A wealth of data exists for incompressible rough-wall flows1-3
. Fully rough flows are defined such that the
frictional loss is independent of the viscosity1. This occurs for ks
+>70, where ks
+ is the equivalent sand-grain
roughness3. Equivalent sand-grain roughness can be calculated for any rough surface, in order to attempt to relate
the topology to a densely packed sand-grain topology and estimate the degree of downward shift in the velocity
profile. Schlichting formulated an empirical relation to calculate the equivalent sand-grain roughness for a given
roughness pattern, but this relation has proven inadequate for certain geometries2.
In response to the difficulty of using ks+ as the sole description for a given roughness geometry, Perry
2 defined
two canonical roughness topologies: “d-type” and “k-type”. Roughness patterns exhibiting “d-type” behavior
generally have a roughness spacing of w/d < 3, meaning that the roughness spacing is less than three times the
element length. A densely packed topology will trap vortices in the cavities, “shielding” the elements from the flow.
The equivalent sand-grain roughness of a “d-type” pattern is proportional to the boundary layer height. A “k-type”
topology will have a roughness spacing of w/d > 3, allowing any vortices formed in the cavity to be shed
downstream. This exposes the elements to the bulk of the flow; the equivalent sand-grain roughness is proportional
to the roughness height.
For high-speed flows, Morkovin’s hypothesis and van Driest II scaling have been proposed to relate mean data
between supersonic and incompressible rough-wall flows4,5
. For turbulence statistics, Raupach et al. has modified
Townsend’s similarity rule to account for roughness6,7
. The rough-wall similarity states that turbulent motions
outside the roughness sublayer are independent of roughness topology, except for the influence upon friction
velocity and boundary layer thickness. By extension, only the turbulent motions within the inner region should be
affected by the roughness elements. Data by Ekoto et al8 and Latin & Bowersox
9 have shown that turbulent motions
outside the roughness sublayer can be affected by certain roughness topologies. Jimenez10
has theorized that
Townsend’s rough-wall similarity is only applicable when δ/k > 50. If k is larger than 2% of the boundary layer
thickness, the flow “sees” the roughness elements as obstructions, not surface roughness.
The degree of complexity inherent within high-speed rough-wall turbulent flows requires further extensive
testing. The available data is primarily for mean flow quantities, and exists only for very few test conditions, most of
which are at relatively low supersonic Mach numbers (< 3.0). More turbulence data is needed for a range of δ/k, in
order to further test existing theories. As roughness research matures, these data sets will be needed to validate
predictive codes for high-speed rough-wall flows. The primary purpose of the present Mach 5.0 study is to quantify
the Mach number sensitivity of the mechanical non-equilibrium effects on the mean and turbulent flow properties
described in the Ekoto et al Mach 3.0 study.8
The momentum thickness Reynolds numbers were similar between the
two studies at 40,000.
II. Facilities
All experiments were performed in a supersonic blow-down tunnel (Fig. 1) located in the National
Aerothermochemistry Laboratory (NAL) housed at Texas A&M University. The nozzle was machined from
stainless steel, with a throat height of 0.305cm and an exit measuring 7.62 cm x 7.62 cm. This produced a flow with
a nominal Mach number of 4.89. The test section bolted directly to the nozzle exit and extended 71.12 cm
downstream. Optical access was provided 15.9 cm and 29.8 cm downstream from the nozzle exit (see Fig. 2). The
coordinate system is arranged so that x is measured in the downstream direction, with x = 0 at the nozzle exit.
Coordinates y and z are measured vertically from the wall and laterally from the centerline, respectively.
Fig. 1 Supersonic blow-down wind tunnel
Fig. 2 Mach 5 nozzle and test section
Total temperature was measured using an Omega JQSS thermocouple amplified through an OMNI AMP-IV
amplifier. An Omega PX303 0-3048 kPa pressure transducer (± 0.25% full-scale accuracy) was attached to a Pitot
probe in the settling chamber to monitor the total pressure. Static pressure within the test section was monitored
using an MKS Series 902 0-101 kPa pressure transducer (± 1% full-scale accuracy). Signals from the thermocouple
and pressure transducers were transmitted to a National Instruments SC-2345 signal conditioner block before being
collected by a National Instruments 6036E data acquisition board. Freestream axial and transverse turbulence
intensities were both 1.5%. The total temperature was set to 370K to prevent liquefaction of air in the test section.
Starting conditions required the total pressure to be set at 2200 kPa (320 psia). These settings allowed for a run time
of greater than 30 minutes. The resulting test section conditions are summarized in Table 1.
Table 1 Tunnel test conditions
Mach number Static pressure (Pa)
Static temperature (K)
Static density (kg/m^3) Reynolds number
(Re/m)
4.89 4825.4 62.7 0.27 52.2 x 10^6
The experimental models were machined from acrylic, and designed by Ekoto et al8 so that each model would
serve as the test section floor. The top surfaces of the roughness elements were aligned with the floor of the nozzle.
A hydraulically smooth model was created for baseline comparisons; the estimated roughness Reynolds number k+
was 0.14, Ekoto et al.11
The diamond roughness model was designed to create localized mechanical non-
equilibrium; Figure 3 shows the roughness topology.
The diamond pattern was designed as periodic rather than isolated elements, which allows for comparisons with
the wealth of data available for “sand grain roughness”1-3
. These diamond elements measure 1.59 mm wide by 9.0
mm long, with a half-angle of 10.0 degrees. The roughness height k is 0.80 mm. Machining was performed using a
1.59 mm (1/16 in.) diameter ball end mill. The swept nature of the elements allows for any vortices formed in the
Nozzle
Test Section
Flow direction
cavities to be convected downstream, exposing the elements to the supersonic flow. This mechanism produces a “k-
type” roughness behavior.
Fig. 3 Roughness topology11
III. Experimental Procedures
The following section describes the experimental set-up used in collecting data. Only non-intrusive optical
methods were employed, to minimize disturbing the flowfield. These methods include schlieren photography and
particle image velocimetry (PIV).
A. Schlieren Photography
Schlieren photography was performed using two different light sources: spark-source and continuous-source.
The continuous-source was necessary to perform color schlieren, while the spark-source was needed to resolve
turbulent structures. For both methods, a Z-type configuration was used. The angle between the light source and
collimated beam was less than 15 degrees, to minimize astigmatism; this angle was matched for both mirrors,
negating any coma errors12
. The mirrors were 6-inch diameter first-surface spherical concave mirrors with a 36-inch
focal length and a 1/10-wave surface accuracy. The cutoff filter was positioned horizontally with the continuous-
source schlieren to measure wall-normal gradients. For spark-source schlieren, data were collected for both a
horizontal and vertical cutoff filter.
The continuous-source configuration used a 50 W incandescent bulb which was focused onto a horizontal
aperture, producing a 0.8 mm-thick horizontal line source. The cutoff used was a three-color filter shown in Fig. 4.
Undisturbed flow features were imaged in green, and density gradients appeared as red or blue. A Nikon D5000
SLR digital camera was used to collect the images. The exposure time for the camera was 2.5 ms, which was
sufficient to resolve steady-state structures such as shocks and expansions, but turbulent structures remained blurry.
The spark-source configuration utilized a laser-induced spark as the light source. A Spectra-Physics Lab 150-10
pulsed laser was used to initiate the spark. The laser emitted a 532 nm beam at 10 Hz with a pulse width of 5 ns. The
maximum energy of the beam was measured as 360 mJ/pulse. A 6-inch focal length lens focused the laser beam into
a gas calibration cell (see Fig. 5). The calibration cell was continuously purged with argon gas and kept at a pressure
of 280 Torr. Argon has a lower ionization energy than nitrogen, increasing the intensity and stability of the spark13
.
The spark was estimated to have a duration of less than 500 ns. This short duration allowed for turbulent structures
0.8 mm
1.6 mm
1.6 mm
Flow
9.0 mm
Top View
Side View
0.8 mm
1.6 mm
1.6 mm
Flow
9.0 mm
Top View
Side View
to be imaged without blurring. A 60 mm Nikon lens focused the spark onto a 0.75 mm diameter pinhole, providing
a point source. A Cooke PCO 1600 CCD camera recorded the images with an exposure time of 1 µs. Camware
v2.19 collected the image data and controlled the exposure time. Because the Cooke camera is only capable of
recording black-and-white images, a razor-blade cutoff was used.
Fig. 4 Filter for color schlieren
Fig. 5 Schlieren spark-source gas calibration cell
B. Particle Image Velocimetry
Particle image velocimetry (PIV) was performed to measure the 2-D mean and fluctuating velocity components
of the flowfield. The laser used to illuminate the particles was a dual-head, dual-aperture New Wave Solo 120 PIV
laser. The maximum energy is 120 mJ/pulse, with a 5ns pulse width and 15Hz repetition rate. A -25.4 mm focal
length cylindrical lens formed a 0.5 mm-thick sheet at the tunnel centerline (z = 0). The beam was trimmed using a
pair of razor blades positioned above the test section. A Cooke PCO 1600 interline transfer CCD camera recorded
the image pairs. A Quantum Composer model 9618 pulse generator triggered both the laser and camera with Δt =
500 ns. Camware v2.19 recorded the images from the camera.
Seeding was introduced upstream of the nozzle, through a strut level with the tunnel floor. Two types of seeding
apparatus were tested: a liquid seeder using dioctyl phthalate (DOP) and a cyclonic seeder using titanium dioxide
(TiO2). The liquid seeder is a TSI 9306 Six Jet Atomizer, utilizing six Laskin nozzles to produce liquid particles
with a nominal diameter of 400 µm. The cyclonic seeder is a 4” x 12” Sch. 40 pipe, filled to 10% capacity with TiO2
(see Fig. 6). The manufacturer’s quoted nominal particle size of the TiO2 is 50µm. Supply air enters the TiO2 seeder
from the top and turns sharply towards the side wall. This forms the centrifugal motion that separates the lighter
particles, which exit through an outlet at the top center.
Processing of the image pairs was performed using ISSI’s dPIV software package15
. dPIV performed cross-
correlations between the images in each pair with successive interrogation windows of 256 x 256, 128 x 128, 64 x
64, and 32 x 32 pixels, each with a 50% overlap. The resulting output from dPIV produced a vector field for each
image pair. For the smooth wall data, the vectors were averaged in the streamwise direction to produce a single
profile. This was not performed on the diamond roughness, due to streamwise variations in the near-wall velocity.
Post-processing of the vector fields was performed using an in-house code to ensemble average each of the data sets.
Fig. 6 Cyclonic seeder for TiO2
IV. Results and Discussion
Results are presented for each of the experimental techniques employed. Non-intrusive techniques were used to
minimize any impact upon the flow field.
A. Schlieren Photography
Schlieren data were collected for the smooth and rough models for both spark-source and continuous-source
modes. The spark-source images were collected using both vertical and horizontal cutoff filters. Continuous-source
images were collected only with a horizontal cutoff.
The continuous-source images utilized a color filter to produce a color mapping of the density gradients in the
wall-normal direction (see Fig. 7). The diamond roughness schlieren in Fig. 7a shows strong gradients emanating
from the roughness elements, corresponding to shocks and expansions fans. These flow features were not confined
to the roughness sublayer, but penetrated into the outer layer of the boundary layer. Estimation of the boundary layer
height for the diamond roughness was difficult due to the presence of these non-isentropic features. Conversely, the
smooth wall schlieren in Fig. 7b showed a clear delineation between the boundary layer and freestream.
The increased boundary layer thickness over the diamond roughness is consistent with theory1. However, the
presence of roughness-induced shocks and expansions throughout the boundary layer indicates that the roughness
may have affected the turbulence quantities outside the inner layer,8,11
and therefore violated Townsend’s rough-wall
similarity6,7
. Detailed turbulence measurements are required to clarify this observation.
10 mm
a) Diamond roughness b) Smooth wall
Fig. 7 Continuous-source schlieren
The spark-source schlieren was capable of capturing the turbulent motions of the flow, due to the short duration
of the light source (< 500 ns). Images captured using a horizontal knife-edge cutoff show a strong gradient in the
wall-normal direction, for both smooth and rough walls. While these instantaneous images show unsteadiness in the
flow due to turbulence, most of the structures are hidden by the large wall-normal gradient (Fig. 8).
The images acquired while using a vertical knife-edge cutoff allow for direct imaging of the turbulent structures
in the boundary layer, due to the insensitivity to the wall-normal gradient (Fig. 9). For the smooth model, the relative
size of the structures is seen to decrease as the flow approaches the wall, as expected. The diamond model does not
show this trend as readily. Any turbulent structures are masked by the strong non-isentropic features produced by
the diamond roughness. The authors predict that these shocks and expansions will be the dominant features of the
diamond roughness flow.
B. Particle Image Velocimetry
The PIV data presented in this paper include both smooth-wall and rough-wall data. All smooth-wall PIV data
presented herein were collected and analyzed by Nathan Tichenor, using 3000 image pairs to form a statistically
converged average. This smooth-wall data is used as a baseline comparison for the rough-wall data collected in this
study. The rough-wall data is to be considered preliminary, due to the low sample size that was acquired.
Initial PIV data was collected over the diamond roughness using a liquid seeder, filled with DOP. Seeding
density in the freestream was sufficient to cross-correlate the images into vector fields. However, the seeding density
dropped dramatically near the wall. This variation is expected, as the calculated density ratio ρ/ρw is approximately
6:1. Increasing the output of the seeder resulted in a higher seed density at the wall, but with increased reflections.
The majority of reflections encountered while using the liquid seeder were due to seeding accumulation at the
wall. Seed particles would stick to the model, and flow downstream through the channels between the roughness
elements. This flowing “oil slick” reflected the laser sheet, forming a large reflection at y/δ < 0.2 (see Fig. 10).
Increasing the seeder output resulted in a larger reflection near the wall, occluding any additional seed particles that
were introduced. The authors concluded that liquid particles were not suitable for a rough-wall flow at high Mach
numbers.
After abandoning liquid particles, seeding was attempted using TiO2. The solid particles did not stick to the
model as DOP did, resulting in lower reflections near the wall (Fig. 10). The seeding density is lower in the
freestream, but still sufficiently high to cross-correlate into velocity vectors. Near the wall, the seeding density is
slightly higher than with DOP. Due to the lower reflections, more particles are captured by dPIV, resulting in more
a) Diamond roughness a) Diamond roughness
b) Smooth wall b) Smooth wall
Fig. 8 Spark-source schlieren, horizontal
cutoff
Fig. 9 Spark-source schlieren, vertical cutoff
velocity vectors. However, increasing the seeder output further was not possible due to mass-flow limitations on the
seeder. At current seeding levels, approximately 40% of the acquired images result in usable velocity fields.
Due to the above-mentioned seeding difficulties, only 140 velocity fields were available to be ensemble
averaged. Despite the low sample size, the data set was obtained at a sufficiently high-resolution of 82.7 pixels/mm,
which places the first velocity vector 0.2 mm above the wall. The resulting velocity map can be seen in Fig. 11.
From the schlieren images, the authors expect to see a streamwise variation in the velocity due to the periodic
shocks and expansions produced by the roughness elements. Some variation can be seen near the wall in Fig. 11, but
it is unknown at this point whether this is due to flow features or increased reflections at the leading edges of the
elements.
a) Seeding with DOP b) Seeding with TiO2
Fig. 10 Sample images using liquid and solid seeding
Fig. 11 Mean streamwise velocity over
diamond roughness
The streamwise variation seen in Fig. 11 prevented the authors from conclusively averaging the data over the
entire image to form a 1-D profile. Instead, three separate profiles were performed to compare the velocity variations
near the wall. Along with a profile formed across the entire image, profiles were formed centered over the element
crests and over the element troughs. Figure 12 shows that the velocity profiles over both the element crests and the
entire image agree reasonably well near the wall. Some variation is seen for the profile centered over the element
intersections. This may be due to increased reflections, or the presence of a shock wave emanating from the leading
edge of each roughness element, as seen in the schlieren images (Fig. 7).
Comparing the rough-wall profiles to the smooth-wall data shows a clear effect near the wall. As expected, the
roughness elements cause a velocity defect at the wall; this defect diminishes up to y/δ ≈ 0.7. Above this level, both
the smooth- and rough-wall data collapse onto each other. From the given velocity profiles, the authors calculate
Reθ ≈ 46,000. The estimated boundary layer thickness for the smooth wall is 8.57 mm, based up 99.5% of Ue. The
estimation of boundary layer thickness for the rough wall was more difficult due to variations in the velocity profile;
the thickness was estimated at 9.47 < δ < 10.0 mm.
V. Future Work and Conclusions
Periodic surface roughness was investigated using diamond roughness. Experimental tests were performed in a
high-speed (Mach 5), high Reynolds number (Re/m = 52x106) wind tunnel. The data were collected using schlieren
photography and particle image velocimetry. Preliminary data show that the diamond elements produce strong
attached shocks and expansion waves that induce cyclical variations in the near-wall velocity profile. These
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0.00 0.20 0.40 0.60 0.80 1.00 1.20
y/δ
U/Ue
Element trough
Element crest
Full profile
Smooth wall
Fig. 12 Velocity profile over diamond roughness
variations center around a near-wall velocity that is approximately 30% lower than the smooth-wall case, measured
at y = 0.2 mm. Tests showed that liquid particles are not suitable for a rough-wall flow at high Mach numbers.
Unfortunately, due to mass-flow limitations in the TiO2 seeder, an extensive set of PIV data was not possible.
Future work will focus upon improving the seeder capacity for PIV, in order to increase the density of seed
particles near the wall. Larger diameter air supply lines will be run to alleviate the issue of mass-flow limitations.
Higher seeding density will allow for a full PIV set of > 1000 image pairs, producing statistically converged sets of
mean and turbulent quantities. This turbulence data can be used to verify the authors’ conjecture that roughness-
induced shocks and expansions will violate Townsend’s rough-wall similarity6,7
. PIV data will also be collected in a
spanwise sweep to detect the presence of 3-D flow fields due to roughness. The resulting data from these future
testing campaigns will be used to quantify the Mach number sensitivity of the mechanical non-equilibrium effects
on the mean and turbulent flow properties described in the Ekoto et al Mach 3.0 study.8
Acknowledgments
The authors would like to acknowledge the work of Nathan Tichenor in collecting and analyzing the smooth-
wall PIV data presented in this paper. All rough-wall data was collected with the assistance of Ray Humble.
This work was sponsored by the U.S. Air Force Office of Scientific Research. The views presented in this paper
are those of the authors, and do not necessarily represent the views of the sponsoring organization.
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