David O. Davis

Glenn Research Center, Cleveland, Ohio

CFD Validation Experiment of a Mach 2.5

Axisymmetric Shock-Wave/Boundary-Layer

Interaction

NASA/TM—2015-218841

September 2015

AJK2015–06342
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David O. Davis

Glenn Research Center, Cleveland, Ohio

CFD Validation Experiment of a Mach 2.5

Axisymmetric Shock-Wave/Boundary-Layer

Interaction

NASA/TM—2015-218841

September 2015

AJK2015–06342

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

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cosponsored by ASME, JSME, and KSME

Seoul, Korea, July 26–31, 2015
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is gratefully acknowledged. This work was sponsored by the Transformative Aeronautics Concepts Program at the NASA Glenn 

Research Center.
CFD Validation Experiment of a Mach 2.5 Axisymmetric

Shock-Wave/Boundary-Layer Interaction

David O. Davis

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

Preliminary results of an experimental investigation of a 

Mach 2.5 two-dimensional axisymmetric shock-wave/

boundary-layer interaction (SWBLI) are presented. The 

purpose of the investigation is to create a SWBLI dataset 

specifically for CFD validation purposes. Presented herein are 

the details of the facility and preliminary measurements 

characterizing the facility and interaction region. These results 

will serve to define the region of interest where more detailed 

mean and turbulence measurements will be made.

Introduction

Experimental investigations of specific flow phenomena can 

provide great insight into the flow behavior but often lack the 

necessary detail and documentation to be useful as CFD 

validation experiments. Reasons for this include, but are not 

limited to:

• Undefined boundary conditions

• Inconsistent results

• Undocumented 3D effects (centerline only measurements)

• Lack of uncertainty analysis

In 1994, Settles and Dodson (Refs. 1 and 2) reviewed a large 

number of supersonic and hypersonic experiments and 

evaluated them for suitability to be used as CFD validation 

experiments. Of the hundreds of experiments reported in the 

open literature, over one hundred were subjected to rigorous 

acceptance criteria. Of these, only nineteen (12 supersonic,

7 hypersonic) were deemed to be acceptable for CFD 

validation. Aeschliman and Oberkampf (Ref. 3) recognized the 

need to develop a specific methodology for experimental 

studies intended specifically for validation purposes.

SWBLI CFD validation experiments performed in

non-circular wind tunnels pose a particularly challenging 

problem, as streamwise and transverse pressure gradients 

induced by the SWBLI turn a nominally two-dimensional flowfield into a three-dimensional flow-field (Refs. 4 and 5). This is 

illustrated in Figure 1 by oil flow visualization obtained in 

NASA Glenn Research Center’s (GRC) 15×15 cm Supersonic

Wind Tunnel (SWT) with an M = 2.0 oblique SWBLI.

The view is of the floor of the tunnel where an impinging/

reflected oblique shock wave interacts with the boundary layers 

on the floor and sidewalls and α is the angle of the shock 

generator plate. For a weak, unseparated interaction

(Figure 1(a)), the flow remains mostly two-dimensional with a 

slight bottlenecking of the limiting wall streamlines in the 

vicinity of the impingement location. For a stronger, separated 

interaction, (Figure 1(b)), centerline measurements alone would 

not be representative of a two-dimensional interaction and the 

entire flow-field would need to be surveyed for this case to be 

useful as a CFD validation case.

The Transformational Tools & Technologies (TTT) Project 

under NASA’s Transformative Aeronautics Concepts Program 

is tasked, in part, with providing quality experiments for the 

purpose of validating CFD codes and turbulence models. A 

Mach 2.5 SWBLI has been identified as one of the test cases 

desired. The primary objective of the current study is to provide 

a comprehensive dataset for a Mach 2.5 SWBLI that is of 

sufficient quality to be used as a validation test case.

In order to avoid the pitfalls of a rectangular configuration, 

an axisymmetric configuration is proposed that is twodimensional in the mean. The selected interaction is illustrated 

in Figure 2. A Mach 2.5 core flow approaches a cone-cylinder 

centerbody that generates a conical shock that impinges and 

reflects off the cylindrical test section wall, interacting with the 

naturally occurring test section boundary layer. The 

approximate measurement area of interest is indicated by the 

rectangular box shown in the figure. NASA GRC’s supersonic 

facilities, however, all have square or rectangular test sections 

so a new facility has been designed specifically for this study. 

This configuration is similar to a study performed by Rose

(Ref. 6), which was considered for Settles and Dodson’s 

validation database, but was rejected due to questions about the 

accuracy of the hot-wire measurements. A new 17 cm diameter 

axisymmetric supersonic wind tunnel (Axi-SWT) has been

installed in Test Cell W6B and replaces the existing 15×15 cm 

configuration. The facility design allows for relatively easy 

changes between the square and circular configurations.

The goal of the initial characterization is to define the 

interaction region of interest where more refined and redundant 

measurements will be taken. These measurements will include 

hot-wire data to quantify the turbulence structure through the 

interaction region.

NASA/TM—2015-218841 1
a) α = 7.5°

b) α = 9.5°

Figure 1.—M = 2.0 oblique SWBLI oil flow.

Figure 2.—M = 2.5 Axisymmetric SWBLI.

(box indicates region of interest).

Nomenclature

A Area

CD Discharge coefficient

Cf Skin friction coefficient

CL Centerline

D Diameter

gc Proportionality constant

Hi Incompressible boundary-layer shape factor

Lt ASME bellmouth throat length (Figure 5)

M Mach number

N Number of redundant measurements (Table 1)

p Pressure

R Radius

R1 ASME nozzle ellipse major radius (Figure 5)

R2 ASME nozzle ellipse minor radius (Figure 5)

Rc Radius of curvature

Rair Gas constant for air

ReD Reynolds number based on diameter

ReDs Scaled Reynolds number (ReDs = ReD × 10E-06)

T Temperature or throat tap location (cm, Figure 5)

U Velocity

w Mass flow rate

xsup Axial coordinate relative to C-D nozzle throat

(Figure 6)

x,y,z Cartesian coordinates

x,r,θ Cylindrical coordinates

Greek Symbols

α Shock generator cone half-angle (deg)

β Ratio of ASME nozzle-to-approach pipe diameter

γ Ratio of specific heats for air (1.4)

δ Boundary-layer thickness

δ* Boundary-layer displacement thickness

δXi Uncertainty of measureand Xi

θ Boundary-layer momentum thickness

μ Molecular viscosity

ρ Density

Subscripts

0 Pertaining to plenum conditions

bm Pertaining to the ASME bellmouth

e Pertaining to boundary-layer edge condition

i Pertaining to ideal conditions

noz Pertaining to the C-D nozzle

t Pertaining to total conditions

th Pertaining to throat conditions

ts Pertaining to the test section

w Pertaining to wall conditions

Axisymmetric SWBLI

As previously mentioned, an axially symmetric SWBLI is the 

only practical way to ensure a two-dimensional flow in the 

mean. A number of axisymmetric SWBLIs have been 

investigated over the years. These include supersonic flow over 

a double-cone, over a cylinder-flare, an impinging-centerbody 

SWBLI, and the present configuration of an impinging-duct

SWBLI as shown in Figure 3.

The impinging duct configuration was chosen for two 

reasons. First, inasmuch as the intent of the investigation is to 

provide CFD validation data, this configuration allows for a 

relatively thick incoming boundary layer so highly resolved

NASA/TM—2015-218841 2
Figure 3.—Axisymmetric SWBLI configurations.

measurements are possible. And second, although not intended 

to mimic any particular application, it is of the same general 

configuration as a SWBLI occurring on the cowl surface of 

axisymmetric inlets with supersonic internal compression.

Previous investigations of this flow configuration include the 

development of integral flow models for solid and porous walls 

by Seebaugh et al. (Ref. 7). An experimental investigation by 

Seebaugh and Childs (Ref. 8) presented surface static and 

flowfield Pitot pressure measurements under Mach 2.82 and 

3.78 flow conditions with cone angles of 10°, 13°, and 15°. 

Rose (Ref. 6) acquired detailed turbulence measurements using 

hot-wire anemometry under Mach 3.88 flow conditions with a 

9° cone angle. Neither of the latter two studies, however, were 

considered to meet the criteria for CFD validation purposes as 

proposed by Reference 1.

Facility Description

The new 17 cm axisymmetric facility is located in Test Cell 

W6B at NASA GRC. W6B is a continuous flow supersonic 

facility with Mach number variation achieved by 

interchangeable fixed-geometry nozzle blocks. The plenum 

chamber is supplied with dry ambient temperature compressed 

air up to 377 kPa. The exhaust side of the tunnel is connected 

to lab-wide altitude exhaust which is maintained at less than 

13.8 kPa. The 17 cm Axi-SWT utilizes the same plenum 

chamber and exhaust as NASA GRC’s 15×15 cm SWT. A test 

section diameter of 17 cm was selected so as to maintain similar 

flow area as the 15×15 cm SWT. Figure 4 shows a section view 

of both facilities.

With reference to Figure 4(a), installation of the 15×15 cm 

SWT bellmouth requires removal of the 44 in. flanged bulkhead 

on the plenum chamber. To allow the facility to be reconfigured 

between the two configurations with a minimum of effort, the 

bellmouth for the 17 cm Axi-SWT was designed so as to only 

require removal of the 18 in. interface flange. A new bellmouth 

for the 15×15 cm SWT is currently in the design cycle to allow 

similar installation.

As illustrated in Figure 4(b), the 17 cm Axi-SWT required 

design and fabrication of three major components: the 

bellmouth, the convergent-divergent (C-D) supersonic nozzle, 

a) 15×15 cm SWT

b) 17 cm Axi-SWT

Figure 4.—Section view of W6B test facility.

and the test section. Beyond these basic components for the 

facility, the Shock Generator (SG) hardware is also required. A 

brief description of each component follows.

ASME Bellmouth

The bellmouth for the axisymmetric facility serves two 

purposes. First, it is used to provide a uniform, low Mach 

number flow to the C-D nozzle, and second, it is used to 

measure the total mass-flow through the facility:

wnoz CD,bm wnoz,i = ⋅ (1)

where wnoz,i is the ideal mass-flow given by:

2 ( 1)

( 1)

2

,0

,0

, 2

1 1 ⋅ γ−

− γ+





 



 ⋅ γ − ⋅ + ⋅ ⋅ ⋅ γ ⋅ = noz

t

t noz noz

air

c noz i M

T

p M A

R

g w (2)

Geometry

The elliptical bellmouth geometry is based on an ASME

Long-Radius Flow Nozzle with throat taps and is a scaled version 

of similar bellmouths used at NASA GRC. A schematic of the 

bellmouth and a photo of the actual hardware are shown in

Figure 5(a) and Figure 5(b), respectively. This design conforms 

to the Low-β Nozzle with Throat Taps illustrated in Figure II-III14 of Reference 9 with the following two exceptions. First, no 

approach pipe exists before the nozzle (Dapp = ∞), hence β =

Dnoz/Dapp=0. And second, the nozzle exit flow does not exhaust 

into a sudden expansion but rather a constant area diffuser.

a) Double-Cone b) Cylinder-Flare

c) Impinging-Centerbody d) Impinging-Duct

Plenum (Common) 44” Flange

18” Flange

Test Section #3

(Common)

Bellmouth

C-D Nozzle

Square Test

Section

Bellmouth

C-D Nozzle

Circular Test

Section

NASA/TM—2015-218841 3
NASA/TM—2015-218841 4 

a) Schematic 

b) Hardware 

Figure 5.—ASME bellmouth. 

ASME Nozzle Discharge Coefficient 

The discharge coefficient for the bellmouth was determined 

from a computational calibration performed on a geometrically 

similar nozzle. The details of the calibration are given in 

Reference 10. 

CD,bm  CD,M 0.5  f   M (3) 

where 

D bm

CD M

,

, 0.5 Re

6.73896   0.993003  (4) 

and 

  2 0.00863415 ( ) 0.999514 1- 0.2    f M Mbm (5) 

and 

bm

bm bm bm

D bm

U D



   Re ,  (6) 

For the current M = 2.5 C-D nozzle, the ratio of bellmouth 

throat area to nozzle throat area (Abm,th/Anoz,th) is 2.636, so the 

Mach number in the ASME bellmouth will be approximately 

Mbm,th = 0.21. 

C-D Nozzle 

A schematic of the C-D nozzle is shown in Figure 6. The 

requirements for the C-D nozzle design include: 

1) Exit Mach number of 2.5 

2) Inlet and exit diameter equal (17 cm) 

3) Length approximately the same as 1515 cm nozzles 

(~66 cm) 

The second requirement allows for the C-D nozzle to be 

replaced with a constant area duct so that the facility can also 

be run subsonically. 

The steps for designing the nozzle include: 

1) Definition of the inviscid, shock-free supersonic contour. 

2) Definition of the subsonic contour (contraction). 

3) Correction of the supersonic contour for B.L. growth. 

4) Adjustment of the subsonic contour. 

For the first step a Method of Characteristics (MOC) approach 

was used. To define the inviscid supersonic contour, the exit 

Mach number, the radius of curvature at the throat (Rc,th), and a 

function for the initial expansion are required. To minimize 

distortion of the sonic line at the throat, Rc,th should be large. 

But as Rc,th is increased, the correction for boundary-layer 

growth becomes more significant and the nozzle length is 

Figure 6.—C-D nozzle schematic. 
increased, thus a balance must be achieved. For the current 

nozzle, given the length constraints, Rc,th was selected as:

Rc th Rth = 8.0⋅ , (7)

where Rth is the nozzle radius at the throat. For the initial 

expansion, a parabolic function was chosen:

2

sup

2 ,

1.0 















⋅

















⋅ = +

c th th

th

th R

x

R

R

R

r (8)

where xsup is the axial coordinate with origin at the inviscid 

nozzle throat.

For the subsonic contour, the parabolic function for the initial 

supersonic contour was extended upstream to an arbitrary point. 

Then a 5th order polynomial function was specified to transition 

from the upstream constant area section to the parabolic section. 

A 5th order polynomial allows for continuous second 

derivatives of the contour.

There are a number of methods available to correct for the 

boundary-layer growth in a nozzle. The most common is to 

correct the contour by an estimate of the displacement thickness 

growth through the nozzle. For this nozzle, we chose to estimate 

the displacement thickness growth by performing a numerical 

simulation using the Wind-US flow solver (Ref. 11) in 

conjunction with the Menter Shear Stress Transport (SST)

turbulence model (Ref. 12). With reference to Figure 7(a), the 

computational domain included the plenum tank, ASME 

bellmouth, C-D nozzle, test section and dump diffuser. The 

resulting boundary-layer parameter variations through the 

facility are shown in Figure 7(b).

1

In this figure, the line labelled “Trans” is the location where 

the contour transitions from the 5th order polynomial function 

to the parabolic function. Between this location and the nozzle 

exit, the displacement thickness distribution was fit with a 6th

order polynomial and the nozzle contour was adjusted for 

displacement thickness growth. The final step was to reevaluate 

the 5th order polynomial coefficients to account for the adjusted 

downstream contour.

Test Section

The test section is basically a constant area cylinder. Two test 

sections have been fabricated. The first is instrumented with 

wall static taps and two opposing windows as shown in

Figure 8. The primary purpose of the windows is to allow access 

for probe setup and alignment of the shock generator 

centerbody. These windows will also be used to evaluate a 

dynamic skin friction film measurement technique.

1

The waves in the boundary-layer thickness (δ) are an artifact of the 

algorithm used to locate the boundary-layer edge.

a) CFD computational domain

b) Normalized B.L. parameters

Figure 7.—C-D nozzle B.L. correction (Rth = 5.235 cm).

Figure 8.—Test section schematic.

The second blank test section is a plain cylinder with 

provisions to mount the end flanges. This section will be 

modified at a later date to include optical access for a Particle 

Image Velocimetry (PIV) system that is currently being

designed. A photo of the C-D nozzle and test section are shown 

in Figure 9. Currently the windows in the test section are 

aluminum blanks which will be modified to accept additional 

instrumentation once the extent of the interaction region has 

been defined. The interior surface of the window is contoured 

to conform with the circular test section.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

-15 -10 -5 0 5 10 15 20 25

Normalized B.L. Parameters

xsup/Rth

δ/Rth

δ*/Rth

θ/Rth

Inlet

Trans

Throat

Exit

NASA/TM—2015-218841 5

 
Figure 9.—C-D nozzle and test section.

Shock Generator

The shock generator (SG) is a cone-cylinder located on the 

centerline of the wind tunnel as shown in Figure 10. The 

investigation will initially focus on two SG configurations. 

Both have a cylinder diameter of 3.135 cm, however, the cone 

angles differ with one having a half-angle of 10.0° and the other 

having a half-angle of 13.5°. The former is expected to generate 

a relatively weak interaction, while the latter will generate a 

stronger interaction with the possibility of creating boundarylayerseparation. The axial placement of the cone tip was chosen 

so that the conical shock generated by the cone impinges at 

approximately the center of the window. The window is placed 

in the downstream half of the test section to minimize the length 

of the cantilevered SG and also to allow for maximum 

boundary-layer development.

The centerbody diameter was chosen to minimize blockage 

of the cantilevered probe configuration. The concern was that 

in the vicinity of the interaction, the presence of the probe 

support might cause a local unstart of the wind tunnel. The 

relatively small centerbody diameter, however, causes closecoupling of the shock-wave and expansion which results in a 

rapid pressure rise and fall. Once these two baseline interactions 

are documented, a larger centerbody will be considered as a 

future test case.

The SG is cantilevered from the end of the test section as 

show in Figure 11. For the initial measurements, the cone 

configuration is changed by replacing the entire cone-cylinder. 

A cylinder with removable tips is currently being designed to 

allow changing the cone configuration without requiring 

realignment of the cylinder.

Instrumentation

For the initial characterization of the interaction regions, 

conventional pressure instrumentation is used. This consists 

primarily of wall static pressure taps and Pitot probes for 

flowfield measurements. Figure 12 shows the general layout of 

this instrumentation. The throat of the ASME bellmouth has 

eight equally spaced static pressure taps. Similarly, the C-D 

nozzle also has eight equally spaced static pressure taps located 

near the exit plane.

a) α = 10.0°

b) α = 13.5°

Figure 10.—Shock generator schematic.

Figure 11.—Shock generator assembly.

Figure 12.—Pressure instrumentation.

Window CL

3.135

31.542

49.530

Dimensions in cm 8.500

Window CL

3.135

49.530

8.500

33.122

Dimensions in cm

Bellmouth (8)

Test Section (156)

C-D Nozzle (8) Press. Probe (12)

Exhaust (6)

Test Section #3

NASA/TM—2015-218841 6
Figure 13.—Test section static pressure taps.

These taps are located 2.54 cm downstream from the end of the 

nozzle contour and 3.81 cm upstream of the start of the test 

section (x = 0 plane).

The test section has 156 static pressure taps laid out as shown 

in Figure 13. The first tap for all the stations begins 5.08 cm 

downstream from the test section inlet plane. Along the top 

(AA) and bottom (BB), there are 49 equally spaced taps. Along 

CP and CS there are 23 equally spaced taps. The axial spacing 

for the taps along AA, BB, CP, and CS are 1.28 cm. There are 

three equally spaced taps along DP, DS, EP, and ES. The axial 

spacing at these stations is 35.56 cm.

With reference to Figure 12, the flow from the circular test 

section dumps into what is referred to as Test Section #3 which 

is a 25.4×25.4 cm square section. Up to six base pressures can 

be measured where the flow from the circular test section exits 

as a free-jet into the square section. Test Section #3 also has a 

probe traversing capability. Plates on the top and bottom of this 

section translate in the traverse horizontal direction. An actuator 

that can be mounted on either the top or bottom plate allows a 

probe to be translated in the vertical direction. Thus, the 

combination of these allows a probe to be located anywhere 

within the test section cross-plane. Both the horizontal and 

vertical directions are driven by remotely actuated stepper 

motors. The position of each axis is measured with digital 

encoders. Currently, positioning the probe in the axial direction 

is a manual operation.

In addition to surveying in the axisymmetric test section, the 

facility can also be configured to survey the exit plane of the

C-D nozzle. An interior photo of Test Section #3 showing a 

probe setup for a boundary-layer survey at the C-D nozzle exit 

is shown in Figure 14. The nose of the probe sting is electrically 

isolated from the support rod using a nylon threaded rod and 

washer. This allows probe wall touch to be established by 

electrical continuity.

In addition to the aforementioned instrumentation, total 

temperature and total pressure in the plenum chamber are also 

recorded. Inasmuch as the total temperature is at ambient 

conditions and can drift over time, the facility controls are setup 

to automatically adjust the plenum total pressure to maintain a 

constant Reynolds number.

Figure 14.—C-D nozzle exit plane survey.

TABLE 1.—MEASURAND UNCERTAINTY

Uncertainty Considerations

A detailed uncertainty analysis is still in progress but the 

measurand uncertainties have been estimated and are 

summarized in Table 1. These uncertainties include the sensor 

uncertainty as well as the uncertainty associated with the signal 

processing in the data acquisition system (Ref. 13). The variable 

N represents the number of redundant transducers associated 

with a measurand. These uncertainties will be combined with 

estimates of the probe (static tap and Pitot probe) measurement 

uncertainties which will then be propagated through the 

calculation procedures.

AA

BB

CP CS

ES

DS

EP

DP

VIEW AA-BB VIEW LOOKING UPSTREAM

AA1 AA25 AA49

BB1 BB25 BB49

EP1 EP25 EP49

DP1 DP25 DP49

CP1 CP23

FLOW

5.08 cm

i Description Xi δXi Ν δXi Units

1 Plenum total temp. T t,0 1.39 2 0.982 °K

2 Plenum total pressure p t,0 0.0689 1 0.0689 kPa

3 Bellmouth throat static pressure p bm 0.0255 8 0.0090 kPa

4 Bellmouth throat diameter D bm 0.0013 1 0.0013 cm

5 Bellmouth discharge coefficient C D,bm 0.0025 1 0.0025 -

6 C-D nozzle exit plane static pressure p noz 0.0621 8 0.0219 kPa

7 Probe position, x x prb 0.0064 1 0.0064 cm

8 Probe position, y y prb 0.0064 1 0.0064 cm

9 Probe position, z z prb 0.0064 1 0.0064 cm

10 Probe pitot pressure p prb 0.0621 1 0.0621 kPa

NASA/TM—2015-218841 7
Results and Discussion

ASME Bellmouth and C-D Nozzle Condition

The facility was initially setup to survey the C-D nozzle exit 

plane as shown in Figure 14. Prior to performing the surveys, 

the nozzle Mach number was measured. The Mach number was 

calculated from the isentropic relation:

























− 













 ⋅ 















γ − =

















γ

γ−

1

1

2

1

,0

noz

t noz p

p M (9)

where pt,0 is the plenum total pressure and pnoz is the average of 

the eight static pressures located at near the nozzle exit. The

C-D nozzle exit plane Mach number as a function Reynolds 

number is shown in Figure 15. The uncertainty in the Mach 

number measurement based on values in Table 1, which 

excludes the pressure tap uncertainty, is estimated to be less 

than 0.05 percent over the Reynolds number range plotted. The 

design Mach number of 2.5 is achieved at a Reynolds number 

of approximately 4.0E+06. This Reynolds number was 

subsequently selected as the operating point for the 

characterization of the facility.

The mass-flow through the facility was measured with the 

ASME bellmouth by the method described in Reference 10. 

The mass-flow as a function C-D nozzle Reynolds number is 

shown in Figure 16. The uncertainty in the mass-flow 

measurement based on values in Table 1, which excludes the 

pressure tap uncertainty, is estimated to be less than 0.4 percent 

over the Reynolds number range plotted. The mass flow at 

ReD,noz = 4.0E+06 is approximately 4.7 kg/s.

With reference to Figure 13, Pitot pressure surveys were 

taken along vertical (AA, BB) and horizontal (CP, CS) planes. 

These surveys, plotted in terms of Mach number, are shown in 

Figure 17. From this plot, the core profile is seen to be quite 

uniform with good agreement with the bulk Mach number from 

Figure 15. The largest deviation in Mach number occurs near 

the centerline which is somewhat typical of C-D nozzles.

The boundary-layer region of the profiles shown in Figure 17

was analyzed to calculate relevant boundary-layer parameters. 

The boundary-layer profiles plotted in terms of velocity 

normalized by the boundary-layer edge velocity and in terms of 

van Driest (Ref. 14) scaled variables are shown in Figure 18(a) 

and Figure 18(b), respectively. With reference to Figure 18(b), 

the profiles generally follow the law-of-the-wall, but perhaps 

with a slightly elevated slope which is likely a result of 

distortion by the strong favorably pressure gradient in the 

nozzle. The average boundary-layer parameters from the four 

profiles are summarized in Table 2 (EXP, x = –3.81 cm). Also 

shown in this table for comparison are the results of the Wind 

CFD analysis (WIND, x = –3.81) used to correct the nozzle 

contour. Note that this is an approximate comparison since the 

Wind results were for the inviscid nozzle contour which results 

in a slightly lower Mach number.

Figure 15.—C-D nozzle bulk Mach number.

Figure 16.—17 cm Axi-SWT mass flow.

Figure 17.—Mach number at C-D nozzle exit, ReDs,noz = 4.0.

2.484

2.486

2.488

2.490

2.492

2.494

2.496

2.498

2.500

2.502

2.504

0.0 1.0 2.0 3.0 4.0 5.0 6.0

C-D Nozzle Mach Number

C-D Nozzle Reynold Number, ReDs

RUN 12, SWP 1

All Preliminary Data 

Taken at ReDs=4.0

y = 1.176x - 0.039

R2 = 1.000

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Mass-flow, w (kg/s)

C-D Nozzle Reynold Number, ReDs

RUN 12, SWP 1

Linear (RUN 12, SWP 1)

NASA/TM—2015-218841 8
a) Normalized velocity profile

b) Law-of-the-wall

Figure 18.—Boundary-layer profiles at C-D nozzle exit.

Figure 19.—Wall pressure distribution through test section.

2For clarity, the distributions s are shifted by Pw/Pt,0 = 0.01.

TABLE 2.—BOUNDARY-LAYER PARAMETERS

The measured boundary-layer thickness at the nozzle exit is 

approximately 0.61 cm, which is somewhat thinner than the 

results of the Wind analysis (0.69 cm). The integral properties, 

however, are in quite good agreement. The incompressible 

shape factor at the nozzle exit, which is typically about 1.3 for 

a fully turbulent, zero pressure gradient boundary layer, is 

slightly elevated and likely a result of the transition from strong 

favorable pressure gradient to mild adverse pressure gradient at 

the nozzle exit.

Shock-Free Flow Through Test Section

After completion of the preliminary measurements of the 

nozzle, the facility was reconfigured with the test section as 

shown in Figure 4(b). Without a shock generator, the flow 

through the test section is supersonic developing pipe flow with 

friction, or Fanno line flow.

Wall static pressure distributions at a Reynolds number of 

ReDs,noz = 4.0 are show in Figure 19.

2 As expected, the pressure 

rises slightly through the test section. There is observed to be 

some slight scatter in the data and also slight differences 

between the upper (AA) and lower (BB) distributions in the 

second half of the test section. This will be investigated further 

by checking alignment with the nozzle and also by rotating the 

test section 180° and repeating the measurements. In fact, one 

aspect of this investigation will be to document and quantify the 

sensitivity of the results to tunnel assembly procedure and 

configuration.

With reference to Figure 13, Pitot pressure surveys were 

taken along vertical (AA, BB) and horizontal (CP, CS) planes 

at the last static pressure tap location (x = 66.0 cm) at a scaled 

Reynolds number of ReDs,noz = 4.0. These surveys, plotted in 

terms of Mach number, are shown in Figure 20. At this station 

the Mach number in the core has dropped to about 2.4. The 

profiles at CP and CS show a slightly higher than core point at 

the edge of the boundary layer which is absent from the profiles 

at AA and BB. This has been traced to a small forward facing 

step at the downstream end of the window. The windows are 

currently being modified to eliminate this step.

The boundary-layer profiles at the test section exit plotted in 

terms of velocity normalized by the boundary-layer edge 

velocity and in terms of van Driest (Ref. 14) scaled variables 

are shown in Figure 21(a) and Figure 21(b), respectively. The 

average boundary-layer parameters at the test section are 

summarized in Table 2. The edge Mach number is reduced to

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0 10 20 30 40 50 60 70

pw/pt,0

x (cm)

AA

BB

CP

CS

DP

DS

EP

ES

0.06

0.06

0.06

0.06

0.06

0.06

0.06

x (cm) M e δ (cm) δ* (cm) θ (cm) H i Cf

WIND -3.81 2.46 0.693 0.162 0.041 - -

EXP -3.81 2.50 0.608 0.161 0.041 1.39 0.00186

EXP 43.2 2.44 1.312 0.334 0.090 1.33 0.00157

EXP 66.0 2.44 1.465 0.389 0.106 1.31 0.00152

NASA/TM—2015-218841 9

 
Figure 20.—Mach number at test section exit, ReDs,noz = 4.0.

a) Normalized velocity profile

b) Law-of-the-wall

Figure 21.—Boundary-layer profiles at test section exit.

M = 2.38 and the boundary-layer thickness has approximately 

doubled through the test section to 1.37 cm. The profiles used 

to accumulate these data were the same as the profiles at the 

nozzle exit and it can be seen that there is a lack of resolution 

at the boundary-layer edge. These profiles will be repeated as 

part of the quest for high fidelity measurements. With reference 

to Figure 21(b), the profiles, which have been developing in a 

mild adverse pressure gradient, follow the theoretical

law-of-the-wall better than the nozzle exit profiles. 

Flow Through Test Section With Shock Interaction

The final set of preliminary measurements was performed 

with the two shock generator configurations shown in

Figure 10. The wall static pressure distributions on the upper 

(AA) and lower (BB) positions are shown for the 10.0° and 

13.5° shock generators in Figure 22(a) and (b), respectively. To 

estimate the shock impingement location, surface flow 

visualization was performed using an oil and florescent dye 

mixture. These results are shown at the top of the figures. For 

both cases, symmetry between the upper and lower pressure tap 

positions is observed to be quite good. As anticipated, the 

interaction region for both cases is located in the vicinity of the 

window centerline. The magnitude of the peak pressure and the 

axial extent of the interaction region is, as expected, greater for 

the stronger interaction case. For the 10.0° case, the oil flow 

shows a light line indicating the upstream influence of the shock 

impingement, but no flow separation appears to be present. This 

line also corresponds with the initial rise in wall pressure. For 

the 13.5° case, the oil flow shows a small pooling of oil 

indicating flow separation. The upstream edge of the pooling 

also corresponds with the initial rise in wall pressure.

Pitot pressure profiles were taken at twelve axial stations

through the interaction region at position BB for the α = 10.0° 

and 13.5° cases. The location of the profiles are indicated in 

Figure 22 and the profiles at all 12 stations are shown in

Figure 23. The first profile is located at x = 43.2 cm and the 

remaining profiles are equally spaced at 1.28 cm increments. 

The profiles plotted are the Pitot pressure normalized by the 

plenum total pressure. The wall static pressure normalized by 

the nozzle exit static pressure (Pw/Pnoz) is also plotted as a dotted 

line. At the first station it is reasonable to assume that the wall 

static pressure is constant across the boundary-layer. Boundarylayer parameters were calculated for this station and are 

summarized in Table 2. One of the conclusions from Reference 

8 is that when the ratio of upstream boundary-layer thickness to 

duct radius is greater than 0.1, a planar two-dimensional 

analysis cannot be used to predict flow separation because 

changes in the boundary-layer properties are larger for conical 

incident shock waves in an axisymmetric duct. For the present 

case, the ratio of boundary-layer thickness to duct radius is 

0.154 indicating that the axisymmetric analysis must be used.

NASA/TM—2015-218841 10
The incident shock plotted in the figures is based on inviscid 

theory using the cone angle and Mach number at the cone tip. 

This cone tip Mach number was interpolated from 

measurements made at the nozzle and test section exits. For the 

first four profiles, horizontal lines are drawn from where the 

incident shock crosses the data station to the Pitot profile. For 

both cases, these lines are in excellent agreement with the shock 

position indicted by the Pitot probe. Also indicated by vertical 

lines on the first four profiles is the normal shock total pressure 

ratio associated with Mach number at the cone tip. This agrees 

well with the measured normalized Pitot pressure below the 

incident shock.

The reflected shock shown in the plots is based on the 

location inferred from the Pitot pressure profiles. As expected, 

the presence of the boundary layer moves the virtual origin of 

the reflected shock upstream of the incident shock impingement 

location.

a) α = 10.0°

b) α = 13.5°

Figure 22.—Wall pressure through interaction region.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

35.0 40.0 45.0 50.0 55.0 60.0 65.0

pw/pt,0

x (cm)

AA

BB

Window Leading Edge

Window Centerline

Window Trailing Edge

1 2 3 4 5 6 7 8 9 10 11 12

CL

0.00

0.02

0.04

0.06

0.08

0.10

0.12

35.0 40.0 45.0 50.0 55.0 60.0 65.0

pw/pt,0

x (cm)

AA

BB

Window Leading Edge

Window Centerline

Window Trailing Edge

1 2 3 4 5 6 7 8 9 10 11 12 CL

NASA/TM—2015-218841 11
a) α = 10.0°

b) α = 13.5°

Figure 23.—Pitot profiles development through interaction region, ReDs,noz = 4.0.

NASA/TM—2015-218841 12
Concluding Remarks

A new facility for investigating a Mach 2.5, 2-D shock-wave 

boundary-layer interaction has been presented along with 

preliminary measurements characterizing the flowfield. The 

data generated, once vetted by uncertainty estimates and 

redundant measurements, is intended to be used for CFD 

validation efforts. The preliminary results indicate that the 

facility is suitable for this purpose. From these preliminary data, 

refined flowfield measurement stations and surface dynamic 

pressure locations will be identified. Once the mean flow field 

has been characterized by conventional pressure measurements, 

constant-voltage hot-wire anemometry and PIV will be used to 

characterize the turbulence field throughout the interaction 

region.

References

1. Settles, G.S., and Dodson, L.J., 1994, “Supersonic and 

Hypersonic Shock/Boundary-Layer Interaction 

Database,” AIAA Journal, Vol. 32, No. 7, pp. 1377-1383.

2. Settles, G.S., and Dodson, L.J., 1991, “Hypersonic 

Shock/Boundary-Layer Interaction Database,” NASA CR 

177577.

3. Aeschliman, D.P., and Oberkampf, W.L., 1998, 

“Experimental Methodology for Computational Fluid 

Dynamics Code Validation,” AIAA Journal, Vol. 36,

No. 5, pp. 733-741.

4. Benek, A.J., Suchyta, C.R., and Babinsky, H., 2013, “The 

Effect of Wind Tunnel Size on Incident Shock Boundary 

Layer Interaction Experiments,” AIAA Paper 2013-0862, 

51st AIAA Aerospace Sciences Meeting, Grapevine, TX.

5. Bruce, P.J. K., Burton, D.M. F., Titchener, N.A., and 

Babinsky, H., 2011, “Corner Effect and Separation in 

Transonic Channel Flows,” J. Fluid Mechanics, Vol. 679, 

pp. 247-262.

6. Rose, W.C., 1973, “The Behavior of a Compressible 

Turbulent Boundary Layer in a Shock-Wave-Induced 

Adverse Pressure Gradient,” NASA TN D-7092.

7. Seebaugh, W.R., Paynter, G.C., and Childs, M.E., 1968, 

“Shock-Wave Reflection from a Turbulent Boundary 

Layer with Mass Bleed,” J. Aircraft, Vol. 5, No. 5,

pp. 461-467.

8. Seebaugh, W.R., and Childs, M.E., 1970, “Conical 

Shock-Wave Turbulent Boundary-Layer Interaction 

Including Suction Effects,” J. Aircraft, Vol. 7, No. 4,

pp. 334-340.

9. Bean, H.S. (ed), 1971, Fluid Meters: Their Theory and 

Application, 6th Ed., American Society of Mechanical 

Engineers, New York.

10. Davis, D.O., Friedlander, D.J., Saunders, J.D., Frate, F.C., 

and Foster, L., 2012, “Calibration of the NASA GRC 16

Mass Flow Plug,” FEDSM2012-72266, 2012 ASME 

Fluids Engineering Division Summer Meeting, Puerto 

Rico, USA.

11. Towne, C., “Wind-US User’s Guide, Version 2.0,” Glenn 

Research Center, NASA/TM—2009-215804, Oct. 2009.

12. Menter, F.R., “Two-Equation Eddy Viscosity Turbulence 

Models for Engineering Applications,” AIAA Journal, 

Vol. 32, No. 8, 1994, pp. 1598-1605.

13. Blumenthal, P.Z., 1995, “A PC Program for Estimating 

Measurement Uncertainty for Aeronautics Test 

Instrumentation,” AIAA Paper 1995-3072, 31st AIAA 

Joint Propulsion Conference and Exhibit, San Diego, CA.

14. van Driest, E.R., 1951, “Turbulent Boundary Layer in 

Compressible Fluids,” J. Aeronautical Sciences, Vol. 18, 

pp. 145-160.

NASA/TM—2015-218841 13