RESEARCH ARTICLE

Particle image velocimetry measurements of a shockwave/turbulent boundary layer interaction

R. A. Humble Æ F. Scarano Æ B. W. van Oudheusden

Received: 29 September 2006 / Revised: 14 March 2007 / Accepted: 27 April 2007 / Published online: 23 June 2007

� Springer-Verlag 2007

Abstract Particle image velocimetry is used to investi-

gate the interaction between an incident shock wave and a

turbulent boundary layer at Mach 2.1. A particle response

assessment establishes the fidelity of the tracer particles.

The undisturbed boundary layer is characterized in detail.

The mean velocity field of the interaction shows the inci-

dent and reflected shock wave pattern, as well as the

boundary layer distortion. Significant reversed flow is

measured instantaneously, although, on average no re-

versed flow is observed. The interaction instantaneously

exhibits a multi-layered structure, namely, a high-velocity

outer region and a low-velocity inner region. Flow turbu-

lence shows the highest intensity in the region beneath the

impingement of the incident shock wave. The turbulent

fluctuations are found to be highly anisotropic, with the

streamwise component dominating. A distinct streamwise-

oriented region of relatively large kinematic Reynolds

shear stress magnitude appears within the lower half of the

redeveloping boundary layer. Boundary layer recovery

towards initial equilibrium conditions appears to be a

gradual process.

1 Introduction

The interaction between a shock wave and a turbulent

boundary layer (SWTBLI) creates a series of complicated

flow phenomena that have long been a problem area of

modern high-speed fluid dynamics. The interaction

embodies all of the problems associated with compress-

ibility, flow separation and turbulence, which present for-

midable challenges to experimentalists and theoreticians

alike. Numerous efforts over the decades have therefore

sought to gain a better understanding of its complex

behaviour. SWTBLIs are typically characterized as com-

pression ramp or incident shock wave interactions. The

former case has been extensively studied for a wide variety

of flow conditions and configurations (e.g. Settles and

Dodson 1991). The salient features of this type of inter-

action can be found in references given by Dolling (2001)

and Smits and Dussuage (2006). These studies have shown

that when the boundary layer separates, the shock foot and

interaction zone undergo an unsteady motion at frequencies

much lower than those of the incoming boundary layer. A

variety of authors have tried to correlate this unsteady

shock wave motion with upstream conditions (Andreopo-

ulos and Muck 1987), as well as the internal dynamics of

the separated flow region itself (Dolling and Murphy

1983). Beresh et al. (2002), using conditional analysis,

showed that the low-frequency motion could be related to

the fullness of the instantaneous velocity profile of the

incoming boundary layer. Yet in the conditional sampling

analyses performed by Thomas et al. (1994), no discern-

able statistical relationship could be found between the

upstream boundary layer and shock wave motion. The

precise mechanisms involved in the low-frequency

dynamics are still therefore not fully understood.

In comparison to the compression ramp interaction, the

latter case of incident shock wave interaction has received

less attention. Studies mapping the mean flow properties as

functions of Mach number and Reynolds number, as well as

the incident shock wave strength and state of the incoming

R. A. Humble (&) � F. Scarano � B. W. van Oudheusden

Faculty of Aerospace Engineering,

Delft University of Technology, Kluyverweg 1,

2629 HS Delft, The Netherlands

e-mail: r.a.humble@tudelft.nl

123

Exp Fluids (2007) 43:173–183

DOI 10.1007/s00348-007-0337-8

boundary layer have been conducted (e.g. Holder et al.

1955; Chapman et al. 1958; Green 1970). The unsteadiness

properties of this type of interaction, however, have been

less well documented. Yet, behaviour similar to the com-

pression ramp case has been found, such as low-frequency

motion of the reflected shock wave when the interaction

involves boundary layer separation (Dupont et al. 2006).

In general, experimental studies of SWTBLIs have been

hampered by the limitations of the experimental techniques

used (Dolling 2001). Whilst hot-wire measurements, wall

pressure measurements and laser Doppler velocimetry have

been indispensable in providing detailed information on the

nature of SWTBLIs, without whole-field quantitative

information, an instantaneous velocity characterization of

the flowfield cannot be made. Furthermore, whilst numer-

ical simulations of these flows have achieved some degree

of success, being able to predict the mean flow properties

reasonably well, the accurate prediction of the associated

turbulence properties still remains problematic (Knight and

Degrez 1998). Recently, however, large eddy simulation

(LES) and direct numerical simulation (DNS) have been

applied to the SWTBLI problem with significant success

(e.g. Garnier and Sagaut 2002; Pirozzoli and Grasso 2006).

Advances in laser and digital imaging technology have

led to the improvement of nonintrusive, planar diagnostic

tools, such as particle image velocimetry (PIV) in partic-

ular. This technique is capable of performing direct

instantaneous velocity flowfield measurements, making it

suitable to investigate large-scale unsteady flow phenom-

ena. Together with the ability to acquire large amounts of

data, this technique offers the opportunity to investigate the

spatial structure of SWTBLIs. From an instantaneous and a

statistical point of view, PIV has historically found wide-

spread application as a standard diagnostic tool in low-

speed incompressible flows (Raffel et al. 1998). Efforts to

extend the technique into the high-speed compressible flow

regime became possible with the introduction of high-en-

ergy short-pulsed lasers, short interframe transfer CCD

cameras, as well as developments in image interrogation

methods (Scarano and Riethmuller 2000). Despite efforts

being hindered by the technical difficulties associated with

optical diagnostics in supersonic wind tunnels, namely,

flow seeding, illumination and imaging, PIV has been ap-

plied to a variety of high-speed flow problems of practical

interest, including SWTBLIs (e.g. Unalmis et al. 2000;

Beresh et al. 2002; Hou et al. 2003). These investigations,

however, have typically considered ramp or blunt-fin

configurations. Comparatively few PIV studies have con-

sidered the impinging shock wave interaction (e.g. Haddad

2005). The need for a better understanding of this type of

flow, as well as the potential of nonintrusive measurement

techniques, provide the impetus for the application of PIV

to this flow problem.

The subject of the present paper is to report on the

application of PIV to the interaction between an incident

shock wave and a turbulent boundary layer. A particle

response assessment is first presented, which establishes

the fidelity of the tracer particles under measurement

conditions. The undisturbed boundary layer is then char-

acterized in detail, in terms of its mean velocity and tur-

bulence properties. Mean and instantaneous whole-field

velocity measurements of the interaction region are ob-

tained, from which inferences about the turbulence prop-

erties are made. These results may be useful for analytical

and computational modelling purposes.

2 Apparatus and experimental technique

2.1 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 Tech-

nology. The facility generates flows in the Mach number

range 0.5–4.2, in a test section of dimensions

280 mm · 270 mm. 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 cor-

rected for by automatic fine adjustment of the choke. The

tunnel operates at unit Reynolds numbers ranging from

30 · 106 to 130 · 106 m–1, enabling a blow-down operat-

ing use of the tunnel of approximately 300 s.

Two types of experiment were conducted in the present

study. First, the undisturbed boundary layer was charac-

terized in detail, followed by an experiment to characterize

the interaction. The boundary layer on the top wall of the

wind tunnel was investigated in both cases. The boundary

layer developed on a smooth surface under nearly adiabatic

flow conditions for a development length of approximately

2 m. Upon entering the measurement domain, the bound-

ary layer thickness was d99 = 20 mm. A thick boundary

layer is advantageous for PIV studies, since it provides an

increase in the scales of the mean and fluctuating flowfield,

enabling them to be better resolved. The experimental

conditions are summarized in Table 1.

The displacement thickness d* and momentum thick-

ness h are the compressible values. The density variation

was deduced from the velocity distribution using the adi-

abatic Crocco-Busemann relation with a constant recovery

factor r = 0.89, with the assumption that the static pressure

in the wall-normal direction remains constant. A 100 mm

long single-sided aluminium wedge was placed at the

centre of the test section to generate the incident shock

wave, providing a flow deflection angle of 8�. The gener-

ator was rigidly mounted on one side of the wind tunnel

174 Exp Fluids (2007) 43:173–183

123

and spanned 96% of the test section. A schematic repre-

sentation of the experimental apparatus is shown in Fig. 1.

2.2 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. Titanium dioxide (TiO2) particles

(Kemira UV-TITAN L830) were adopted with a nominal

crystal size of dp = 50 nm and bulk density of

qb = 200 kg/m3. The effective particle size is approxi-

mately 400 nm (see ‘‘Particle response assessment’’). A

high-pressure cyclone pressurized at 1,000 kPa generated

the seeded stream, which was introduced into the settling

chamber of the wind tunnel through a 2D rake distributor.

The seeding rake spanned 26 · 30 cm2 with six vertical

airfoil-type bars, each with six orifices. Hot-wire ane-

mometry measurements performed in the freestream of the

facility revealed no noticeable difference in the mean

velocity field, and only a 0.2% increase in turbulence

intensity (~1%) as a result of the seeding device. The

seeded flow was illuminated by a Big Sky CFR PIV-200

double-pulsed Nd:Yag laser, with a 200 mJ pulsed energy

and a 7 ns pulse duration at wavelength 532 nm. Tunnel

access for the laser light was provided by a probe inserted

70 cm downstream of the shock generator. The probe

shaped the light beam into a light sheet approximately

1.5 mm thick inside the test section. The laser pulse sep-

aration in the boundary layer and interaction experiments

was 0.6 and 2 ls, respectively, which gave particle dis-

placements of approximately 0.3 and 1 mm, respectively,

in the freestream flow. These correspond to 26 and 11 pixel

displacements, respectively. 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. The sensor was cropped to 1376 · 432, given

the large aspect ratio of the investigated flow region, and at

the same time to achieve an increased recording rate of

10 Hz. A narrow-band-pass 532 nm filter was used to

minimize background ambient light. In the boundary layer

experiment, the camera was rotated 90� to maximize the

spatial resolution. Table 2 summarizes the PIV recording

parameters.

The optical settings result in a particle image diameter

ds for the boundary layer and interaction experiments of

ds = 16 lm (2.4 pixels) and ds = 11 lm (1.7 pixels)

respectively. Data sets of 500 and 1,500 image pairs were

acquired respectively. Both sets of recorded images were

interrogated using the WIDIM algorithm, as described by

Scarano (2002). This method is based upon the deforma-

tion of correlation windows with an iterative multi-grid

scheme, which is particularly suited for highly sheared

flows. Image pairs in the boundary layer and interaction

experiments were interrogated using windows of size

61 · 7 and 21 · 17 pixels respectively, with an overlap

factor of 75%.

2.3 Particle response assessment

The fidelity of the tracer particles was evaluated by con-

sidering their dynamic response when passing through a

steady oblique shock wave (OSW). The OSW generated in

Table 1 Experimental conditions

Parameter Test case

Undisturbed

boundary layer

Interaction

experiment

M¥ 2.05 2.07

U¥ (m/s) 505 518

d99 (mm) 20 20

d* (mm) 3.9 4.4

h (mm) 1.3 1.4

us (m/s) 19.4 19.4

cf 1.6 · 10–3 1.52 · 10–3

P0 (kPa) 226 276

T0 (K) 278 286

Reh 3.96 · 104 4.92 · 104

Fig. 1 Schematic representation of the experimental setup

Table 2 PIV recording parameters

Parameter Test case

Undisturbed

boundary layer

Interaction

experiment

Field of view, W · H (mm2) 5 · 16 129 · 40

Interrogation volume (mm3) 0.7 · 0.08 · 1.5 1.9 · 1.6 · 1.5

Digital resolution (pix./mm) 86 11

Recording distance (cm) z0 = 15 z0 = 60

Recording lens f = 105 mm f = 60 mm

f-number f# = 8 f# = 8

Pulse delay (ls) 0.6 2

Exp Fluids (2007) 43:173–183 175

123

the freestream of the interaction experiment was used for

such an assessment. The PIV measurement returns the

velocity spatial distribution, making it possible to extract a

velocity profile across the OSW. The velocity component

normal to the shock wave was considered for this purpose.

Figure 2 shows the distribution of the mean normal

velocity along with the shock-normal abscissa s.

To assess the spatio-temporal response of the particles,

the profile of the velocity is shown against s in Fig. 3,

where s = 0 denotes the shock wave position. Here �un1 and

�un2 are the upstream and downstream mean velocity,

respectively, normal to the shock wave. Observe an

appreciable distance before the particle velocity down-

stream of the shock wave reaches its reference value. The

effects of a finite spatio-temporal resolution are also evi-

dent, where it can be seen that the velocity begins to de-

crease approximately one-quarter of a window size

upstream of the shock wave as a result of the averaging

effect intrinsic to the PIV interrogation method. The par-

ticle relaxation time sp was obtained with an exponential

curve fit of �un ¼ �un sð Þ and yielded sp = 2.1 ls, corre-

sponding to a frequency response fp = 476 kHz. This value

of sp is consistent with previous OSW particle response

assessments reported by Scarano and van Oudheusden

(2003) using similar particles.

The present particle response behaviour can be com-

pared with a modified Stokes drag law, valid for small

spherical particles. Given the relatively small particle

Mach number and Reynolds number, the following drag

relation to determine sp applies (Melling 1986)

sp ¼ d2p

qb

18lf

1þ 2:7Kndð Þ ð1Þ

where Knd is the Knudsen number based upon dp, and lf is

the fluid viscosity. An expression for the Knudsen number

in terms of the Mach number and Reynolds number is

provided by 1.26�c(MDu/Red) (Schaaf and Chambre 1958),

where c is the ratio of specific heats, taken as c = 1.4 for

air. The Mach number MDu is based upon Du, the maximum

particle slip velocity, which occurs downstream of the

shock wave. This was determined to be MDu = 0.38. The

downstream Reynolds number based upon dp was deter-

mined to be Red � 1. Using Eq. 1, this results in a relax-

ation time sp of less than 1 ls. The discrepancy between

this result and the measured result is ascribed to particle

agglomeration, a phenomenon which introduces an uncer-

tainty on the effective particle size and hence response

characteristics. Inserting the experimentally determined sp

back into Eq. 1, gives an effective particle agglomerate

size of dp � 900 nm, a value not dissimilar to the

dp = 400 nm size found from electron scans of the porous

agglomerates, as reported by Schrijer et al. (2006).

The particle dynamic effects can be further parameter-

ized by the Stokes number St, defined as the ratio between

sp and a time scale of the flow sf. For accurate flow tracking

at the time scale represented by sf it is necessary to meet

the criterion that St << 1. Assuming an outer flow time

scale of d/U¥, then this gives sf = 38 ls. The correspond-

ing Stokes number is therefore St � 0.06, which is of the

same order as that reported by Urban and Mungal (2001) in

their high-speed turbulent shear layer experiments.

3 Results and discussion

3.1 Undisturbed boundary layer properties

The van Driest effective velocity concept is used to give a

suitable description of the boundary layer velocity profileFig. 2 Distribution of �un=�un1 across the OSW. Shock-normal

abscissa s is shown in yellow

Fig. 3 Particle response assessment across the OSW

176 Exp Fluids (2007) 43:173–183

123

within the log-law region (White 1991). The nondimen-

sional velocity u+ and length scale y+ normalized with the

friction velocity us are defined as

uþ ¼ �u

us; yþ ¼ usy

vw; us ¼

ffiffiffiffiffiffi

sw

qw

r

ð2Þ

where v is the kinematic viscosity, s is the shear stress, q is

the fluid density and the subscript w denotes the wall

condition. The mean experimental velocity profile �u yð Þdetermined from the boundary layer experiment is

transformed into an effective velocity ueq using the van

Driest compressibility transformation, given for an

adiabatic flow by

ueq ¼Ue

asin�1 a

�u

Ue

� �

¼ us1

jln yþ þ B

� �

where a ¼ 1� Te

Taw

ð3Þ

Here T is the temperature with constants j = 0.41 and

B = 5.0. The subscripts e and aw denote the boundary layer

edge and adiabatic wall conditions respectively. The right-

hand side of Eq. 3 is the ordinary incompressible form of

the law-of-the-wall; the left-hand side is the effective

velocity. The corresponding law-of-the-wall fit for the

present experimental data is shown in Fig. 4. The statistical

uncertainty associated with the mean velocity due to the

limited number of realizations is <1%U¥. The experi-

mental effective velocity profile coincides with the theo-

retical profile when a friction velocity of us = 19.4 m/s is

assumed. The corresponding skin friction coefficient

determined from cf = 2us2qw/qeUe

2 gives cf = 1.6 · 10–3,

which agrees to within 10% of the van Driest II skin

friction formula for a flat plate.

Within the logarithmic region, there is excellent agree-

ment between the experimental data and the van Driest

effective velocity. Spalding (1961) has provided a single

composite formula for the entire wall-related region given

by

yþ ¼ uþ þ e�jB ejuþ � 1� juþ � 1

2juþð Þ2 � 1

6juþð Þ3

� �

ð4Þ

A departure of the experimental data from the single

composite formula can be observed for approximately

y+ < 30. Here, the lower edge of the interrogation window

becomes influenced by the presence of the wall. The

closest point to the wall, however, lies within the viscous

sublayer (y+ < 5). To the author’s knowledge, PIV mea-

surements within the viscous sublayer of a supersonic

boundary layer have never been reported. A wake com-

ponent, characteristic for turbulent boundary layers, can

also be identified. The Coles wake parameter G, which is

used to help describe the deviation of the outer layer profile

from the law-of-the-wall was determined to be G = 0.45,

which is in reasonable agreement with the value of 0.55

commonly admitted for zero-pressure-gradient incom-

pressible boundary layers when Reh > 5,000 (Cebeci and

Cousteix 1999). It should be remarked, that G varies with

boundary layer history and somewhat with Mach number.

The variation of the streamwise <u¢> and vertical <v¢>turbulence intensity, as well as the kinematic Reynolds

shear stress u0v0 are shown in Fig. 5, where <�> denotes the

root-mean-square quantity. The statistical uncertainty due

to the limited number of realizations for the turbulence

intensity and kinematic Reynolds shear stress is approxi-

mately 3 and <10% respectively. Symbols are drawn at the

Fig. 4 Experimental comparison with the law-of-the-wall Fig. 5 Undisturbed boundary layer turbulence properties

Exp Fluids (2007) 43:173–183 177

123

first data point and subsequently at data points that are at

least 3% of the figure height distance from the previously

plotted data point. The compressible momentum thickness

is chosen to scale the wall-normal coordinate because it can

be determined more accurately than the boundary layer

thickness. The variation of <u¢> compares favourably with

turbulence measurements made within a variety of super-

sonic boundary layers (e.g. Petrie et al. 1986; Johnson

1974), as well as those obtained by means of PIV (Hou

et al. 2002). Note that the turbulence properties do not

attain their freestream values because the complete

boundary layer is not resolved.

3.2 Mean flow properties of the interaction

To first give a general description of the interaction, the

mean flow topology is shown in Fig. 6. Mean velocity

streamlines are displayed with mean vertical velocity

contours in order to qualitatively illustrate the important

flow features. The origin of the reference coordinate sys-

tem, in these and subsequent results, 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. Spatial

coordinates are normalized with the undisturbed boundary

layer thickness. The streamlines verify a uniform outer

flow upstream, and illustrate the distortion of the flowfield

as a result of the interaction process. Regions of flow

compression typically appear as densely spaced vertical

velocity contours, whereas sparsely spaced vertical veloc-

ity contours typically 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. It reflects from the sonic line as an

expansion fan, as labelled in Fig. 6. Observe the com-

pression waves generated within the incoming boundary

layer approximately two boundary layer thicknesses up-

stream 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 undergoes a recovery process farther down-

stream. Subsonic fluid close to the wall, which has passed

through the interaction begins to contract, causing the outer

fluid to move back towards the wall. Although difficult to

discern, a gradual recompression process takes place far-

ther downstream, as fluid is slowly turned back towards the

streamwise direction.

An instantaneous PIV recording from the interaction

experiment is depicted in Fig. 7. It shows some nonuniform

seeding concentration. The incident and reflected shock

waves can be visualized, whereas the boundary layer is

highlighted by a comparatively lower seeding level. Tur-

bulent activity within the downstream boundary layer can

also be observed, as well as the intermittent nature of the

boundary layer edge. Laser light reflections were mini-

mized during the experiments by illuminating almost tan-

gent to the wall.

The mean flow behaviour is described by the average

streamwise velocity field in Fig. 8. Velocity vectors are

under-sampled (showing 1 in 22 in the streamwise direc-

tion for clarity). The incident and reflected shock waves are

visible as a sharp flow deceleration and change of direction

for the first, whereas the reflected shock wave exhibits a

somewhat smoother spatial variation of the velocity due to

its unsteady nature and the averaging effect. From the

mean velocity vectors, no reversed flow can be detected,

although it appears that the flow is close to separation.

Downstream of the interaction, the distorted boundary

layer appears to increase in thickness and develops with a

relatively low rate of recovery.

3.3 Two-dimensionality of the interaction

To examine the effects of spanwise nonuniformities that

are often present in nominally two-dimensional flows, a

multi-planar assessment of the interaction region was car-

ried out within the range –2.5 £ z/d £ 2.5, in increments of

z/d = 0.5 (i.e. 9 planes). A total of 50 images were acquired

at each spanwise location. Recording and interrogation

settings were the same as those used in the interaction

experiment. Figure 9 shows three isosurfaces of mean

Fig. 6 Mean flow topology. Mean velocity streamlines are shown

along with mean vertical velocity contours Fig. 7 PIV recording of the interaction

178 Exp Fluids (2007) 43:173–183

123

Mach numbers 0.5, 1.0, and 1.5, determined using the

adiabatic flow assumption. Also shown are under-sampled

velocity vectors (showing 1 in 30 in the streamwise

direction for clarity). It can be seen that a relatively small

change in Mach number occurs within the spanwise region

considered. The rapid dilation of the subsonic layer is

evident, as it responds to the adverse pressure gradient

imposed by the incident shock wave. The outermost

isosurface of Mach 1.5 shows the displacement of the outer

layer of the incoming boundary layer, as well as the

reflected shock wave pattern farther downstream.

Figure 10 shows a rendered representation of the mean

flow organization within the interaction. Flooded contours

of streamwise velocity are shown, illustrating the low-

speed velocity region. Mean stream tubes are also shown

within the lower part of the boundary layer. The variation

of the streamwise velocity around these tubes illustrates

that slight three-dimensional effects exist. However, they

seem characteristic of the fluid dynamic processes present

and not due to the sidewall boundary layers. (Note that the

test section width–boundary layer thickness aspect ratio is

14:1.) The measured flow properties show an appreciable

deviation from the centre-line values at distances from the

centre-line greater than 30% of the test section width. This

behaviour is ascribed to the lower measurement confidence

level due to the finite size of the incoming seeded flow.

3.4 Instantaneous flow properties of the interaction

The instantaneous velocity fields reveal several interesting

features associated with the unsteady behaviour of the

interaction. Figure 11 illustrates two fields of the instan-

taneous streamwise velocity, which typify the dynamical

events that take place. The time that elapses between

consecutive recordings (10 Hz framing rate) is significantly

greater than any characteristic flow time scale, leading to

the measurement of uncorrelated velocity fields. It can be

Fig. 8 Mean streamwise velocity distribution �u=U1: Velocity

vectors show 1 in 22 in the streamwise direction

Fig. 9 Spanwise survey of interaction. Mean Mach number isosur-

faces of 0.5, 1.0 and 1.5 are shown along with velocity vectors

showing 1 in 30 in the streamwise direction

Fig. 10 Mean flow organization of the interaction. Mean stream

tubes are shown flooded with mean streamwise velocity

Fig. 11 Uncorrelated instantaneous streamwise velocity distributions

u/U¥

Exp Fluids (2007) 43:173–183 179

123

seen that the outer freestream flow remains steady and

there is no appreciable motion of the incident shock wave.

The global structure of the interaction region, however,

varies considerably in time. A thickening of the upstream

approaching flow can be observed. In Fig. 11b, fluid close

to the wall is redirected upstream, leading to the formation

of a separated flow region. This configuration forces fluid

to detach and move away from the wall. The separation

bubble length is found to vary within the range between 0

and 2d, with the velocity in the reversed flow region often

attaining a value 10% of U¥. However, recall that the

average velocity field shows that the boundary layer re-

mains attached, indicating that reverse flow occurs only

instantaneously.

After inspection of numerous realizations (not shown

here for brevity), the interaction can be characterized, on

an instantaneous basis, as containing irregularly shaped

layers of relatively uniform streamwise velocity, most

readily observed in the velocity vectors within the rede-

veloping boundary layer. The term layer is used here to

emphasize that whilst they are defined instantaneously,

they typically extend across the measurement domain.

The interaction contains a high-velocity outer layer (typi-

cally u/U¥ > 0.5), and a low-velocity inner layer (typically

u/U¥ < 0.5). They therefore loosely correspond to the

supersonic and subsonic parts of the boundary layer

respectively. The outer layer comprises most of the

incoming boundary layer and includes fluid that is lifted

above the interior fluid near the wall. It retains most of its

streamwise velocity throughout the interaction. In contrast,

a noticeable reduction in streamwise velocity occurs within

the inner layer. This layer contains values of the same order

as found within the near-wall region of the incoming

boundary layer. It grows rapidly as it enters the first part of

the interaction, often reaching its maximum thickness when

it intersects with the incident shock wave.

These layers are typically separated by a thin region of

relatively high shear. The interface is therefore a region of

relatively large spanwise vorticity. Observe how the outer

fluid often penetrates deep into the boundary layer in

Fig. 11b. The interface therefore has an irregular and

intermittent nature, which is a particularly dominant fea-

ture of the redeveloping boundary layer. The supposition of

smaller scales is evident by the jagged edges of the inter-

face between the high- and low-speed boundaries. It is

interesting to observe, that whilst the subsequent reat-

tachment process takes place within a relatively short dis-

tance, the overall velocity deficit within the inner layer

persists much farther downstream. This behaviour is

substantiated by the turbulence properties presented in

‘‘Turbulence flow properties of the interaction’’.

Furthermore, by inspection of Fig. 11, and other real-

izations, it can be inferred that when the reversed flow

region expands, the reflected shock wave is often displaced

away from the wall; and when it contracts, the reflected

shock wave is brought closer to the wall. This mechanism

has also been shown by Erengil and Dolling (1993) to be

associated with the large-scale motion of the shock wave,

upon examining a hypersonic two-dimensional compres-

sion ramp interaction. No clear quantitative relationship

could be formulated, however, based upon the present data.

Overall, 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.

3.5 Turbulence flow properties of the interaction

Figure 12a and b show the spatial distributions of <u¢> and

<v¢> respectively. These results reflect the mixing that

takes place within the interaction and the distributed nature

of the turbulence. Note that <v¢> is scaled three times as

sensitive as <u¢>. A substantial increase in <u¢> occurs

throughout the interaction, initiating itself within the re-

flected shock foot region, and reaching a maximum value

of approximately 0.2U¥ beneath the incident shock wave.

These results are comparable to the laser velocimetry

measurements of Rose and Johnson (1975), Moderass and

Johnson (1976) and Meyer et al. (1997), as well as the LES

computations of Garnier and Sagaut (2002), which have all

considered an incident shock wave interacting with a flat

plate turbulent boundary layer. Maximum levels of <u¢>are over 300% greater than maximum levels of <v¢>,

Fig. 12 Turbulence intensity distributions, a streamwise component

<u¢>/U¥, b vertical component 3<v¢>/U¥

180 Exp Fluids (2007) 43:173–183

123

indicating that appreciable turbulence anisotropy is present.

Since the upstream flow is often lifted and turns around the

bubble, whereas in other instances it remains fully at-

tached, it can be inferred that the locus of large <u¢> within

the first part of the interaction is a result of the averaging of

this intermittently separated flow. Farther downstream,

<u¢> can be seen to rapidly decay. At the downstream edge

of the measurement domain, the familiar near-wall peak of

<u¢> is now just beginning to reappear, indicating that the

boundary layer is recovering.

In the case of <v¢>, significant fluctuations can be ob-

served across the reflected shock wave, highlighting its

unsteady behaviour. The incident shock wave appears as a

relatively steady feature, except for the part that penetrates

the boundary layer. Within the redeveloping boundary

layer, elevated levels of <v¢> are broadly distributed across

the lower half of the boundary layer. Whilst <u¢> rapidly

decreases in this region, it can be seen that the elevated

levels of <v¢> persist downstream. This behaviour is

associated with the redistribution of turbulent kinetic en-

ergy, mainly through the pressure–strain correlation terms

(Ardonceau et al. 1980). The different turbulence evolu-

tions of <u¢> and <v¢> can be readily understood when one

considers the production term associated with each com-

ponent. Following along the lines of turbulence studies

concerning transonic SWTBLIs (Delery and Marvin 1986),

consider first the production term of the streamwise com-

ponent transport equation, written for an incompressible

flow for simplicity as

Pu ¼ �2u0v0o�u

oy� 2u02

o�u

oxð5Þ

It should be noted that there is an appreciable variation of

mean density across the undisturbed boundary layer in the

present study ð�q=�qe � 0:57 at Me ¼ 2:1Þ and so only a

general discussion will be given. In the first part of the

interaction, the strain rate o�u=oy within the boundary layer

is typically large. Furthermore, it is generally accepted that

u0v0\0 when o�u=oy > 0: (The reader can confirm this by

looking ahead at Fig. 13.) With o�u=ox 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 large

positive terms. This explains its substantial increase in the

first part of the interaction. Consider now the production

mechanism for the vertical component given by

Pv ¼ �2u0v0o�v

ox� 2v02

o�v

oy� �2u0v0

o�v

oxþ 2v02

o�u

oxð6Þ

The reader will notice that the production mechanism for

the vertical component contains terms, which are less

important than those occurring in the streamwise compo-

nent transport equation. Here, o�v=oy can be replaced with

�o�u=ox, 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

shock waves. If o�v=ox is considered small throughout the

interaction, then with o�u=ox being typically negative, it can

be deduced that only the second term in Eq. 6 is important

(and actually tends to decrease the production of the ver-

tical component in the first part of the interaction behind

the reflected shock foot as shown). Farther downstream, the

flow begins to accelerate, and o�u=ox becomes positive.

This leads to the relatively slow production of the vertical

turbulence intensity farther downstream. It is now clear that

the typical boundary layer assumption of a sufficiently

small wall-normal pressure gradient (¶p/¶y � 0) may no

longer be valid in the interaction, since there is an appre-

ciable variation of the vertical velocity fluctuations normal

to the wall.

The increased level of fluctuations along the incident

and reflected shock waves in the freestream (approximately

4 and 7%U¥ respectively) is typically encountered in these

experimental conditions and is ascribed to the combined

effect of decreased measurement precision and to small

fluctuations of the shock wave position. The reflected

shock wave exhibits a relatively higher level of velocity

fluctuations, which is ascribed to its unsteady motion.

Interestingly, an increased level of <u¢> can be observed at

the tip of the incident shock wave, indicating that it

undergoes an increased motion in this region. This con-

firms the observations made in the DNS of an incident

SWTBLI performed by Pirozzoli and Grasso (2006), where

it was observed that coherent structures propagate in this

region leading to an increased oscillatory motion at the

shock wave’s tip. A weak feature immediately upstream of

the incident shock wave (roughly parallel to it) can also be

Fig. 13 Kinematic Reynolds shear stress distribution u0v0=U21 � 103

Exp Fluids (2007) 43:173–183 181

123

observed. This is due to optical aberration effects intro-

duced by the inhomogeneous index of refraction field of

this compressible flow (Elsinga et al. 2005).

Consider now the Reynolds shear stress distribution.

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 tur-

bulence closure models, since theoretical efforts are gen-

erally hampered by the difficulties of representing the

turbulence terms in the time-averaged equations. For

compressible flows, the Reynolds shear stress is conven-

tionally expressed by qu0v0; when the density fluctuations

are ignored. In this paper, the kinematic term u0v0=U21 is

regarded as being representative of the Reynolds shear

stress. The spatial distribution of kinematic Reynolds shear

stress u0v0=U21 is shown in Fig. 13.

Initially moderate levels of �u0v0 are present within the

undisturbed boundary layer. A substantial increase in

magnitude occurs within the incident and reflected shock

foot regions. This increase is expected, since it is known

that supersonic flow, which undergoes a compression is

associated with turbulence augmentation. There appears to

be a systematic change of kinematic Reynolds shear stress

farther downstream. The redeveloping boundary layer can

be characterized by the presence of a distinct streamwise-

oriented region of relatively large kinematic Reynolds

shear stress magnitude in its lower part. Note the over-

whelmingly negative values in this region, indicative of

slower moving (u¢ < 0), upward-oriented (v¢ > 0) fluid,

and/or faster moving (u¢ > 0), downward-oriented (v¢ < 0)

fluid, relative to the mean flow. As noted by Ardonceau

(1983), who studied the structure of turbulence in SWT-

BLIs, these large kinematic Reynolds shear stresses imply

the existence of large-scale eddies, consistent with the

instantaneous results of the present study, and also indi-

cated by the recovery of the boundary layer velocity profile

with downstream development. The recovery of the tur-

bulence properties, however, appears to be a gradual pro-

cess with the present measurement domain insufficient to

observe the boundary layer returning to its initial equilib-

rium conditions.

4 Conclusions

This paper has reported on the application of PIV to the

interaction between an incident planar shock wave and a

turbulent boundary layer. A particle response assessment

established that the fidelity of the tracer particles was

consistent with similar studies. The experimentally inferred

porous agglomerate size agreed with the electron scans

reported in literature. The mean velocity profile and de-

duced skin friction coefficient of the undisturbed boundary

layer showed good agreement with theory. The interaction

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. The global structure of the

interaction region varied considerably in time. Patches of

reversed flow were frequently observed. Although signifi-

cant reversed flow was measured instantaneously, on

average, no reversed flow was observed. The interaction

could be characterized instantaneously as exhibiting a

multi-layered structure, namely, a high-velocity outer re-

gion and a low-velocity inner region. These two layers

were separated by an interface containing relatively high

shear. The mean flow is therefore a somewhat simplified

representation of the interaction.

The streamwise and vertical turbulence components

evolved differently throughout the interaction. The turbulent

fluctuations were found to be highly anisotropic, with the

streamwise component dominating. The highest turbulence

intensity occurred in the region beneath the impingement of

the incident shock wave. An increased level of <u¢> was

observed at the tip of the incident shock wave, indicating that

it undergoes an increased motion in this region. A distinct

streamwise-oriented region of relatively large kinematic

Reynolds shear stress magnitude appeared within the lower

half of the redeveloping boundary layer. Boundary layer

recovery was observed to initiate downstream of the inter-

action. The recovery towards the initial equilibrium condi-

tions, however, appeared to be a gradual process.

Acknowledgments This work is supported by the Dutch Technol-

ogy Foundation STW under the VIDI-Innovation Impulse program,

grant DLR.6198.

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