“Stepping Stone Test-Case 05: Nozzle with
rectilinear, forced shock oscillation (UFAST case)”
Author: Lionel Temmerman
NUMECA Int. S.A.
5, avenue Franklin Roosevelt
B-1050 Brussels
Belgium
e-mail: lionel.temmerman@numeca.be
Tel : 00.32.2.642.28.25
Fax : 00.32.2.647.93.98
12 October 2009
Contract No. ACP8-GA-2009-233710-ATAAC
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Table of Contents
1 Introduction .................................................................................................................................... 3
2 Classification of the test case ......................................................................................................... 3
3 Geometric description .................................................................................................................... 3
4 Description of available reference data .......................................................................................... 4
4.1 Steady case ............................................................................................................................. 4
4.2 Unsteady case ......................................................................................................................... 5
5 Design and assessment parameters .............................................................................................. 5
6 Description of errors and known uncertainties ................................................................................ 5
7 Physical phenomena and modelling challenges ............................................................................. 6
8 Relevant modelling techniques ...................................................................................................... 6
9 Flow and boundary conditions........................................................................................................ 6
9.1 Steady case ............................................................................................................................. 6
9.2 Unsteady case ......................................................................................................................... 7
10. Non-dimensional quantities ......................................................................................................... 7
11 Grids ............................................................................................................................................ 8
12 Computational guidelines ............................................................................................................. 8
13 Pre- and post-processing tools ..................................................................................................... 8
14 Mandatory and optional results .................................................................................................... 9
14.1 Steady case ........................................................................................................................... 9
14.2 Unsteady case ....................................................................................................................... 9
15 Others .......................................................................................................................................... 9
16. References ................................................................................................................................. 9
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1 Introduction
Summary description of the test case including its history (i.e. has it been used in previous projects
or workshops).
This case has been experimentally investigated by Bruce and Babinsky (2008) and extensively studied
numerically using RANS, hybrid RANS/LES and LES (see Bruce et al, 2010) during the UFAST project, a
FP6 European project. The case is also described in Doerffer (2009). The case consists of a naturally
growing turbulent boundary on the floor of the tunnel interacting with the tunnel’s normal recovery
shockwave. Different geometry convergent-divergent nozzle liners are used to vary the test section free
stream Mach number as required. Excitation of the shock wave is achieved by rotating an elliptical shaft
mounted in the tunnel downstream of the interaction to form a second throat with a continuously varying
cross sectional area. Measurements were performed by Bruce and Babinsky (2008) for three flow conditions
M = 1.3 and Re* = 14770, M = 1.4 and Re* = 13600, M =1.5 and Re* = 13000. Re* is the Reynolds
number based on the displacement thickness * and M is the Mach number.
The main features of this flow are the unsteady interaction of the shock with the boundary layer and the
corner recirculating flows as well as the shock-induced separation. The challenge in simulating this flow is in
accurately predicting these phenomena. Numerical investigations carried out in the FP6 UFAST European
project showed that CFD had major difficulties in capturing these flow features for the cases at M = 1.4 and
M = 1.5 in steady mode. RANS and URANS solutions, obtained with the Spalart-Allmaras model for
example, were shown to be asymmetric. Further investigation showed that a likely cause for this nonsymmetric behavior is the unability of current turbulence models to properly predict the corner flow
separation. It is hoped that more complex models, such as those investigated in ATAAC, will be able to
improve this matter.
2 Classification of the test case
States here whether it is a stepping stone case being studied or if it is an application challenge
case and to which stepping stones it relates.
This is a stepping stone case. It relates to the following Application Challenges:

DLR F6 (AC02);

HiRETT (AC03);

UAV configuration (AC05);

F5 configuration (AC06).
3 Geometric description
This should contain a clear definition of the geometry (mathematical formula, clean CAD in a wellknown format such as IGES or CATIA) and the computational domain size (important in external
aerodynamics for example). Dimensions must be clearly specified. SI units are preferred. Please
upload CAD file or others describing the geometry.
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The general experimental arrangement is shown in Figure 1 here below. The shock is held at the centreline of
the viewing window by controlling the settling chamber pressure. The convergent-divergent nozzle liners are
interchangeable to obtain the different Mach numbers of 1.3, 1.4 and 1.5. The walls of the wind tunnel are
solid. The tunnel exhausts to atmosphere. Accurate coordinate profiles (x, y, z) for the convergent-divergent
nozzles are available (Table 1). Table 2 summarizes the dimensions of the working section.
Recovery
Shock wave
M = 1.3, 1.4, 1.5
Eliptical cam shaft
acting as 2nd throat
Figure 1: Overview of the wind tunnel working section.
M
File name
1.3 UCAM_M1.3_liner.dat
1.4 UCAM_M1.4_liner.dat
1.5 UCAM_M1.5_liner.dat
Table 1: File names of the convergent-divergent coordinate profiles.
Test section height
178 mm
Test section width
114 mm
Distance from nozzle throat to shock 516 mm
Table 2: Wind tunnel dimensions
4 Description of available reference data
Describe here the data available for comparison and the storage format. Please upload all
necessary data on the website.
4.1 Steady case
Available data includes:

Schlieren photographs at M = 1.3, 1.4 and 1.5 (jpg images)
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
Centreline pressure measurements (mean values) at M = 1.3, 1.4 and 1.5 for –70 mm < x < 70 mm
(xls spreadsheet)
 Centreline streamwise velocity (mean and fluctuating) from LDA (xls spreadsheet):
 5 inflow profiles for M = 1.3, 1.4 and 1.5, -200 mm < x < 0 mm, 0.1 mm < y < 10 mm
 15 interaction profiles for M = 1.3, 1.4 and 1.5, -30 mm < x < 40 mm, 0.1 mm < y < 30 mm
 Surface oil visualizations at M =1.3 (floor only) and M = 1.4, 1.5 (floor and side walls) (jpg images)
where, here, x = 0 represents the mean streamwise shock location and y = 0 is the wind tunnel floor.
The data are contained in the file steady_interaction.zip
4.2 Unsteady case
Available data includes:





High speed Schlieren images at M =1.3, 1.4 and 1.5 for frequencies = 16, 23, 43, 70 and 90 Hz (avi
movies and jpg images)
Unsteady shock dynamics data (cycle-averaged position, velocity and acceleration) at M =1.3, 1.4
and 1.5 for frequencies = 16, 23, 43, 70 and 90 Hz (xls spreadsheet)
Downstream pressure variation at cam at M =1.4 and 1.5 for frequencies = 16, 23, 43, 70 and 90 Hz
(xls spreadsheet)
Phase-averaged centerline pressure measurements at M =1.4 and 1.5 for frequencies = 16, 23, 43, 70
and 90 Hz (xls spreadsheet), -70 mm < x < 70 mm
Phase-averaged centerline mean streamwise velocity at M =1.4 and 1.5 for frequency = 43 Hz (xls
spreadsheet), -40 mm < x < 40 mm, 0.1 mm < y < 15 mm
where, here, x = 0 represents the mean streamwise shock location and y = 0 is the wind tunnel floor.
The data are contained in the file unsteady_interaction.zip.
5 Design and assessment parameters
List here design or assessment parameters. This points to global parameters of interest such as
aerodynamic coefficients, heat load, noise levels, etc. It is useful, from an engineer perspective, to
assess the uncertainty in these parameters for a given modelling approach.
6 Description of errors and known uncertainties
Describe errors and known uncertainties such as geometry inaccuracies (undefined trailing edges
e.g.), measurement uncertainties, known problems affecting the data (3d effect, repeatability
issues, etc), missing data, etc
Several uncertainties can potentially affect the outcome of a CFD computation and its comparison with the
experimental data. There are two major known uncertainties:


The position of the laminar-to-turbulence transition is unknown
There is no information available on the level of turbulence at inflow
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7 Physical phenomena and modelling challenges
List the main physical phenomena and the main modelling challenges.
The main modelling issues are:
 Pressure-induced separation
 Shock-induced separation
 Corner separation
The main challenge resides in correctly predicting the corner flow separation.
8 Relevant modelling techniques
Specify whether the case is considered for one or different
(RANS/DES/URANS or others).
modelling approaches
This case is suitable for steady and unsteady simulations.
9 Flow and boundary conditions
In this section, the flow and boundary conditions have to be clearly defined (SI units preferred). In
case of missing data (e.g. unavailability from experiments), clear guidelines on how to define these
data should be given. It can also happen that, for the geometry considered, different flow
conditions can be considered, the one on which the partners must focus should be clearly
specified.
9.1 Steady case
The fluid used is air. The walls must be treated as solid.
The inflow boundary condition are specified for each test case in Table 3. P0 and T0 are total pressure and
total temperature, respectively. There is no information avalaible on the turbulence level at inlet as well as
where the laminar-to-turbulence transition is taking place. The Mach number quoted in Table 3, as in
other places of this document, is calculated from tunnel floor static pressure measurements at 30 mm
upstream from the shock location.
M
P0, inlet
T0, inlet Inflow velocity direction
(1,0,0)
1.3 205000 Pa 293 K
147500
Pa
293
K
(1,0,0)
1.4
(1,0,0)
1.5 171000 Pa 294 K
Table 3: Inflow boundary conditions.
The outflow pressure has to be set at a value such that the shock is located at x = 516 mm downstream of the
nozzle throat which corresponds, for the meshes described in Section 11 to 330 mm upstream of the outflow
boundary. Table 4 here below shows values of the Static pressure obtained with the Fine/TurboTM solver for
different RANS models. These values may also depend on other parameters such as the grid or the CFD
solver used for example, and are thus given as an indication.
Table 5 lists the characteristic parameters of the incoming boundary layer for all 3 Mach numbers measured
at 30 mm upstream of the shock location.
RANS models
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M
SA
SST
v2-f
k-
1.3 110000 Pa 113000 Pa 105000 Pa 110000 Pa
1.4 83900 Pa
92000 Pa 96000 Pa
1.5
Table 4: Sample values for the specification of the outflow boundary condition.
M  (mm) * (mm)
H
Cf
 (mm)
Re*
4.6
0.52
(0.63)
0.42
(0.40)
1.24
(1.54)
14700
0.00225
1.3
0.49 (0.59) 0.40 (0.38) 1.22 (1.55) 13600 0.00214
1.4 4.7
0.50 (0.58) 0.40 (0.38) 1.24 (1.54) 13000 0.00223
1.5 4.5
Table 5: Characteristics parameters of the incoming boundary layer for all three Mach numbers, measured
at x = -30 mm using the setup for steady tests. Incompressible values are given with compressible values in
parentheses.
For Table 5, the definition of the quantities is as follow:



M is the Mach number (
) based on a, the speed of sound and u0, the local freestream velocity
 is the boundary layer thickness
* is the boundary layer displacement thickness, defined as:
o
for the incompressible value
for the compressible value, with 0, the freestream density
o

 is the boundary layer momentum thickness, defined as:
o
for the incompressible value
o



for the compressible value
is the boundary layer shape factor
is the Reynolds number based on the boundary layer displacement thickness
is the friction coefficient defined as
where w is the wall shear stress.
Please, take note that those quantities are defined at 30 mm upstream of the mean location of the
shock.
9.2 Unsteady case
In this case, the unsteadiness is driven by imposing an oscillatory outflow pressure (sinusoidal function)
whose mean value is obtained from the corresponding steady computation, whose amplitude is 4-5 % of the
outlet mean pressure and whose frequency is selected among the following values 16, 23, 43, 70 and 90 Hz
measured in the experiment. All others boundary conditions remain as defined in Section 9.1 for the steady
case.
10. Non-dimensional quantities
List and define all non-dimensional quantities.
Dimensional and non-dimensional quantities are defined in the different sections of this document.
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11 Grids
Describe the mandatory grid or family of grids (if a grid convergence study is required) (SI units
preferred). The format of the grids posted onto the website should be either widely used (e.g cgns,
plot3d, etc) or accompanied by a few lines of pseudo-code to allow partners to read the mesh. In
order to allow the majority of partners to contribute to the test case, a structured mesh is
mandatory. Unstructured meshes can also be made available. If a mesh is not provided or liberty is
given to partners to generate their own grids, guidelines have to be provided. Please upload
mandatory grid(s).
There are 3 meshes (see Table 6 here below) available on the website for this test case, one for each Mach
number. The dimensions are mm. These meshes are structured and stored in plot3d multiblock ASCII
format and structured cgns format. The plot3d files should be uncompressed prior usage. The difference
between the three meshes is the shape of the inflow nozzle.
M
1.3
1.4
1.5
1.3
1.4
1.5
Nx
265 nodes
265 nodes
265 nodes
265 nodes
265 nodes
265 nodes
Ny
129 nodes
129 nodes
129 nodes
129 nodes
129 nodes
129 nodes
Nz
file name
file format
97 nodes Ufast_channel_M1.3f.cgns structured cgns
97 nodes Ufast_channel_M1.4f.cgns structured cgns
97 nodes Ufast_channel_M1.5f.cgns structured cgns
97 nodes Ufast_channel_M1.3f.g.gz
ascii plot3d1
97 nodes Ufast_channel_M1.4f.g.gz
ascii plot3d1
97 nodes Ufast_channel_M1.5f.g.gz
ascii plot3d1
Table 6: Mesh description.
While the use of the meshes listed in Table 6 is mandatory, additional meshes can be generated using either
these meshes as a basis or the throat profile listed in Table 1 and available on the website. The dimensions of
the cross section are given in Table 2. Please refer to the meshes listed in Table 6 for the exact length of the
computational domain and shape of the inflow.
12 Computational guidelines
List all important aspects of how to drive the computations. Important information such as, but not
limited to, initial flow field, spanwise extent, minimal sampling time, time-step, what criteria makes
a grid convergence study satisfactory, etc must be given here.
For the unsteady case (M = 1.4 and f = 90 Hz), 10 cycles are necessary in URANS to reach a periodic state
in term of the shock oscillation.
13 Pre- and post-processing tools
Describe any pre- and/or post-processing provided to the partner. These tools have to be uploaded
on the website.
1
Pseudo code to read the multiblock ascii plot3d format:
READ(10,*) NBLOCK
READ(10,*) (NX(n),NY(n),NZ(n),n=1,NBOCK)
DO M = 1,NBLOCK
READ(10,*) (((X(I,J,K,M),I=1,NX(M)),J=1,NY(M)),K=1,NZ(M)),
(((Y(I,J,K,M),I=1,NX(M)),J=1,NY(M)),K=1,NZ(M)),
(((Y(I,J,K,M),I=1,NX(M)),J=1,NY(M)),K=1,NZ(M))
ENDDO
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No tools.
14 Mandatory and optional results
Provide a description of the data expected from each partner contributing to the test case,
including pictures if necessary. Provide the format in which you need the data for cross-plotting
purposes. Specify which data are mandatory and which are optional. If necessary, please upload a
template on the website. In case pictures are requested for qualitative comparisons (e.g. color
contours, structures visualisations), it is preferred that the coordinator collects the necessary data
from all partners and generate the pictures her/himself. This will allow homogeneous comparison
on a per test case basis and will improve the readability of presentations and publications.
14.1 Steady case
The mandatory case is M = 1.3. Once successful, participants are invited to compute the case at M = 1.4 and
1.5. Meshes described in Section 11 must be used. Grid convergence studies are welcome and encouraged.
Pressure and velocity profiles as listed in Section 4.1 must be provided at all locations in ascii format (x y z
quantity) with one file per location. A picture of the shock taken in the middle section as well as a view of
the streamlines showing the separation bubbles in the duct corners at the shock location are also required
(pictures + corresponding data set in ascii format and a description of the format). Partners are free to report
additional data or figure they feel of interest.
14.2 Unsteady case
The mandatory case corresponds to M =1.4 and a frequency of 43 Hz. The mesh for the case M = 1.4
described in Section 11 must be used and has been designed with this particular case in mind.
A second case to be computed is M = 1.4 and a frequency of 90 Hz. For this case, the mesh given in Section
11 can be use as initial mesh but is likely to be too coarse due to the fact the that the shock oscillation only
occurs on a limited distance of approximately 6 mm around the shock mean location.
Data and movie corresponding to the experimental data described in Section 4.2 have to be reported. Partners
are free to report additional data or figures they feel of interest.
15 Others
Please enter here any information that you will feel is needed for the complete definition of the test
case but which does not enter into any of the previous sections.
Let me know as soon as possible if you encounter any problem.
Regarding mesh generation issues, if you decide that you want to generate a new mesh or if you are not
happy with the current mandatory mesh, please contact and let me know the reasons behind this choice as
this may benefits all participants to this test case as well as the outcome.
16. References
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Bruce, P.J.K., Babinsky, H. (2008) “Unsteady shock wave dynamics”, J. Fluid Mech., vol. 603, pp. 463-473.
Bruce, P.J.K., Babinsky, H., Tartinville, B., Hirsch, Ch. (2010) “An experimental and numerical study of an
oscillating transonic shock wave in a duct”, to be presented at 48th AIAA Aerospace Sciences Meeting,
Orlando, Florida, USA.
Doerffer, P. (editor) (2009) “UFAST Experiments: Unsteady effects of shock wave induced separation –
Data Bank”.
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