This document may be of more than historical interest,
because "Attachment D" represents the organizers' judgement
of the best/most relevant test cases available to them in
1990. "Attachment E" contains instructions on how to run the
various test cases, and these may still be useful
suggestions. Some anachronisms have been removed.
_____________________________________________________
Attachment D (to project Newsletter 2)
Collaborative Testing of Turbulence Models
LIST OF PROPOSED TEST CASES
1. INTRODUCTION
In addition to the comments from all Collaborators requested
in Newsletter no. 1, we have asked some Collaborators to
make informal reviews of the data for certain types of flows
on which they are experts. The list below is an
interpretation (mainly due to Bradshaw) of the replies
received. The object is provide a range of test cases which
almost all modellers should be able to do, plus some harder
ones representing practical problems. If nobody produces
calculations for some of the practical cases, that is in
itself a piece of evidence about the state of turbulence
modelling - which the funding agencies will note!
We do not propose to give each new test case a code number -
name of author and/or type of flow will be used instead.
2. EXISTING DATA LIBRARIES
The basis for the test cases is still the 1980/81 Stanford
meeting data library, compiled in packed ASCII format by
Brian Cantwell. In some cases we will supply more recent
data sets as direct substitutes. The 1.44 MB IBM PC disks,
serial nos. D1-D3 contain nearly all 80/81 cases. The
exceptions are 0411 (circular cylinder), 0441 (stalled
airfoil), 0511 (wing-body junction), 0512 (curved duct) and
8602 (shock/BL interaction): these five are very long files
but can be requested from Bradshaw. All files have names
equal to the 80/81 cases, with prefix "F", e.g. F0141 for
80/81 case 0141, Samuel/Joubert boundary layer. Files with
updated data are on Disk D4 onward and have suffix "A": for
example, unpacked and interpolated data for 80/81 case 0141
are on file F0141A.
The compressible-flow test cases have been taken from the
latest in the review series initiated by Hans Fernholz and
John Finley, AGARDograph 315 "A survey of measurements and
measuring techniques in rapidly distorted compressible
turbulent boundary layers" by H.H. Fernholz, P.J. Finley,
J.P. Dussauge and A.J. Smits. We have all the data on disk,
but only the most popular test cases are being circulated:
the full data set is available from NASA Sci. and Tech.
Info. Ctr., phone (301) 621-0204, or from the AGARD National
Centers listed on p. 1-3 of AGARDograph 315. Note that AGARD
publications may not be officially available outside NATO
countries.
3. DATA FORMATS
3.1 Data from the Stanford 1980/81 library tape
The 80/81 library is in Brian Cantwell's standard format:
all values are given as integers, "intval", in the range 0
to 10000, with maximum and minimum values in separate files,
so the real value is "(min)+(intval)*(max-min)/10000": see
the extract from the 80/81 Proceedings at the end of this
Attachment. The enclosed Disks 1-3 differ from the tape only
in that each case occupies only one file: the beginnings and
ends of the original tape files, counting serially from
"file 1" in the first test case, are labelled in the disk
file. Note that internal references to "file" numbers start
from no. 1 in each test case.
In some cases, the 80/81 files have been superseded by
"plain-format" files whose names are those of the 80/81
files, with suffix "A". We have not used Cantwell's
normalized format in the new data. In Disk D4, File F0141A
contains interpolated initial data and a skin-friction plot
for the Samuel-Joubert boundary layer in increasing adverse
pressure gradient, 80/81 case 0141: File 8501A contains
Papamoschou and Roshko's data for compressible mixing
layers, to supersede the correlation in 80/81 case 8501. At
least two more updates of 80/81 files will be distributed in
"plain-format" style, with instructions for use as test
cases. If in doubt, use a file with suffix "A" rather than
the original.
3.2 Compressible data from the Fernholz & Finley review.
The AGARDograph 315 data are in conventional format, though
that on the disks is an improvement over that in the
AGARDograph - the double quote used for exponentiation has
been replaced by the standard "E". The present organizers
have added a few lower-case comments but made no other
changes: in particular we have NOT inserted the "skip then
read" values discussed in the next section. File names look
similar to 80/81 compressible cases but are distinct. The
internal notation should be obvious, but note that "Pitot"
pressure is the total pressure downstream of a normal shock.
3.3 New test cases
For the new test cases, the effort available has allowed us,
at most, to edit the data files so that a given line
contains either alphabetic information (titles, etc) or
numerical values, but not both. That is, modellers will
merely have to edit out, or arrange their data-reading
programs to ignore, lines that begin with alpha characters,
and then use free-format reads for numerical data. We assume
that all Collaborators will be able to read free format
numbers separated by spaces, e.g.
1729 2.71828 6.6E-23 ........
We are adopting one of two courses. For the shorter data
files such as correlations, which are more likely to be
edited and plotted than read into the prediction program
directly, we are, at most, inserting a "%" sign as the first
character of every alphabetic line (this is the "comment"
character in TeX and in the PROPLOT plotting utility:
modellers who prefer another "ignore this line" sign should
be able to edit the "%" sign into something else). For
longer files, we are inserting a standard "skip then read"
line before each cluster of alphabetic lines followed by
data lines, as in the following example..........
3 5 .... (2I3) skip three lines, then read five
In the second century of the Christian era, the Empire of
Rome comprehended the fairest part of the earth, and the
most civilised portion of mankind.
4004
8008
8080
8086
80286
1 2 .... another skip/read pair
94.305
30.30
................The modeller's program must be set up to
read the two numbers on the "skip/read" line (NS, NR), then
read NS lines into a dummy string, then read NR lines, then
read the next skip/read pair.
4. TEST CASE DATA - MARCH 1990 DISTRIBUTION
To focus modellers' efforts and to give an overview of
results as soon as possible, we have nominated a few
"Priority" cases for early attention.
4.1 Incompressible-flow "Priority" cases.
4.1.1 Simulation results
A major breakthrough since 1980/81 is the availability of
simulation data, potentially including all possible
turbulence statistics. Data for the NASA Ames simulations of
a constant-pressure boundary layer (Spalart, J. Fluid Mech.
187, 61) and a 2D duct ("channel") flow (Kim, Moin and
Moser, e.g. J. Fluid Mech. 194, 15) are together in file
SIMUL1.DAT on Disk D4. These are nominally easy test cases,
but provide a check on individual terms in turbulence models
which cannot be measured directly.
4.1.2 80/81 test cases
Of the cases in the Stanford 80/81 data library, the Samuel-
Joubert boundary layer in increasing adverse pressure
gradient (case 0141) tests the ability to handle rapidly-
growing flows, which can defeat transport equations for
length scale (or time scale or dissipation).
The homogeneous turbulence test cases (0371-0376) 80/81 are
replaced by fewer and more recent data, except for the
classical Comte-Bellot/Corrsin results (0371) for decay of
isotropic turbulence.
The plane mixing layer (case 0311) may be a difficult one,
since its turbulence structure is very different from that
of a boundary layer. We need to check which, if any, models
can handle it. As in 80/81 calculations should start from a
well-developed, but low-Re, turbulent boundary layer and be
run long enough for the growth rate to asymptote.
The backward-facing step with inclined top wall was a
"predictive" test case in 80/81, the measurements being
reported by Driver and Seegmiller (AIAA J. 23, 163, 1985).
We request that modellers should also compare with the same
authors' data for a parallel top wall.
4.3 Compressible flow "Priority" cases.
There were comments that the unusually high wall temperature
in entry test case (iv) may have contributed to scatter
between codes using different properties for air. The
Fortran programs for generating the Van Driest skin-friction
correlation, circulated with Newsletter no. 1, use the
following properties in SI units:-
Gas constant 287.2, ratio of specific heats 1.4, Prandtl
number 0.72, viscosity 1.458E-6*T**1.5/(T+110.4).
Modellers using substantially different properties should
check their influence.
Stanford 80/81 test cases 8101 and 8201 are for the
compressible boundary layer in zero pressure gradient; 8101
requires skin friction on an adiabatic wall over a range of
Mach numbers, and 8201 the skin friction on a cooled wall
over a range of temperatures at M=5. In view of the scatter
in Entry test cases (iii) and (iv) of the present effort, a
full re-run of 8101 and 8201 seems desirable - with the
additional requirement of Stanton number for case 8201.
The two-stream mixing layer, case 8501 (new data in file
F8501A), is the only flow which undoubtedly suffers from
compressibility effects at non-hypersonic Mach numbers. None
of the methods presented at the 1981 Stanford meeting could
predict these effects - except by inserting M-dependent
coefficients which were not checked for accuracy in wall
flows. Despite the remarks about the legitimacy of
computerized adjustment of coefficients in Section 3.2 of
Newsletter no. 1, we request that, to start with, people
should use the exactly the same model for the mixing layer
and the boundary layer - i.e. no flow-dependent adjustments
as such. This still allows the coefficients to be functions
of any Mach number that can be legitimately defined both in
the boundary layer and in the mixing layer, e.g. (turbulent
k.e.)1/2 / (speed of sound), but the "entry case" boundary-
layer computations should of course be repeated if a model
is changed to deal with the mixing layer.
The boundary layer and mixing layer are nominally self-
similar flows, so that initial conditions need not be
standardized - but, again, runs should be long enough for
self-similarity to be reached.
____________________________________________________________
Attachment E - Instructions for "March 1990" test cases (for
a discussion, see Section 4 of Attachment D, above).
1. Contents of disks.
Disk D1 contains incompressible data from the Stanford 80/81
Data Library (with a few omissions)
Disks D2 and D3 contain compressible data from the Stanford
80/81 Data Library (again with a few omissions).
Disk D4 contains new incompressible data, mainly amendments
of or replacements for the 80/81 test cases.
Disk D5 contains new compressible data, notably four cases
from the AGARDograph 315 data library.
2. General instructions
"Priority" cases are marked by an asterisk at the start of
the subsection: others are at present optional but may be
raised to priority level to settle later disputes. It is
desirable that all modellers should attempt case 0141
(section 3.1), but apart from this modellers may concentrate
on either the incompressible or the compressible cases. To
minimise the amount of paper to be circulated, only a very
few plots per case are required to begin with. For cases
which are expensive or awkward to compute, please keep
complete results for each measurement station, in a form
that can be plotted at short notice for further discussion.
Experimental or simulated results should be always be
plotted on the same graph as the computations, and two
graphs should be fitted on to each page (A4 users please
leave at least 25mm bottom margin!) Each graph should carry
the modeller's name, the name of the data file (usually an
index number from 80/81 or AGARDograph 315, or an
abbreviation of the experimenter's name), and where
necessary a description of the sub-case (e.g. "BL" or "DUCT"
in file SIMUL1). Velocity profiles should be plotted as U
against y, not y against U. Don't use color!
3. Incompressible test cases
*3.1 Boundary layer in increasing adverse pressure gradient.
This is 80/81 case 0141 (Samuel and Joubert, J. Fluid Mech.
66, 481, 1974). The 80/81 file, F0141 on Disk D1, is just for
general background: use file F0141A on Disk D4 for corrected,
smoothed and interpolated data. Original turbulence profiles
are poorly defined near the boundary-layer edge. Note that
pressure data are an accurate numerical integral of dp/dx
data and that "dissipation" at the first station has been
assumed equal to production.
Start at x=1.04m (first station with turbulence
measurements: mean profiles in F0141A are interpolated
between x=.855 and x=1.16). Continue to x=3.4m (normal
pressure gradient may be significant for x > 2.9m).
Plot calculated local skin-friction coefficient against x,
compared with the first of the three tabulations in F0141A.
Also plot max. shear stress at each x, normalized by local
edge velocity, compared with values from uv profiles in
F0141A.
3.2 Boundary layer and duct simulation data
The object in both cases is to plot and compare profiles of
the highest-order turbulence quantities your model generates
(even if you do not normally print them out), normalized by
friction velocity and delta (boundary-layer thickness or
half-width of duct). For example, for two-equation models
plot the dissipation and the turbulent diffusion of kinetic
energy; for stress-equation models, plot the "fast" and
"slow" pressure-strain terms in the uv equation and their
sum, the turbulent transport ("diffusion") of uv, and the
dissipation. We doubt the value of comparing with the
individual terms in the dissipation equation, especially at
low Reynolds numbers.
*3.2.1 Run a constant-pressure boundary layer calculation to
match the simulation data (Spalart, J. Fluid Mech. 187, 61),
which nominally replace 80/81 test case 0612 (Wieghardt's
flow 1400 from the 1968 Stanford meeting).
Three sets of profiles are given, all at low Reynolds number
(Retheta = 300, 640 and 1400). This creates difficulties
about the decay of initial conditions (necessarily at
Retheta of at least 300-400), as well as uncertainty about
low-Reynolds number effects as such. Therefore we recommend
modellers to check that their predicted "wake parameter"
asymptotes to, or at least runs parallel to, Coles' data
correlation at Re < 10000 (for consistency this check should
be done assuming Coles' values of the log law constants,
K=0.41 and C=5.0, whether or not the calculation agrees with
them). In the table below, "dU" is defined as the maximum
deviation of U/u* from the log.law at given Retheta, where
u* is the friction velocity: thus dU is (2/K) times the wake
parameter. The skin friction coefficient cf is given to help
in setting up initial conditions: note that half a cosine
curve is a fair approximation to a shear-stress profile.
R,th 425 590 855 1150 1450 2050 2650 4150 5650 8600 11500
105cf 590 524 464 426 398 363 340 308 290 269 255
dU 0 .58 1.12 1.46 1.76 2.10 2.34 2.59 2.68 2.68 2.68
One way of allowing initial conditions to decay is to start
at Retheta = 300 (failing which, the lowest Reynolds number
at which your model allows turbulence to survive) and march
forward, increasing the viscosity at each step so that
Retheta remains constant, until the results cease to change:
then fix the viscosity and run on to Retheta = 600 and 1400.
Plot cf and H against Retheta, as well as plotting your
highest-order quantities or budget terms to compare with the
simulation.
*3.2.2 Run a two-dimensional duct calculation at the same
pressure gradient (or surface shear stress) as the
simulation (Kim, Moin and Moser, e.g. J. Fluid Mech. 194,
15). A run at the same mass flow rate (i.e. using the
simulation results as the initial velocity profile of a
marching calculation) may be easier to set up and should be
adequate, since all results are to be normalized by friction
velocity.
3.3 Homogeneous turbulence
3.3.1 Run 80/81 case 0371 (Comte-Bellot and Corrsin, J.
Fluid Mech. 25, 657, 1966: see Disk D1). Specification as in
80/81 Proceedings, p. 408: initial conditions are u2=0.306
m2/s2, v2=0.254, w2=0.254, epsilon=15.52m2/s3. Assume
standard atmospheric conditions, e.g. kinematic viscosity =
1/66500 m2/s, and run to t=0.35 sec. Plot turbulent kinetic
energy against time and deduce decay exponent with free
choice of virtual origin (expected value -1.25+0.06).
3.3.2 Calculate two cases of return to isotropy after
irrotational plane strain, using data of Le Penven et al.
for (Frontiers in Fluid Mechanics, S.J. Davis and J.L.
Lumley, eds., Springer 1985, p.1): see Disk D4, files
PENVEN.DAT and PENVEN.FOR (for skip and read). The two Le
Penven flows, for different signs of stress tensor invariant
III, were nominally uniform over the tunnel cross section at
exit from the distorting duct, with negligible shear
stresses in the chosen axes. Deduce initial dissipation, or
other length-scale equivalent used in your model, from given
initial Reynolds number, assuming kinematic viscosity =
1/66500 m2/s. Plot the decay trajectory as invariant II
against invariant III.
*3.3.3 Calculate development of turbulence in a simple
shear, using the data of Tavoularis and Karnik (J. Fluid
Mech. 204, 457, 1989): see file TAVOU.DAT on Disk D4. The
Tavoularis flow is again nominally homogeneous over the
cross section, but note that a spatially-developing shear
flow cannot remain homogeneous because the x-wise distance
that fluid travels in a given time depends on local mean
velocity: thus, even if development in time were
homogeneous, inhomogeneity over the cross-setion would
arise. Perform a genuine spatial-marching computation, with
a shear layer thickness of at least 0.3m (the tunnel
height). Plot q**2, -uv (equal to K12*q**2), and microscale
lambda. Assume that dissipation is 15 nu u2 / (lambda)2,
both to get initial dissipation and to deduce lambda from
calculations.
3.4 Free shear layers
With the exception of the round jet, we propose these as
"blind" test cases. The Reynolds numbers and other boundary
conditions are approximately those of well-respected
experiments in the literature, and later detailed
comparisons can be made with these experiments.
*3.4.1 Run calculations for the round jet in still air at
Reynolds numbers, based on nozzle exit velocity and diameter
(d), of 10000 and 100000 (note that product of exit velocity
and diameter is [momemtum flux/(.785 rho)]1/2). At each
Reynolds number, report best fit to spreading rate in
60