronautics III. Results and Discussion A. Undisturbed Boundary Layer Properties The undisturbed boundary layer properties determined from the boundary layer experiment are shown in Fig. 2. All data points are shown spaced at a maximum Fig. distance of 3%. Figure 2a shows the mean velocity, static temperature and mass-flux profiles. The statistical uncertainty associated with the mean velocity is estimated to be 0.3%U∞. The skin friction coefficient was determined by fitting the experimental data to the compressible van Driest log-law and was found to be cf=1.52×10-3, which agrees to within 3% of the van Driest II skin friction formula for a flat plate. The variation of the streamwise <u'> and transverse <v'> turbulence intensity, as well as the Reynolds shear stress ¯ u'v' is shown in Fig. 2b, where <·> denotes the root-mean-square quantity. The statistical uncertainty associated with the turbulence intensity and Reynolds shear stress is estimated to be 3% and <10% respectively. From these results it can be concluded that the freestream turbulence level does not exceed 1%. All profiles vary appreciably within the boundary layer, with <v'> and –¯ u'v' reaching maximum values of 2.3% and 0.05%U∞ respectively at approximately y/δ=0.21. The variation of <u'> is quantitatively similar to turbulence measurements made within a variety of supersonic boundary layers,14-16 as well as those obtained by means of PIV.17 Whilst both u'v' decrease in the proximity of the wall, it can be seen that <u'> increases significantly. The precise <v'> and –¯ determination of the maximum value of <u'> is therefore problematic, due to the difficulties in obtaining reliable results very close to the wall using PIV. a) b) Figure 2. Undisturbed boundary layer properties. a) Mean properties, b) Turbulence properties B. Description of the Interaction Region To first give a general description of the interaction region the mean flow topology is shown in Fig. 3. Mean velocity streamlines are displayed with mean velocity vectors and transverse velocity contours. The streamlines verify a uniform outer flow upstream, and illustrate the distortion of the overall flowfield as a result of the interaction process. Regions of flow compression appear as densely-spaced transverse velocity contours, whilst sparsely-spaced transverse velocity contours indicate regions of flow expansion. The incident shock wave can be seen to enter the boundary layer where it begins to curve in response to the decreasing local Mach number. Compression waves are generated within the boundary layer approximately two boundary layer thicknesses upstream of the extrapolated wall impact point of the incident shock wave. These compression waves coalesce as they leave the boundary layer to form the reflected shock wave. The flow passes through a series of complicated flow patterns and undergoes a recovery process further downstream. Subsonic fluid close to the wall that has initially passed through the interaction region begins to contract, causing the outer fluid to create an expansion fan behind the reflected shock wave. Although difficult to discern, a gradual recompression process takes place further downstream as fluid turns back towards the streamwise direction. 4 American Institute of Aeronautics and Astronautics Figure 3. Mean flow topology C. Two-Dimensionality of the Flowfield It has been noted that there is often a tendency for the presence of spanwise cellular non-uniformity in nominally two-dimensional flowfields that are characterized by large-scale separated flow regions.18 To examine these effects in the present study, PIV measurements were made at several spanwise locations in increments of z/δ =0.5 with 50 images acquired at each location. Recording and interrogation settings were the same as those used in the interaction experiment. Figure 4 shows the mean streamwise velocity distribution, where z/δ=0 indicates the wind tunnel centre-line. It can be seen that the mean flow remains rather uniform over the spanwise region considered. The inset illustrates that although slight three-dimensional effects appear to exist within the separated flow region, they seem characteristic of the fluid dynamic processes present and not due to the side wall boundary layers. Mean flow properties show appreciable differences however, at distances greater than 30% of the test section width. This behaviour is ascribed to both the limited span of the shock generator, as well as the increasingly intermittent nature of the incoming seeded streamtube. Figure 4. Spanwise survey of the interaction region D. Mean Flow Properties of the Interaction Region The mean flow behaviour is described by the averaged streamwise and transverse velocity fields, which are shown in Figs. 5a and 5b respectively. Mean velocity vectors are also shown, under-sampled in the streamwise direction for clarity. The mean velocity fields illustrate the incident and reflected shock waves, as well as the boundary layer distortion. A significant variation of the mean velocity is observed throughout the interaction region. For instance, subsonic fluid near to the wall can be seen moving with a positive streamwise velocity of less than 0.1U∞ whereas a maximum negative transverse velocity of approximately 0.15U∞ occurs immediately downstream of the incident shock wave. 5 American Institute of Aeronautics and Astronautics Within the boundary layer, it can be seen that the transverse velocity remains virtually zero in the vicinity of the incident shock wave. Here fluid is initially moving away from the wall (as a result of the upstream influence) and is brought back towards the wall further downstream. The locus of points where the transverse velocity passes through zero traces the trajectory of the incident shock wave through the boundary layer. A similar observation can be made immediately behind the reflected shock wave, where fluid that is initially moving towards the wall behind the incident shock wave is temporarily turned parallel to the wall before entering the expansion fan. Although an appreciable recovery of the redeveloping boundary layer occurs, it does not attain the freestream velocity value away from the wall, nor does its transverse component become everywhere zero, except in the proximity of the wall due to the wall damping effect. It is clear that the boundary layer thickness increases as a result of the interaction process. a) b) Figure 5. Mean velocity distributions. a) ū/U∞, b) v̄/U∞ From the analysis of the instantaneous velocity fields, patches of reversed-flow are frequently observed at several locations. Although in some cases significant reversed-flow is found to be measured instantaneously (see section F), on average no reversed-flow is observed. This behaviour has also been observed in other shock wave/turbulent boundary layer studies that have considered ramp flow19 in which the configuration did not span the width of the test section. It is not known at the present time whether or not the lack of mean reversed-flow is associated to the fact that the shock generator is not full-span and therefore the consequent three-dimensional relieving effect may be weakening the interaction. The evolution of the streamwise mean velocity profile is presented in Fig. 6 at various streamwise locations. Figure 6. Evolution of mean streamwise velocity profile 6 American Institute of Aeronautics and Astronautics The undisturbed boundary layer profile represents a fully developed turbulent boundary layer with negligible transverse velocity component (∂p/∂y≈0). Within the first part of the interaction, an overall retardation of the velocity profile occurs, this effect being particularly important close to the wall. Note the presence of the incident shock wave in this region, evident in the outer part of the boundary layer. At a certain streamwise location a maximum retardation effect is reached. Negative velocities indicating reversed-flow however, are not detected in the mean profiles. Further downstream, the velocity profile slowly begins to recover towards its initial state, this process again being particularly important close to the wall. Consistent with the velocity field distributions it can be deduced from the inspection of these profiles that the boundary layer does not fully recover to its initial equilibrium conditions within a distance of two boundary layer thicknesses downstream of the extrapolated wall impact point of the incident shock wave. E. Integral Parameters Mean velocity profiles are integrated at various streamwise locations to obtain values of the incompressible displacement thickness δ*inc and the momentum thickness θinc, as well as the related shape parameter Hinc given by ∞  ∗ = ∫ 1 − δ inc 0  u   dy, U∞  θinc = ∫ ∞ 0 u  u  1 −  dy , U∞  U∞  ∗ H inc = δ inc θinc (1) The evolution of these integral parameters is shown in Fig. 7. The parameters remain relatively constant within the undisturbed boundary layer, and undergo a significant variation throughout the interaction region. A rapid increase in the displacement thickness occurs during the first part of the interaction, reaching a maximum value of over 50% of the undisturbed boundary layer thickness. This is followed by a decrease further downstream. In contrast, the momentum thickness steadily increases throughout the interaction, with only a slight decrease further downstream. This behaviour can be readily understood when one considers the (incompressible) momentum integral equation. Since both the pressure gradient and skin friction coefficient generally remain positive throughout the first part of the interaction, the rate of change of momentum thickness must also remain necessarily positive. The behaviour of the shape parameter is therefore primarily determined by the displacement thickness. It is interesting to note that the shape parameter attains a maximum incompressible value of approximately 1.8, appreciably less than the commonly admitted values associated with turbulent separation. It should be noted however, that an accurate determination of the shape parameter is difficult in regions of strong streamwise gradients. Figure 7. Variation of boundary layer integral parameters F. Instantaneous Flow Properties of the Interaction Region The instantaneous velocity snapshots reveal several interesting features associated with the unsteady behaviour of the interaction region. Figure 8 illustrates fields of the instantaneous streamwise velocity. The time that elapses between consequent recordings (10Hz framing rate) is significantly greater than any characteristic flow time scale, which leads to a series of uncorrelated velocity snapshots. 7 American Institute of Aeronautics and Astronautics The outer freestream flow remains steady and there appears to be no appreciable motion of the incident shock wave. The global structure of the interaction region however, varies considerably in time. Specifically, the reflected shock wave appears to be highly unsteady, as well as the undisturbed boundary layer, which has a clearly intermittent nature. Regions of reversed-flow frequently occur within the interaction region of the order –0.1U∞. In other cases however, the flow remains fully attached with no observable reversed-flow. When the reversed-flow region occurs, it has a typical streamwise length that can be of the order of the boundary layer thickness. This separated flow region experiences distortions in both the streamwise and transverse directions, but whose motion is found mainly to be in the streamwise direction. Qualitatively, at least in some instances, the reflected shock wave appears to be displaced away from the wall when the size of the reversed-flow region increases, and moves towards the wall when the size of the reversed-flow region decreases. This suggests that the large-scale motion of the reflected shock wave is associated with the shock’s displacement due to the expansion and contraction of the separated flow region. This is consistent with previous related studies20 which examined hypersonic separation shock foot unsteadiness in a two-dimensional compression ramp interaction. Figure 8. Uncorrelated instantaneous streamwise velocity distributions u/U∞ It is now clear that the mean flow organization is a somewhat simplified representation, since it is constructed from a statistical analysis of an instantaneous flowfield that is highly fluctuating and significantly more complex. Over the last decades several efforts have tried to determine the main causes of this flow unsteadiness.21,22 Previous authors have hypothesized that a relationship may exist between the undisturbed boundary layer thickness and the motion of the reflected shock wave.23 However, attempts to correlate the motion of the reflected shock wave with changes in undisturbed boundary layer thickness have so far been somewhat unsuccessful. Recent experimental evidence suggests that the reflected shock wave unsteadiness may in fact be associated with the streamwise velocity fluctuations within the boundary layer.24 G. Turbulence Flow Properties of the Interaction Region Figures 9a and 9b show the distributions of <u'> and <v'> respectively. These results reflect the large mixing that takes place within the interaction region and the distributed nature of the turbulence. A substantial increase in <u'> occurs within the interaction region, initiating itself within the reflected shock foot region, and reaching a maximum value of approximately 0.21U∞ underneath the incident shock wave’s intersection with the sonic line. This value is comparable to laser velocimetry measurements,10,11 as well as Large Eddy Simulations25 which have all considered an incident shock wave interacting with a flat plate turbulent boundary layer. The increase in the streamwise component is over 100% greater than the increase in the transverse component indicating that appreciable turbulence anisotropy is present. The streamwise component however, can be seen to recover much more quickly than the transverse component with downstream development. 8 American Institute of Aeronautics and Astronautics According to previous studies considering compression ramp flow,26 the turbulent kinetic energy is essentially produced on the streamwise component <u'> and redistributed to the transverse <v'> and spanwise <w'> components. Indeed, one can envisage the transfer of kinetic energy from the mean flow to <u'> by normal advection across the mean velocity gradient. Simultaneously, since <u'> is generally larger than both <v'> or <w'> energy is redistributed (mostly to <w'>) mainly through the pressure-strain correlation. Furthermore, it has been hypothesized that large <u'> production does not necessarily balance the tendency towards isotropy when the streamwise extent of the interaction process is insufficient.27 Indeed, it can be seen in the present results that the streamwise component remains systematically greater than the transverse component despite its rapid recovery downstream of the interaction. Such anisotropy has also been observed in related experiments using hot-wire and laser velocimetry.9 That study is particularly interesting to the present work, since it considered an incident shock wave/turbulent boundary layer interaction, and observed no sizeable separation bubble, the incident shock wave being of insufficient strength to cause mean flow separation. It was found that the streamwise turbulence intensity increased substantially within the interaction region. The study also concluded however, that the transverse component remained almost unchanged, a conclusion that is somewhat different from the present results. Nevertheless, it is interesting to observe such behaviour of the streamwise component without the mean flow being necessarily separated. The higher level of fluctuations associated with the incident shock wave (approximately 4%U∞) is typically encountered in these experimental conditions and is ascribed to the combined effect of the decreased measurement precision and to small fluctuations of the shock wave position. The reflected shock wave exhibits a relatively high level of fluctuations, which in this case should not be regarded as turbulence but is ascribed to its significant unsteady motion. The increased level of fluctuations across these shock waves within the boundary layer is thought to be due to their interaction with the convection of turbulent coherent structures, as well as their increased unsteadiness. It is striking how the turbulence intensity distributions reveal the curvature of both shock waves in this region. Two weak features downstream of the reflected shock wave (one parallel and the other roughly perpendicular to it) can also be observed in both the streamwise and transverse components. These features are thought to be due to optical aberration effects introduced by the inhomogeneous index of refraction field of this compressible flow.28 a) b) Figure 9. Turbulence intensity distributions. a) <u'>/U∞, b) <v'>/U∞ Iso-surfaces of <u'> deduced from the spanwise study are shown in Fig. 10 flooded with mean streamwise velocity. Increasingly larger iso-surface values highlight the boundary layer and illustrate the deflection of the supersonic flow as the interaction region is approached. The spanwise variation of these iso-surfaces, particularly in the outer flow, may be the result of poorer seeding levels away from the centre-line. The largest iso-surface values highlight the separated flow region. Iso-surfaces of <v'> are shown in Fig. 11 and verify that the freestream turbulence is isotropic. Within the boundary layer however, flow anisotropy prevents the same values being used as for the streamwise component. Increasingly larger iso-surface values highlight the incident and reflected shock waves, as well as the undisturbed and redeveloping boundary layer, despite the large differences in velocity present in these regions. The largest iso-surface values highlight only the reflected shock wave and redeveloping boundary layer, indicating that such a turbulence level does not exist within the undisturbed boundary layer, in contrast to what is observed in the streamwise component. 9 American Institute of Aeronautics and Astronautics Figure 10. Iso-surfaces of streamwise turbulence intensity Figure 11. Iso-surfaces of transverse turbulence intensity 10 American Institute of Aeronautics and Astronautics Profiles of <u'> and <v'> throughout the interaction region are shown in Fig. 12. The poorer spatial resolution compared to the boundary layer experiment is evident. Within the first part of the interaction, a substantial increase in both components occurs, particularly in the streamwise component as previously observed. The presence of the incident and reflected shock waves is also evident, where local maxima occur in the outer part of the boundary layer. It is now clear that within this region, the typical boundary layer assumption of a small transverse pressure gradient (∂p/∂y≈0) may no longer be valid since there is now an appreciable variation of the transverse velocity fluctuations normal to the wall. The levels of turbulence intensity within the interaction region reach a maximum away from the wall, exhibiting values that are in fact comparable to experiments investigating reattaching free shear layers29,30 although the trends differ somewhat due to the different configurations. Other authors31 have made the similar observation that the high levels of turbulence match those found in mixing layers. It has been hypothesized that the separated flow region may therefore be capable of producing large-scale perturbations that are convected downstream.32 It is evident from these profiles that the inner and outer regions of the boundary layer undergo different turbulence evolutions. a) b) Figure 12. Turbulence intensity profiles. a) <u'>/U∞, b) <v'>/U∞ The turbulence intensity profiles can be seen to spread broadly over the transverse height of the interaction with downstream development. This vertical diffusion has also be observed in a Mach 2.9 shock wave/boundary layer interaction.33 It is found in the present study that, in spite of the vertical diffusion within the redeveloping boundary layer, the location of the maximum values essentially remains constant with downstream development, also consistent with Ref. 33. An insufficient FOV precludes any further statements to be made upon this recovery period, other than after two boundary layer thicknesses downstream of the extrapolated wall impact point of the incident shock wave, the turbulence intensity profiles still remain affected by the interaction. In order to make further statements regarding the turbulence properties, the evolution of the maximum local turbulence intensity throughout the interaction region is shown in Fig. 13. Figure 13. Evolution of maximum local turbulence intensity 11 American Institute of Aeronautics and Astronautics A significant variation of the maximum local turbulence intensity occurs throughout the interaction region with the streamwise component exceeding the transverse component by over a factor of 3. This large increase in the streamwise component can be readily understood when one considers the production term associated with each component. Following along the lines of previous turbulence studies concerning transonic shock wave/turbulent boundary layer interactions,27 consider first the production term of the streamwise component, written for an incompressible flow for simplicity as Pu = −u ′v′ ∂u ∂u − u ′2 ∂y ∂x (2) It should be noted that there is an appreciable variation of mean density across the undisturbed boundary layer in the present study (ρ̄/ρ¯e=0.57 at Me=2.1) and so only a general discussion will be given. In the first part of the interaction, ∂ū/∂y within the undisturbed boundary layer is large. Furthermore, it is generally accepted that ¯<0 u'v' when ∂ū/∂y>0 (as confirmed in Fig. 14). With ∂ū/∂x a necessarily large negative value in this region since the flow is strongly decelerating, the production term of the streamwise turbulence intensity is essentially the sum of two positive terms. This explains the substantial increase in <u'> in the first part of the interaction region. Consider now the production mechanism for the transverse component given by Pv = −u′v′ ∂v ∂v ∂v ∂u − v′ 2 ≈ −u ′v′ + v′2 ∂x ∂y ∂x ∂x (3) Here the derivative ∂v̄/∂y has been replaced by –∂ū/∂x since the incompressible continuity equation is essentially satisfied for weakly compressible flows at moderate Mach number (M∞<2). This was verified by considering the spatial distribution of these derivatives, where it was found that incompressible continuity was generally satisfied except in the immediate vicinity of the incident and reflected shock waves. If the derivative ∂v̄/∂x is considered small throughout the interaction region, then with ∂ū/∂x being a typically negative as mentioned above, it can be deduced that only the second term in Eq. 3 is important, and which actually tends to decrease the production of the transverse component in the first part of the interaction region as shown. This behaviour is similar to what has been observed in previous experimental studies considering transonic flows.27 Further downstream, the flow begins to accelerate and ∂ū/∂x becomes positive. This leads to the relatively slow production of the maximum transverse turbulence intensity further downstream. Consider now the Reynolds shear stress distribution within the interaction region. Such measurements are principally carried out to aid the modelling of turbulent effects by computational methods. They are of particular importance in the validation of turbulence closure models since theoretical efforts are generally hampered by the difficulties of representing the turbulence terms in the time-averaged equations. For compressible flows, the Reynolds shear stress is conventionally expressed as ρ̄ ¯ u'v' when the density fluctuations are ignored. For practical purposes, the term ¯/U u'v' ∞2 will be regarded as being representative of the Reynolds shear stress. The distribution of u'v' ∞2 is shown in Fig. 14. ¯/U 2 3 Figure 14. Reynolds shear stress distribution u′v′ / U ∞ ×10 12 American Institute of Aeronautics and Astronautics Initially moderate levels of Reynolds shear stress are present within the undisturbed boundary layer, with a substantial increase in Reynolds shear stress magnitude occurring within the incident and reflected shock foot regions. The increase in turbulence in these regions is expected since it is known that supersonic flow which undergoes a compression is associated with turbulence augmentation. Although there appears to be a systematic change of Reynolds shear stress within the separated flow region, its behaviour at this point is unclear. The redeveloping boundary layer can be characterized by the presence of a distinct streamwise-orientated region of relatively large Reynolds shear stress magnitude in the lower part of the boundary layer, reaching a maximum away from the wall. This tendency has been well-documented9,33,34 with these Reynolds shear stresses implying the existence of large-scale eddies,34 consistent with the instantaneous results of the present study, and which is also indicated by the recovery of the boundary layer velocity profile. The evolution of the Reynolds shear stress profiles is shown in Fig. 15. The presence of the reflected shock wave is evident in the first part of the interaction, where a substantial increase in Reynolds shear stress magnitude occurs in the outer part of the boundary layer. Although the Reynolds shear stress can be seen to be greatly attenuated near to the wall, a significant variation in the data systematically occurs in this region where large values are measured. Note the overwhelmingly negative values within the redeveloping boundary layer, indicative of slower moving (u'<0) upward-orientated (v'>0) fluid, and faster moving (u'>0) downward-orientated (v'<0) fluid relative to the mean flow. This region persists downstream for several boundary layer thicknesses and does not show appreciable signs of recovery. Consider now the turbulence production associated with the turbulent kinetic energy transport equation.35 For an incompressible flow the production term after neglecting ∂v̄/∂x is given by P = −u ′v′ ( ) ∂u ∂u − u ′ 2 − v′ 2 ∂y ∂x (4) where the first and second terms are the production by shear stress and normal stress respectively. Profiles of these terms are shown in Fig. 16, where the data have been smoothed due to the uncertainties that arise in the differentiation of experimental data. Also note the different scale for position x/δ=-1. As noted in related studies,35 the production by shear stress is normally the predominant term in these types of flows and is the only term typically retained in predictive methods. It can be readily seen from the present results however, that the production by normal stress can be just as significant, and can actually exceed the production by shear stress in the first part of the interaction where the flow is rapidly decelerating. The normal stress terms in the momentum and turbulence equations may not therefore, be justifiably neglected in the first part of the interaction process, where there is a large turbulence production which mainly affects the streamwise component.35,36 Within the redeveloping boundary layer the production by normal stress decreases rapidly as expected. Overall, the recovery of the turbulence properties appears to be a very gradual process, with the current FOV insufficient to observe the boundary layer returning to its initial equilibrium conditions. Figure 15. Reynolds shear stress profiles Figure 16. Evolution of turbulence production terms 13 American Institute of Aeronautics and Astronautics H. Structural Parameters Two important parameters that can be used to further characterize the turbulence structure of the interaction region, independent of the magnitude of the velocity fluctuations, are the correlation coefficient Ruv and anisotropy parameter v′2 / u ′2 . The variation of these quantities is shown in Fig 17 at several streamwise locations. a) b) Figure 17. Structural parameters. a) Correlation coefficient Ruv, b) Anisotropy parameter v′2 / u ′2 The correlation coefficient −Ruv upstream of the interaction remains at an approximate value of 0.45 for an appreciable portion of the boundary layer and vanishes as the outer region is approached. Similar observations have been made using laser Doppler velocimetry on a Mach 2.3 boundary layer,37 where it was found that −Ruv remained at an approximately constant value of 0.45 within the region 0.1 to 0.8δ. This is in fact, what also occurs in most subsonic flows.38 Other studies39 of a Mach 2.9 boundary layer however, have indicated that −Ruv decreases significantly with distance from the wall. It is therefore difficult to state precisely the effect of compressibility on the correlation coefficient, although these results collectively suggest that the behaviour of the correlation coefficient within moderately compressible supersonic turbulent boundary layers closely resembles incompressible behaviour. A rapid change in the turbulence structure occurs further downstream as a result of the interaction process, with the correlation profiles becoming strongly distorted, particularly in the outer region of the boundary layer due to the presence of the incident and reflected shock waves. Consistent with the correlation coefficient, the anisotropy parameter shows a relatively constant turbulence structure upstream of the interaction, maintaining a reasonably constant value of 0.25 throughout most of the boundary layer. Outside of the boundary layer, changes in the anisotropy parameter become more noticeable with streamwise development and values can be seen to systematically reach above unity for locations x/δ>1. This means that during and downstream of the interaction, contrary to the situation upstream, the transverse fluctuations now become greater than the streamwise fluctuations. Similar observations have been also been made in turbulence studies of a low-speed incompressible boundary layer,40 where this behaviour was attributed to transverse velocity fluctuations occurring in the intermittent outer part of the boundary layer, which do not significantly affect the streamwise velocity fluctuations since the mean flow velocity defect is considered small. It is interesting to observe, that the way in which the anisotropy parameter varies within the boundary layer and outer regions is distinctly different with streamwise development. 14 American Institute of Aeronautics and Astronautics IV. Conclusions Particle Image Velocimetry was applied to the interaction between an incident shock wave and a flat plate turbulent boundary layer at Mach 2.1. The undisturbed boundary layer was characterized by its mean and turbulence properties and showed good agreement with other experimental measurements. The interaction region was characterized by the mean velocity field, which showed the incident and reflected shock wave pattern, as well as the boundary layer distortion. The unsteady flow properties were inspected by means of instantaneous velocity fields. Patches of reversed-flow were frequently observed at several locations. Although significant reversed-flow was measured instantaneously, on average no reversed-flow was observed. Turbulence properties showed the highest turbulence intensity in the region behind the impingement of the incident shock wave. Turbulence anisotropy was found to be present, with the streamwise component dominating. The streamwise component however, recovered much more quickly than the transverse component with downstream development. A distinct streamwise-oriented region of relatively large Reynolds shear stress magnitude appeared in the redeveloping boundary layer and persisted downstream. The recovery of the boundary layer towards its initial equilibrium conditions would therefore appear to be a gradual process. Acknowledgments This work is supported by the Dutch Technology Foundation STW under the ‘VIDI Vernieuwingsimpuls’ program grant DLR.6198. 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