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American Institute of Aeronautics and Astronautics

Measurement of Experimental Boundary Conditions for

CFD Validation of a Supersonic Jet in Transonic Crossflow

Steven J. Beresh,* John F. Henfling,

† Russell W. Spillers,

‡ and Rocky J. Erven

§

Sandia National Laboratories, Albuquerque, NM, 87185

To complement a code validation data set acquired previously for a supersonic jet

exhausting transversely from a flat plate into a subsonic compressible crossflow, wind tunnel

boundary conditions have been experimentally measured. Practical hardware limitations

prevent measurement acquisition at the position of the computational inflow and outflow

planes, so instrumentation must be placed where feasible and the computational approach

adjusted to accommodate such realities. Wind tunnel calibrations provide flow angularity

and nonuniformity data that can be extrapolated to the computational inflow plane. Wall

pressure distributions in the test section characterize the downstream change in Mach

number as the test section blockage increases. Boundary layer properties were measured

from velocity profiles and surface shear stress measurements at one location on the wall

from which the jet would exhaust. A code validation strategy is outlined to incorporate the

experimental boundary conditions into jet interaction simulations.

Introduction

In recent years, the need to establish the accuracy and reliability of numerical simulations for engineering

applications has resulted in increased attention to the validation of computational models. Such needs inspire

experiments designed specifically to provide data for an unambiguous comparison between experimental and

numerical results, as well as to aid the evolution of the underlying physical models. Past efforts have shown that

most existing data sets do not meet the rigorous criteria necessary for such validation activities, and therefore it has

been recommended that experiments should be conducted explicitly for this purpose, providing not just the main

body of data but also the ancillary information necessary for completing the computational domain.1-3 The

mathematical closure of the computation requires provision of boundary conditions appropriate to the problem,4,5

and thus reasonable agreement between simulation and experiment cannot be expected without some knowledge of

the physical environment in which the experiment resides. This is the principal failing of most archival data sets

that otherwise could be employed for validation purposes.3

The need for improved validation data has motivated an experimental program to obtain a comprehensive data

set concerning the far-field of the interaction generated by a transverse supersonic jet exhausting from a flat plate

into a transonic crossflow. This flowfield is dominated by the presence of a counter-rotating vortex pair (CVP),

which is induced as the jet is turned over and realigned by its encounter with the freestream. Measurement of the

velocity field induced by the CVP has been the focus of the experimental program in part because it is central to the

fluid dynamics of the problem and partly because of its importance in jet/fin interaction on flight vehicles possessing

both reaction control rockets and downstream aerodynamic control surfaces.6-8 However, in addition to its direct

bearing on the performance of specific flight systems, jet-in-crossflow interactions encompass a significant range of

*Principal Member of the Technical Staff, Engineering Sciences Center, Senior Member AIAA, correspondence to: P.O. Box

5800, Mailstop 0834, (505) 844-4618, email: sjberes@sandia.gov †Distinguished Technologist, Engineering Sciences Center, Member AIAA. ‡Technologist. §Principal Technologist.

This work is supported by Sandia National Laboratories and the United States Department of Energy. Sandia is a

multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of

Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.

25th AIAA Aerodynamic Measurement Technology and Ground Testing Conference5 - 8 June 2006, San Francisco, California

AIAA 2006-3449

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

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American Institute of Aeronautics and Astronautics

complex physical phenomena, including wall-bounded

flows, free shear flows, turbulent separated flows, and

unsteady flows. These fluid mechanics phenomena

must be accurately simulated not just for specific flight

applications, but also for a wide variety of flowfields

important to other flight vehicles, which makes jet-in-

crossflow interactions especially attractive as a source

of validation data.

To produce the high-fidelity measurement of the

velocity field of the jet interaction, particle image

velocimetry (PIV) previously has been employed in the

solid-wall transonic test section of Sandia’s Trisonic

Wind Tunnel (TWT). Mean two-component velocity

field data gathered in the centerline streamwise plane

have been reported in Ref. 9 for a variety of freestream

Mach numbers M∞ (necessarily less than Mach 1, given

that a ventilated test section was replaced by solid

surfaces to avoid the computational challenges of

modeling the porous wall boundary) and jet-to-

freestream dynamic pressure ratios J. Complementary

turbulence properties are investigated in Ref. 10. These

data provide a measure of the penetration and breadth of the jet and associated CVP as they interact with the

crossflowing freestream. Stereoscopic PIV was implemented in the crossplane for the same values of M∞ and J at a

fixed location 33.8 jet diameters dj downstream of the jet nozzle centerline, which is ideal for identifying the vortex

structure of the interaction; these results are given in Ref. 11. The mean streamwise measurements are reproduced

in Fig. 1 for M∞=0.8 and J=10.2, where the streamwise and vertical velocity components are presented as separate

contour plots for improved clarity as compared to a vector plot. Distances are normalized to dj and velocities to the

freestream velocity U∞. Figure 2 shows the matching data in the crossplane, where in-plane velocities are given by

vectors superposed upon a contour plot of the out-of-plane (streamwise) component. A detailed comparison

between the results from the varied PIV implementations is discussed in Ref. 12 to examine the veracity of the

uncertainty estimation.

Though the aforementioned documents provide a thorough and detailed study of the interaction itself, and even

the associated measurement uncertainties, they lack a treatment of the boundary conditions necessary to complete

the validation data set. The present document rectifies this absence by describing an assortment of measurements of

the experimental boundary conditions imposed by the wind tunnel itself intended to provide the remaining fragments

of information necessary to construct a computational model. These include wall pressure measurements for use in

establishing in-flow and out-flow conditions, wall boundary layer velocity data and surface shear stresses for

simulating the solid-wall boundaries, and wind tunnel calibration data to verify the common assumptions of level

and uniform freestream flow. Many of these measurements were acquired with the jet dormant and replaced by a

wall insert to enable a simulation of the “tunnel-empty” flow; after tuning the computation to reproduce the wind

x/dj

y/dj

20 25 30 35 40 450

5

10

15u/U

∞

1.02

1

0.98

0.96

0.94

0.92

0.9

0.88

0.86

0.84

x/dj

y/dj

20 25 30 35 40 450

5

10

15

v/U∞

0.32

0.28

0.24

0.2

0.16

0.12

0.08

0.04

0

(a) (b)

Fig. 1: Mean velocity field of the jet-in-crossflow interaction for M∞=0.8 and J=10.2 in the streamwise plane; (a)

streamwise component; (b) vertical component. (From Ref. 9.)

z/dj

y/dj

-5 0 50

5

10

15

u/U∞

1

0.98

0.96

0.94

0.92

0.9

0.88

0.86

0.84

0.2U∞

Fig. 2: Mean velocity field of the jet-in-crossflow

interaction for M∞=0.8 and J=10.2 in the crossplane

using stereoscopic PIV. (From Ref. 11.)

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American Institute of Aeronautics and Astronautics

tunnel itself with sufficient fidelity, the jet can be introduced into the domain to validate the jet-in-crossflow

interaction using numerical parameters established from the tunnel-empty exercise. With the needs of this process

in consideration, the current work aims to provide the necessary closure for a comprehensive code validation data

set.

Experimental Apparatus

Experiments were performed in the TWT, which is a blowdown-to-atmosphere facility using air as the test gas

through a 305 × 305 mm2 (12 × 12 inch

2) rectangular test section. The solid-wall transonic test section was used

rather than the traditional porous walls; although this approach imposes a subsonic Mach number limitation, it

provides computationally tractable boundary conditions for unambiguous comparison of experimental data and

numerical simulations, as well as supplying a flat plate from which the jet will issue and superior optical access for

the PIV measurements.

The jet exhausted from a conical nozzle with an expansion half-angle of 15° and an exit diameter of 9.53 mm

(0.375 inch), which fit to a settling chamber instrumented to provide stagnation pressure and temperature

measurements. Nitrogen was used as the working gas for the jet. The nozzle mounted along the centerline of the

top wall of the test section, which served as the flat plate from which it transversely exhausted. A side-wall window

flush with the top wall is positioned downstream of the jet for viewing the far-field of the interaction; a larger

window in the pressurized plenum complements the test section window. A window in the floor of the test section

is located near the position of the side-wall window for introducing the laser sheet, which is matched by a second

laser window in the bottom of the plenum. The relative position of the jet and windows within the test section is

sketched in Fig. 3, which additionally shows the laser sheet configuration for both streamwise and crossplane

measurements; two overlapping imaging regions were employed in the streamwise case to survey a longer length of

the flowfield. Also shown are upstream side-wall pressure taps for measuring the test section static pressure pw used

to establish the freestream Mach number M∞.

The stereoscopic PIV system is used in the present work for producing boundary layer measurements on the

wall from which the jet issues. The laser sheet was positioned in the centerline streamwise plane, as in the

streamwise PIV measurements,9,10 and the cameras aligned to view an imaging region approximately 45 mm in

height covering the overlap region seen in Fig. 3. The light source was a dual-cavity frequency-doubled Nd:YAG

laser (Spectra Physics PIV-400), replacing the lasers used in previous components of this study.9-12 Scattered laser

light was collected by frame-straddling CCD cameras (Redlake MegaPlus ES4.0/E), with a resolution of 2048 ×

2048 pixels and digitized at 8 bits, equipped with Scheimpflug lens mounts to achieve an oblique focal plane.

Fig. 3: Schematic of configurations in the wind tunnel for PIV measurements in both the streamwise plane

and the crossplane, looking in the downstream direction. Flow is from right to left. All dimensions are in

millimeters. Not to scale.

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American Institute of Aeronautics and Astronautics

Camera calibrations have been performed using the multi-plane procedure described by Soloff et al;13 this process

and the subsequent data processing have been accomplished using commercially available software (IDT’s

ProVision 2.02). The TWT is seeded by a thermal smoke generator (Corona Vi-Count 5000) that produces a large

quantity of particles typically 0.2-0.3 µm in diameter from a mineral oil base. A full description of the PIV system

and its use is found in Ref. 11. The present application improves the near-wall measurement capability by inserting

an anti-reflective coated exit window for the laser sheet into the top wall of the wind tunnel.

Wall pressure measurements were made using a Pressure Systems Inc. Model 8400 electronically-scanned

pressure system and ±15 psi pressure transducer modules. Measurements from each pressure port were acquired

simultaneous with measurements of the stagnation pressure and temperature of both the wind tunnel and, when

relevant, the jet settling chamber. Data presented herein are mean values, averaged over five seconds of wind tunnel

flow. Tunnel calibration measurements for flow uniformity were made using a rake of Pitot probes whose pressures

were sampled by the same PSI system. Flow angularity measurements were made using a five-hole probe of 9.53

mm diameter placed on the wind tunnel centerline and possessing a hemispherical head with lateral holes at 45°

from the probe centerline, and all pressures were again measured by the PSI system.

Surface shear stress measurements have been conducted using oil-film interferometry, employing the

methodology of Ref. 14. Dow Chemical 200 Fluid of either 50 cs or 100 cs viscosity was applied to a polished

stainless steel disk inserted into the top wall of the test section where the boundary layer PIV measurements were

acquired, then illuminated with the 546.1 nm line from a mercury-vapor lamp. Reflected light was observed by one

of the PIV cameras used for the velocimetry measurements, binned down to a 512 × 512 pixel image, looking

through a beam splitter placed in the illumination path such that the incident and reflected light both were aligned

normal to the wall. The oil viscosity was calibrated versus temperature prior to the wind tunnel experiments using a

Ubbelohde capillary viscometer suspended in a constant temperature bath.

Results and Discussion

Wind Tunnel Inflow

The inflow conditions of the computational model are expected to be specified using the wind tunnel stagnation

pressure P0, the stagnation temperature T0, and the direction of the freestream vector. The first two quantities are

fundamental properties of the wind tunnel flow measured during each experimental run, so these are readily

specified for all data sets.9-11 The direction of the freestream vector may be estimated from the wind tunnel flow

angularity. Data have been gathered using a single five-hole probe positioned at the wind tunnel centerline at a

station 400 mm downstream of the virtual jet location (i.e., if it were installed). Although the computational model

must specify the flow angle at its inflow boundary, which is well upstream of the probe position in the test section,

practical hardware limitations make such a measurement impossible. Instead, the measurement must be acquired

where feasible, then extrapolated back to the computational boundary.

Flow angularity is determined by acquiring pressures as the probe is swept through a series of angle-of-attack

positions, then computing the normalized pressure difference between the two off-center ports in the pitch plane.

The probe then is rolled 180° and the measurement repeated. The intersection of the two curves yields the flow

angularity with a greater accuracy than the zero-offset found from a single curve, as it removes the influence of

biases due to asymmetric probe geometry.15 Flow

angularity measurements as a function of Mach number

are shown in Fig. 4, which includes data acquired at

supersonic conditions in test sections other than the

solid-wall transonic test section used for the jet-in-

crossflow studies. Values appropriate to the present

work are about 0.3° to 0.35° of downflow, which are

significant for aerodynamic testing although the impact

on the jet interaction is unclear. Additional

measurements were conducted at a tunnel station 200

mm further upstream (i.e., 200 mm downstream of the

virtual jet location) and were found to closely agree

with those shown in Fig. 4. Flow angularity in the yaw

plane cannot easily be measured in the TWT because

the model support only rotates in the pitching plane.

Although no flow angularity measurements off the

centerline of the test section are available at the present

Mach Number

αf(deg)

0.5 1 1.5 2-0.4

-0.3

-0.2

-0.1

0

Fig. 4: Wind tunnel flow angularity in the vertical

centerplane.

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American Institute of Aeronautics and Astronautics

date, a calibration of the wind tunnel using standard single-orifice Pitot probes mounted on a rake spanning 240 mm

of the 305 mm square test section was used to examine the lateral uniformity of the freestream. Results between

Mach 0.5 and 0.8 showed a variation typically of 0.5% but never more than 1.0% of the Pitot pressure; at a nominal

Mach 0.8, this equates to a difference in Mach number of 0.005 to 0.010, respectively. A more recent survey of just

the core 152 mm span of the test section found all spatial variation in the Pitot pressure within 0.5%, which also was

approximately the measurement uncertainty.

The flow angularity of the TWT remains the subject of ongoing investigation. Future experiments seek to

extend the measurements by using a rake of five multi-orifice probes to examine the variation of the flow angularity

across the wind tunnel crossplane, and to extend the probe position forward to determine any axial dependence.

These data may provide a greater understanding of how to extrapolate the flow angularity conditions back to the

inflow plane and in what fashion it varies across the span of the test section.

The sparse and incomplete nature of the flow angularity data is illustrative of the difficulty of providing

precisely those measurements desired by computational methodology in the face of practical hardware

considerations (not to mention fiscal and time-management considerations). None of these measurements actually

provide a clear value to employ at the computational inflow plane for the velocity vector direction, but an

extrapolation of the available data suggest bounding values that can be computationally tested to assess the

importance of their impact upon the simulation results. Of course, it is quite possible that the small values of flow

angularity may have a negligible effect on the results of a simulation and hence can be ignored altogether. However,

the crossplane velocimetry of the jet interaction showed that a small but significant degree of asymmetry was found

in the size and lateral position of the counter-rotating vortex pair.11 Although the source of this asymmetry remains

unidentified, freestream angularity or nonuniformity is a plausible culprit and hence may need to be reproduced (or

compensated) in the computational domain. Moreover, other validation efforts have shown the value of

incorporating freestream nonuniformities.16,17

For the jet-in-crossflow simulations, a second inflow plane exists at the jet inlet. It is most sensible to establish

the inflow plane well upstream of the nozzle throat, where the pressure and temperature are given by the jet

stagnation property measurements made with each wind tunnel run and published with the velocimetry data.9-11 The

direction of the flow vector at this location is not realistically measurable, however, so it must simply be assumed to

align with the nozzle geometry. Nozzle wall pressure measurements discussed in Ref. 18 demonstrate that under

some of the conditions studied, flow separation occurs along the nozzle walls in an asymmetric fashion due to the

backpressure variations induced around the nozzle exit by the jet interaction. This observation demonstrates that a

coupling occurs between the flow in the test section and that within the nozzle, and it therefore may be necessary to

simulate the nozzle flow and not simply place the inflow plane at the nozzle exit.

Wind Tunnel Outflow

Outflow conditions need to be specified at the exit of the simulated test section, but accurately acquiring these

measurements is impractical due to the abundance of wind tunnel control hardware and model support mechanisms

at this position. Instead, wall pressure measurements have been gathered along the side wall of the wind tunnel,

both while the jet was in operation and in the tunnel-empty configuration; it is the latter of these measurements that

(a) (b)

Fig. 5: Mean surface pressures (a) measured on a side wall of the wind tunnel along with the inferred Mach number

distribution (b), given as the increase from the fixed upstream value. Data shown are from the tunnel-empty case.

x/dj

cp

30 40 50 60-0.12

-0.08

-0.04

0M

∞=0.5

M∞=0.6

M∞=0.7

M∞=0.8

x/dj

M∞(x)/M

∞

30 40 50 601

1.02

1.04

1.06

1.08

1.1M

∞=0.5

M∞=0.6

M∞=0.7

M∞=0.8

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American Institute of Aeronautics and Astronautics

is important to establishing the capacity to simulate the wind tunnel flow. Figure 5 shows the wall pressure data and

the inferred freestream Mach number for the tunnel-empty case as a function of the nominal freestream Mach

number M∞. The measured Mach number M∞(x) is specified as the local increase with respect to the Mach number

M∞ fixed at the upstream pressure taps. The line of pressure taps is positioned at the centerline of the side wall and

their distance is specified with respect to the jet nozzle centerline, which is a virtual location for the tunnel-empty

case.

The downstream variation of the wall pressure shown in Fig. 5a highlights an important ramification of the

decision to employ a solid-wall test section. The growth of the wall boundary layers with downstream distance

effectively reduces the test section area and hence increases the Mach number of the flow as witnessed in Fig. 5b.

Although this complicates analysis of the jet-in-crossflow physical behavior because of the gradual rise in Mach

number, it actually simplifies the validation process because this effect should be replicated in the computational

simulation. This approach is preferable to an attempt to simulate the porous-wall boundary condition, which in itself

is a difficult problem unrelated to validating a model’s ability to simulate jet interactions. Figure 5 shows that the

wall pressure drops less through the test section at lower M∞, which is consistent with a thinner boundary layer for

smaller Mach numbers.

The pressure data of Fig. 5, in conjunction with the upstream pressure pw used to establish the tunnel flow

conditions, can be used to determine the computational outflow conditions. The outflow pressure conditions would

be iteratively adjusted in the simulation until the wall pressure matched the two taps that yield pw; then the

distribution along the wall can be examined for a reasonable match with the measured values as a first step in

validating the model’s performance. This approach is superior to matching only pw in that, by comparing the wall

pressure decrease along the line of taps, it ensures that the boundary layer growth has been accurately simulated. In

x/dj

M∞(x)/M

∞

30 40 50 601

1.02

1.04

1.06

1.08

1.1M

∞=0.5

M∞=0.6

M∞=0.7

M∞=0.8

x/dj

M∞(x)/M

∞

30 40 50 601

1.02

1.04

1.06

1.08

1.1

1.12J=2.8J=5.6J=10.2J=16.7

(a) (b)

Fig. 6: Mean surface pressures measured on a side wall of the wind tunnel for the jet-on cases; (a) varying J while

M∞=0.8; (b) varying M∞ while J=10.2.

x/dj

cp

30 40 50 60-0.2

-0.16

-0.12

-0.08

-0.04

0J=2.8J=5.6J=10.2J=16.7

x/dj

cp

30 40 50 60-0.16

-0.12

-0.08

-0.04

0M

∞=0.5

M∞=0.6

M∞=0.7

M∞=0.8

(a) (b)

Fig. 7: Inferred Mach number distribution corresponding to the jet-on pressure data of Fig. 6; (a) varying J while

M∞=0.8; (b) varying M∞ while J=10.2.

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American Institute of Aeronautics and Astronautics

this manner, the lack of actual pressure measurements at the outflow plane can be compensated by those pressure

measurements that were experimentally feasible.

An accurate simulation of the boundary layer growth on the wind tunnel walls demands a selection of the

distance upstream at which to begin the simulation. The wind tunnel itself does not have a simply defined starting

point for its test section walls; rather, they are a natural continuation of the apparatus that lies upstream. The flow

through the tunnel begins in pipes from the pressure storage tanks, passes through a series of valves, then screens

and honeycomb, before finally reaching the contraction section that acts as the inlet to the test section. Clearly, it is

impractical and undesirable to simulate the wind tunnel to this extreme level of fidelity. Instead, the simulated

domain will have an adjustable length to the test section upstream of all pressure taps that may be varied until

growth of the boundary layer reaches the values found at the measurement stations. The combination of adjusting

this inflow length and the outflow pressure condition provide the free parameters needed to establish a

computational domain that can reproduce the experimental conditions found in the test section – not reproduce the

wind tunnel in its entirety, only the most relevant portion. Thus the inflow geometry of the computation differs from

the reality of the wind tunnel, but if the wall pressure distribution in the test section is reasonably matched, then the

growth of the boundary layers probably is simulated with sufficient fidelity.

The wall pressures shown in Fig. 5 can be expected to shift once the jet is turned on, and in fact will differ as

the jet pressures are varied. By definition, all experiments in Refs. 9-12 were conducted with pw=101.7 kPa (14.7

psia), and the wall pressures further downstream were monitored to provide a measure of the changing test section

conditions due to jet operation. Because the jet provides substantial additional blockage of the test section beyond

that due to the wall boundary growth, these pressures drop notably and are given in Fig. 6a at M∞=0.8 for the four

tested values of J and in Fig. 6b for the four values of M∞ while J remains constant at 10.2. Figure 7 recasts the

same measurements in terms of the effect on Mach number. The effects of the greater tunnel blockage due to a

stronger jet are readily apparent in Fig. 6a, where more pressure drop along the test section occurs for larger values

of J. Note that the PIV measurements have shown that the jet spreading rate is not great enough for it to reach the

test section side walls,9,11 so jet impingement cannot be a factor in the pressure distribution on the window blank.

The decrease in wall pressure is clearly stronger than the corresponding tunnel-empty measurement in Fig. 5a, but at

the lowest values of J the increased blockage is small enough that minimal additional pressure drop is witnessed.

Larger values of M∞ produce greater pressure drop at the same value of J as shown comparing Fig. 6b to Fig. 5a,

which is attributable to the greater effects of choking as the Mach number approaches the sonic condition.

The role of the jet-on wall pressures is analogous to the tunnel-empty pressures. Once the simulation is

functioning correctly in the tunnel-empty case and has been tuned to accurately simulate the wind tunnel, the jet is

“turned on” computationally. This will change the outflow boundary condition because the vortices generated by

the jet interaction will exit through this plane. To compensate, the outflow pressure will have to be adjusted to the

new flowfield conditions until, as in the tunnel-empty case, the simulation produces a wall pressure distribution that

compares well with the data of Fig. 6.

A thorough error analysis of the wall pressure measurements concluded that the total estimated uncertainty for

each individual data point of the tunnel-empty measurements is 0.5 kPa (0.08 psi), which translates to ±0.02 cp.18

This value includes instrumentation error, experimental repeatability, tunnel nonuniformity, and bias errors arising

from pressure tap geometry. Assuming bias errors do not correlate between taps, the uncertainty of the linear fit

through the collection of data points is reduced to 0.1 kPa (0.02 psi), or ±0.005 cp. An extended discussion may be

found in Ref. 19.

Boundary Layer Properties

It is not sufficient to declare the accuracy of the computation’s reproduction of the test section properties simply

based upon the wall pressure values. Accurate simulation of the wall boundary layers is necessary as well, both

because the boundary layer growth defines the increase in Mach number in the test section and because past studies

have shown that the boundary layer properties are a significant parameter in the penetration of the jet into the

crossflow.20-23

To this purpose, the stereoscopic PIV system used to acquire the crossplane velocimetry

measurements of the jet-in-crossflow interaction11 was reconfigured to measure the boundary layer on the same wall

of the wind tunnel from which the jet emerges, but with the jet replaced by a blank. The measurement plane was

aligned to the streamwise centerplane and the field of view reduced to about 45 mm vertically rather than the 150

mm used for the jet-on data. Ten wind tunnel runs, each of 150 image pairs from each camera, were conducted for

each Mach number. Data were interrogated with a 32 × 32 pixel window employing adaptive correlations and a

spatial offset to account for the mean streamwise particle displacement. An approximate 50% overlap in adjacent

interrogation windows typically was used to oversample the velocity fields.

Boundary layer surveys of the wind tunnel top wall have been extracted from the PIV velocity fields at the

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American Institute of Aeronautics and Astronautics

centerpoint of the laser exit window, 30.3 dj

downstream of the virtual jet nozzle centerline.

Unfortunately, hardware limitations did not allow the

exit window to be placed such that profiles could be

extracted at the intersection of the jet-in-crossflow PIV

planes (33.8 dj), but as a practical matter, such a small

difference in downstream station does not matter in

validating this facet of a simulation. Figure 8 shows the

resultant mean streamwise velocity profiles for four

values of M∞ in the tunnel-empty configuration. The

profiles are normalized to the 99%-velocity boundary

layer thickness δ, as determined from the same data,

and the local freestream velocity U∞(x), which is

distinguished from U∞ in that the latter quantity is

determined from the two upstream pressure taps and

therefore does not capture the dependence on

downstream distance due to increasing flowfield

blockage as does U∞(x). The measurement uncertainty

is estimated by the same procedure used in Refs. 11 and

12 and predicts an uncertainty in the streamwise

velocity component of 3.8 m/s. However, this

uncertainty is dominated by bias errors arising from the

stereoscopic camera calibration, which remain constant

during the course of the experiments and hence should

cancel out of the normalized velocity profiles in Fig. 8.

Hence, the estimated uncertainty in u/U∞ is reduced to

0.005.

The data of Fig. 8 show that the change in the

profile shape as M∞ is altered is fairly mild; of course,

the change in boundary layer thickness is removed by

the normalization and undetectable when plotted in this

fashion. In fact, the differences between the four cases

appear scarcely significant with respect to the estimated

measurement uncertainty, but this is largely indicative

of the success of the normalization.

A more numerical approach is required to

differentiate the boundary layer properties of these four

cases. The 99%-velocity boundary layer thickness δ

that was used to normalize the data of Fig. 8 is

presented in Fig. 9. The displacement thickness δ* and

the momentum thickness θ are given as well, found by

integrating the velocity profiles. The effects of the

varying density through the boundary layer have been

neglected because this is a weakly compressible flow,

but Fig. 9 still provides a useful approximation of these values; from a validation perspective, this deficiency can

most easily be avoided by validating to the actual velocity profiles rather than the derived thicknesses. The actual

values of U∞(x) used in the normalization in Fig. 8 are 282 m/s, 247 m/s, 215 m/s, and 181 m/s for the M∞=0.8, 0.7,

0.6, and 0.5 cases, respectively.

Ideally, the boundary layer measurements would have been acquired just upstream of the position of the jet

nozzle, but optical access limitations preclude this possibility. However, as a practical matter, if the tunnel-empty

simulation performed prior to any computations of the jet-in-crossflow interaction matches both the wall-pressure

distribution provided in Fig. 6a and the boundary layer profile in Fig. 8, it probably yields accurate boundary layer

data throughout the test section. The tunnel-empty computations then can provide the boundary layer properties at

the desired upstream location to define this parameter for the jet-in-crossflow computations.

A more pressing deficiency, however, is the lack of data points very near the wall. The closest measurements to

the wall were obtained at about y=0.5 mm, which is difficult to substantially improve upon for a PIV measurement

Fig. 9: Boundary layer properties determined from the

profiles of Fig. 8. Dimensions in mm.

M∞(x)

δ

δ* ,

θ

0.5 0.6 0.7 0.811

12

13

14

15

1

1.5

2

2.5

δ

δ*

θ

Fig. 8: Boundary layer streamwise velocity profiles for

the tunnel-empty case at 30.3 dj downstream of the

virtual jet nozzle centerline.

u/U∞

y/δ

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

M∞=0.5

M∞=0.6

M∞=0.7

M∞=0.8

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American Institute of Aeronautics and Astronautics

in a flow of the current length scales. Using the surface shear stress values obtained below, this vertical position

translates to a coordinate in inner variables of y+≈200-300, depending on Mach number. This is a substantial

distance from the wall, especially considering that the log-law region is generally considered to extend only to a y+

of about 300 before outer-region wake effects become strong.24 To provide a measurement at the wall, the surface

shear stresses have been acquired for the tunnel-empty case at the same location as the boundary layer velocimetry

data. Though not strictly necessary to fully specify the computational domain, this additional boundary condition

provides an important further check upon the accuracy of the boundary layer simulation by examining its near-wall

performance and the sufficiency of the grid resolution. Given the limitations of the PIV measurements near the wall

and the fullness of the boundary layer velocity profile, the surface shear stress is an important complement to the

questionable determination of the wall velocity gradient.

Surface shear stress data have been obtained using oil-film interferometry. Sequences of 100 images were

captured 200 ms apart for each wind tunnel run. The resulting fringe patterns were interrogated by locating the

peaks and valleys of the fringe along a line oriented streamwise, then solved for the shear stress using a discretized

one-dimensional form of the oil-film equation and the oil thickness interferometry (Eqns. 30 and 31 in Ref. 14).

Given that the shear stress on the wall is not dependent upon lateral distance or time, and is only minimally a

function of downstream distance over such a short region, many independent data points were computed for each

run and averaged to a single value. The wall temperature was assumed to be the adiabatic wall temperature found

using a turbulent flat plate recovery factor of 0.89, and this value was used to establish the oil viscosity based upon

the calibration previously performed.

The resulting wall shear stress values are shown in Fig. 10, plotted against the local Mach number. Results for

the two different oils are found to be in close agreement, which lends validity to the measurement. Furthermore,

Fig. 10 shows the data to closely match the theoretical approach of Kestin and Persen, as presented by White and

modified by a compressible correction.25 Several other theoretical approaches were examined and found not to

agree as well with the data. It is not clear why increased scatter was seen in the data for the M∞=0.8 case,

particularly because no increase was witnessed in the scatter of the data points comprising each average value;

further experimentation would be required to resolve this question. Nevertheless, these measurements establish an

additional measure of the wall boundary condition and confirm which of many proposed theoretical expressions for

the wall shear stress best suits the present flowfield.

As a final exercise, the velocity profiles of Fig. 8 can now be expressed using inner-law variables, employing

the wall shear stress values given by theory in Fig. 10. These results are shown in Fig. 11.

Conclusion

Particle image velocimetry (PIV) data previously have been acquired in the far-field of the interaction created

by a supersonic axisymmetric jet exhausting transversely from a flat plate into a transonic crossflow. Data included

two-dimensional PIV in the streamwise plane on the centerline of the wind tunnel test section, and stereoscopic PIV

M∞(x)

τw(Pa)

0.5 0.6 0.7 0.80

20

40

60

80

100 50 cs

100 cs

theory

Fig. 10: Wall shear stress values as found by oil-film

interferometry, tested twice using different viscosity

oils. Also shown are values found using a theoretical

approach described in White.25

y+

u+

102

103

104

105

15

20

25

30

35

M∞=0.5

M∞=0.6

M∞=0.7

M∞=0.8

Fig. 11: Boundary layer streamwise velocity profiles

for the tunnel-empty case of Fig. 8, recast using inner-

law variables.

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American Institute of Aeronautics and Astronautics

for three-dimensional measurements in the crossplane of the wind tunnel in a downstream position overlapping the

streamwise measurements. The streamwise data reveal the downstream evolution of the decaying jet and the

induced counter-rotating vortex pair whereas the crossplane stereoscopic measurements directly reveal the

interaction’s vortex structure. Together with a rigorous uncertainty analysis, this comprehensive data set is intended

for the validation of computational models.

Though the detailed velocimetry data provide a thorough characterization of the interaction itself, they lack a

treatment of the experimental boundary conditions imposed by the wind tunnel that are necessary to complete the

validation data set. To characterize the inflow plane needed for the computation, wind tunnel calibrations provide

estimates of the flow angularity and the nonuniformity of the flowfield across the span of the test section. Although

these measurements could not be acquired at the position of the computational inflow plane due to practical

limitations in the wind tunnel hardware, conditions in the test section may be extrapolated upstream to the station

where they are required in the simulation. Similarly, the pressure at the outflow plane could not be measured due to

hardware constraints, but a line of surface pressure taps along one wall of the test section provides a pressure

distribution due to the increased blockage as the wall boundary layer grows, which can be extrapolated to the end of

the computational domain. Mean velocity profiles of the boundary layer on the wall of the test section from which

the jet exhausts were gathered using PIV to characterize this important parameter in the interaction, complemented

by surface shear stress measurements using oil-film interferometry to provide the behavior at the wall. Again, these

measurements are desirable further upstream of the interaction’s location in the wind tunnel, but this was not

experimentally feasible and the computational approach must be adjusted to accommodate such realities.

The intended validation methodology is to first simulate the wind tunnel test section without the presence of the

jet interaction. This tunnel-empty case will be used to establish the model parameters such that the wind tunnel

flowfield is accurately simulated. The outflow pressure and the upstream length of the test section both would be

adjusted until the boundary layer growth and the resulting pressure distribution through the test section replicate that

of the experiment, then the simulation turned to the jet interaction case. A second adjustment of the outflow

pressure would be required due to the vortices now flowing out through the exit plane, until the new pressure

distribution is matched to reflect the increased blockage effects due to the jet. At this point, computational results

may be meaningfully compared with the validation data reported in previous documents.

Acknowledgments

The authors would like to thank Matt Barone, Bill Oberkampf, and Jeff Payne of Sandia National Laboratories

for their thoughtful insights concerning computational boundary conditions, and Prof. Jonathon Naughton of the

University of Wyoming for his assistance with the oil-film interferometry measurements.

References

1Marvin, J. G., “Perspective on Computational Fluid Dynamics Validation,” AIAA Journal, Vol. 33, No. 10, pp. 1778-1787,

1995. 2American Institute of Aeronautics and Astronautics, “Guide for the Verification and Validation of Computational Fluid

Dynamics Simulations,” AIAA G-077-1998, 1998. 3Aeschliman, D. P., and Oberkampf, W. L., “Experimental Methodology for Computational Fluid Dynamics Code

Validation,” AIAA Journal, Vol. 36, No. 5, 1998, pp. 733-741. 4Oberkampf, W. L., and Blottner, F. G., “Issues in Computational Fluid Dynamics Code Verification and Validation,” AIAA

Journal, Vol. 36, No. 5, pp. 687-695, 1998. 5Roache, P. J., Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque,

NM, 1998. 6Cassel, L. A., Durando, N. A., Bullard, C. W., and Kelso, J. M., “Jet Interaction Control Effectiveness for Subsonic and

Supersonic Flight,” Report No. RD-TR-69-21, U. S. Army Missile Command, Redstone Arsenal, Sept. 1969. 7Cassel, L. A., “Applying Jet Interaction Technology,” Journal of Spacecraft and Rockets, Vol. 40, No. 4, 2003, pp. 523-

537. 8Peterson, C. W., Wolfe, W. P., and Payne, J. L., “Experiments and Computations of Roll Torque Induced by a Vortex-Fin

Interaction,” AIAA Paper 2004-1069, January 2004. 9Beresh, S. J., Henfling, J. F., Erven, R. J., and Spillers, R. W., “Penetration of a Transverse Supersonic Jet into a Subsonic

Compressible Crossflow,” AIAA Journal, Vol. 43, No. 2, 2005, pp. 379-389. 10Beresh, S. J., Henfling, J. F., Erven, R. J., and Spillers, R. W., “Turbulent Characteristics of a Transverse Supersonic Jet in

a Subsonic Compressible Crossflow,” AIAA Journal, Vol. 43, No. 11, 2005, pp. 2385-2394. 11Beresh, S. J., Henfling, J. F., Erven, R. J., and Spillers, R. W., “Crossplane Velocimetry of a Transverse Supersonic Jet in

a Transonic Crossflow,” AIAA Paper 2006-0906, January 2006, also submitted to AIAA Journal.

- 11 -

American Institute of Aeronautics and Astronautics

12Beresh, S. J., Henfling, J. F., Erven, R. J., and Spillers, R. W., “Comparison of Data from Three PIV Configurations for a

Supersonic Jet in Transonic Crossflow,” Proceedings of the 21st International Congress on Instrumentation in Aerospace

Simulation Facilities, Sendai, Japan, 2005, pp. 312-322. 13Soloff, S. M., Adrian, R. J., and Liu, Z-C, “Distortion Compensation for Generalized Stereoscopic Particle Image

Velocimetry,” Measurement Science and Technology, Vol. 8, No. 12, 1997, pp. 1441-1454. 14Naughton, J. W., and Sheplak, M., “Modern Developments in Shear-Stress Measurement,” Progress in Aerospace

Sciences, Vol. 38, No. 6-7, pp. 515-570, 2002. 15Clark, E. L., Henfling, J. F., and Aeschliman, D. P., “Calibration of Hemispherical-Head Flow Angularity Probes”, AIAA

Paper 92-4005. 16Maus, J. R., “Investigation of Differences Between Measured and predicted pressures in AEDC/VKF Hypersonic Tunnel

B,” AIAA Paper 97-0566, Jan. 1997. 17Roy, C. J., Oberkampf, W. L., and McWherter-Payne, M. A., “Verification and Validation for Laminar Hypersonic

Flowfields, Part 2: Validation,” AIAA Journal, Vol. 41, No. 10, 2003, pp. 1944-1954. 18Beresh, S. J., Henfling, J. F., and Erven, R. J., “Flow Separation Inside a Supersonic Nozzle Exhausting into a Subsonic

Compressible Crossflow,” Journal of Propulsion and Power, Vol. 19, No. 4, 2003, pp. 655-662. 19Beresh, S. J., Henfling, J. F., and Erven, R. J., “Surface Measurements of a Supersonic Jet in Subsonic Compressible

Crossflow for the Validation of Computational Models,” Sandia National Labs., Rept. SAND2002-1890, Albuquerque, NM, Oct.

2002. 20Schetz, J. A., and Billig, F. S., “Penetration of Gaseous Jets Injected into a Supersonic Stream,” Journal of Spacecraft,

Vol. 3, No. 11, 1966, pp. 1658-1665. 21Gruber, M. R., Nejad, A. S., Chen, T. H., and Dutton, J. C., “Compressibility Effects in Supersonic Transverse Injection

Flowfields,” Physics of Fluids, Vol. 9, No. 5, 1997, pp. 1448-1461. 22Roger, R. P., and Chan, S. C., “Parameters Affecting Penetration of a Single Jet into a Supersonic Crossflow: A CFD

Study – II,” AIAA Paper 98-0425, Jan. 1998. 23Cortelezzi, L., and Karagozian, A. R., “On the Formation of the Counter-Rotating Vortex Pair in Transverse Jets,” Journal

of Fluid Mechanics, Vol. 446, 2001, pp. 347-373. 24White, F. M., Viscous Fluid Flow, 2nd ed., McGraw-Hill, 1991, pp. 412-417. 25ibid, pp. 430-432, 549.