12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

IMPACT OF GRID RESOLUTION ON HYBRID RANS-LES OF TRANSITION
IN A SEPARATED BOUNDARY LAYER

Eike Tangermann
Department of Aerospace Engineering
University of the Bundeswehr Munich
85577 Neubiberg, Germany
eike.tangermann@unibw.deMarkus Klein
Department of Aerospace Engineering
University of the Bundeswehr Munich
85577 Neubiberg, Germany
markus.klein@unibw.de

ABSTRACT

where the flow close to the wall is treated by URANS whereas
LES is applied further away from the wall. Thereby the transition above the separation bubble is captured by the LES mode
as well as the upper part of the boundary layer, which carries most turbulence energy as shown in previous work by theauthors (Tangermann & Klein (2021, 2020)). Its benefit is areduced computational effort while maintaining a good levelof accuracy.
For the application of DNS, the grid cell width is prescribed by the smallest turbulent scales. All other approaches
which involve modeling turbulence partially or completely allow a coarser cell width within a limited range. In computations using RANS it is very common practice to perform astudy of grid dependence and quantify the inaccuracy of thesolution induced by the grid resolution. In that case the grid
dependence is caused purely by errors induced from the discretization of the flow field. When LES is involved, however,the solution depends not only on errors from discretization but
also on modeling errors resulting from the cutoff scale representing the smallest resolved turbulent structures. Since in
LES the grid typically is selected relatively fine compared tothe structures of the mean flow field, the error from modeling usually has more weight than the one from discretization.
Nevertheless, grid dependence studies in LES are very expensive in terms of computational effort and therefore not often
performed. The quality of results is rather assured by criteria
based on the resolved structures.
In hybrid RANS-LES different criteria of mesh resolution apply depending on the location. Within the present
work, hybrid RANS-LES simulations of laminar separation on
a NACA0018 airfoil have been performed at 4◦ angle of attack
and a Reynolds number of Re = 80000 in order to investigate
the impact of grid resolution on the flow prediction. These
conditions offer a generous spacing between separation, transition and reattachment and therefore allow for the observationof these phenomena in a more isolated way. For validation andcomparison purposes, the hybrid RANS-LES data are supplemented by DNS for reference and 2D URANS results. The
latter is considered in order to observe the underlying RANS
model of the hybrid simulations individually.

Laminar separation followed by transition and reattachment on a wing at low Reynolds number has been simulated using hybrid RANS-LES (DDES, IDDES) on differently
refined meshes. The different stages of this process are investigated with respect to mesh resolution in order to determine their particular requirements with the primary focus on
the transition process, for which the development of turbulent
fluctuations and their length scales is discussed. For reference
DNS data of the flow is presented.

INTRODUCTION
In low Reynolds number flow, boundary layers tend to
separate early while still in laminar state. Following the laminar separation on airfoils or similar objects, regions of separated flow occur above which the transition process to turbulent conditions takes place. Often the turbulent fluctuations
bring momentum towards the wall and thereby initiate a reattachment of the flow which continues in a fully turbulent
boundary layer.
The accurate prediction of this process by numerical simulation is challenging, which mostly depends on the treatmentof turbulence in terms of how it is modeled and which part isresolved. Upstream of the separation no turbulence is present
and the model needs to account for the laminar flow and remain inactive. Therefore, a supplementary model is necessary
which, depending on the turbulence model approach, detects
or even predicts the transition process. The range of possible turbulence treatment is very wide in this context. Already
RANS can predict the flow at acceptable accuracy if the integral behavior is more important than local details of transition and turbulence (Catalano & Tognaccini (2010)). On theother hand, for low Reynolds numbers and relatively simple
geometries LES and even DNS are achievable but still require
high computational effort (Galbraith & Visbal (2010)). These
turbulence-resolving methods do not only offer a better prediction of the turbulent part of the boundary layer but especiallyof the transition process.
Hybrid RANS-LES offers an intermediate approach,1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
match the surrounding mesh decreases for the finer meshes.
Consequently, the non-dimensionalized cell width x+ and z+
also also follows a factor of two between the meshes. Since
the mesh is based on equilateral hexahedra, x+ and z+ have approximately the same value. The values for all meshes are provided by Table 1. Only Meshes 1 to 4 have also been applied
for two-dimensional URANS as Mesh 4 already is too coarse.
The 2D mesh is directly derived from the three-dimensional
meshes, it consists of the periodic boundary plane.
The values of x+ and z+ may appear rather small and already suitable for a DNS. However, the common criteria as
for example provided by Piomelli & Chasnov (1996) are formulated for a fully turbulent boundary layer. In the present
case, the resolution of gradients around flow separation andthroughout the transition is the key factor and it will be shownthat these phenomena require an even finer grid spacing.
All simulations have been performed using the OpenFOAM flow solver toolbox. The filtered or averaged NavierStokes equations are considered in an incompressible formulation and discretized with the finite volume method. Pressureand velocity are coupled in a PISO loop with iterative timeadvancement. The discretization is of second order accuracy inspace and time. For time stepping a backward scheme has beenused. In the hybrid RANS-LES computations, the convective
terms of the momentum equation have been discretized using
the linear upwind stabilized transport (LUST) scheme, which
blends central discretization with 25% second order upwind
for increased robustness. Convective transport in the turbulence model equations has been discretized with the vanLeer
TVD scheme. In the DNS, a pure second order central scheme
has been applied.
As mentioned above, the turbulence has been modeled with a hybrid RANS-LES approach, namely detachededdy simulation (DES) in the variants delayed DES (DDES)(Spalart et al., 2006) and improved delayed DES (IDDES)(Shur et al., 2008). As underlying RANS model the SST
model has been selected featuring two transport equations
which in LES mode effectively transform into a one-equation
model. Upstream of the transition, the turbulence model needs
to be deactivated as otherwise the RANS-modeled turbulent
boundary layer would not be able to separate. Only laminarflow will separate under these conditions. Therefore, the γ -Reθ
model according to Langtry & Menter (2009) has been coupledwith the *DES approaches. By solving two additional transport equations, the model prescribes transition and activates
production of modeled turbulence energy. In a more complex
configuration, this approach also could predict transition in an
attached boundary layer which, however, would then feature
fully modeled turbulence.
In the present setup resolved turbulent structures arise
from the shear layer above the separation bubble. The idea
behind DES, treating the flow near the wall by RANS andswitching towards LES once the turbulent structures can be resolved, requires that this transition zone is located in the LES
zone. As will be shown below, DDES fails to resolve the transition process once the grid becomes too coarse. The resulting
flow is undefined URANS with a few resolved scales. In thiscase IDDES, which additionally features a mode of wall modeled LES, still switches into LES and maintains resolved fluctuations in the boundary layer. Therefore the simulations on
the coarser grids haven been performed using IDDES, whereas
DDES is restricted to the finer meshes.
It should be noted that this application could easily betreated with pure LES and also the DNS has been performed on
the same mesh. Hybrid RANS-LES does not necessarily bring

Figure 1: Structure of the mesh around the wing, coarsest

mesh.

GEOMETRY AND NUMERICAL SETUP
The wing is a quasi two-dimensional geometry of
NACA0018 airfoil. Its extension in span-wise direction b ishalf the chord length c with periodically coupled planar boundaries. This span allows the solution to develop independentlyof the periodicity. In the remaining two directions the wingis surrounded by a square shaped farfield boundary which islocated 20 times c from the wing. In previous work this distance was found sufficient to keep the flow in focus unaffectedfrom the boundary condition. The flow approaches the wing at
an angle of attack of 4◦ and a Reynolds number, based on thechord length, of Re = 80000.
The computational mesh is based on hierarchical refinement of hexahedral cells towards the wing surface. Hanging
nodes are avoided by inserted polyhedral cells in the interface
region between the different refinement levels. For an appropriate resolution of the boundary layer in wall normal direction, cell layers are placed immediately on the surface ensuring y+ well below unity in the first cell and a smooth transition
towards the surrounding mesh. Figure 1 illustrates the coarsest of the involved meshes. Leading edge and trailing edge
are refined further than the central part of the wing in order tocapture the strong gradients upstream of the stagnation point
and the geometric features of the slightly blunt trailing edge.
The phenomena of separation, transition and re-attachment all
take place in the uniformly resolved part between these refinedzones.
All meshes follow the same structure but feature different levels of refinement on the wing surface. The cell widthparallel to the wall is doubled in each step of coarsening. The
normal resolution, whereas, is similar as the criterion of y+should not be violated. Thereby the number of cell layers toTable 1: Key figures of the involved meshes (cell width∆/c, non-dimensionalized width x+ , y+ , z+ of first cell
layer).
∆/cy+x + , z+Mesh 1

2D,3D

1/2048< 0.4

1.6

Mesh 2

2D,3D

1/1024< 0.4

3.0

Mesh 3

2D,3D

1/512

< 0.5

6.3

Mesh 4

2D,3D

1/256

< 0.25

10.9

Mesh 5

3D

1/128

< 0.5

21.8

Mesh 6

3D

1/64

< 0.7

43.6
2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

DDES - Mesh 1

DNS

DDES - Mesh 2

DDES - Mesh 3
DDES - Mesh 1

DDES - Mesh 4

IDDES - Mesh 4
DDES - Mesh 3
IDDES - Mesh 5

IDDES - Mesh 6
IDDES - Mesh 5
Figure 3:

Mean eddy viscosity fields together withboundary layer properties: mean separation bubble (orange), 99%-thickness δ99 (light gray), displacement
thickness δ ∗ (black), momentum thickness Θ (darkgray).
IDDES - Mesh 6
ations. The DNS as a reference shows very fine scales which
are not reproduced in the *DES. Considering that DDES on
Mesh 1 features an even finer resolution than the DNS, which
has been obtained on Mesh 2, this fact needs to be attributed
purely to the spatial discretization scheme, which blends injust a small amount of second order upwind in the *DES. The
structures of larger scales remain comparable up to Mesh 5.
By refining the cells, more and more smaller structures fill the
space between the large structures. Mesh 6 clearly approaches
the limit of applicability as also the large structures cannot be
resolved entirely. Only parts of the characteristic horseshoe
vortices are visible in the plot.
Also the transition process shows significant differences
between the cases. The finer cases with *DES show shear
layer Kelvin-Helmholtz instabilities in very straight lines before they break up into three-dimensional turbulence. The
coarser the grid becomes, the sooner this breakup occurs. On
the other hand, the DNS also does not show straight vortices.
The shear layer instabilities immediately appear slightly wrinkled almost comparable to the coarser meshes.
The effect of the turbulence models on the flow fields canbe measured by the levels of eddy viscosity, which is shownin Figure 3 together with properties of the boundary layer. It
needs to be noted that the color is scaled logarithmically to alsovisualize the contributions of different magnitudes. In all cases
the model is turned off until after the flow separates. Together
with the resolved transition, the sub-grid model also becomes
active triggered by the γ -ReΘ model. Once active, the case of

Figure 2: Instantaneous view of the flow field.

Isosurface from Q-criterion colored by stream-wise velocity (white-red) and regions of separated flow (blue).

an advantage in computational efficiency at these conditions of
low Reynolds numbers. However, the present setup has been
selected precisely because it is possible to perform simulations
with all these approaches at bearable computational effort for a
detailed comparison before moving to configurations at higher
Reynolds number beyond reach for LES and DNS.
In order to separate the effects of refinement between LES
and the underlying RANS model, also URANS simulations
have been performed. They are kept purely two-dimensional
due to the planar nature of the flow. In these cases turbulence
is modeled using the SST model with γ -Re − θ transition modeling exactly as the configuration from the *DES setup.

RESULTS AND DISCUSSION
A first overview to the range of solutions obtained fromthe different mesh resolutions can be seen from the plots of
instantaneous flow features in Figure 2. It shows iso-surfaces
from Q-criterion for selected cases together with indications ofseparated flow regions. All cases produce the general processof separation, transition and re-attachment but with clear devi-3

Probability of separation [-]1

Displ. Thickness δ*/c [-]12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

DDES, Mesh1
DDES, Mesh2
DDES, Mesh3
DDES, Mesh4
DNS, Mesh2

0.8
0.6
0.4

SST, Mesh1
SST, Mesh2
SST, Mesh3
0.015 SST, Mesh4
DNS, Mesh2
0.01
0.02

0.005
0
0

0.2

0.2

0.4

0.6

0.8

1

x/c [-]
0

0.1

0.2

0.3

0.4

0.5
x/c [-]

0.6

1

0.7

0.8

0.9

Displ. Thickness δ*/c [-]0
1

IDDES, Mesh4
IDDES, Mesh5
IDDES, Mesh6
DNS, Mesh2

0.8
0.6

0.025

DDES, Mesh1
0.02 DDES, Mesh2
DDES, Mesh3
0.015 DDES, Mesh4
DNS, Mesh2
0.01
0.005
0
0

0.1

0.2

0.3

0.4

0.5
x/c [-]

0.6

0.7

0.8

0.9

1

0.3

0.4

0.5
x/c [-]

0.6

0.7

0.8

0.9

1

0.4
Displ. Thickness δ*/c [-]Probability of separation [-]

0.025

0.2
0
0

0.1

0.2

0.3

0.4

0.5
x/c [-]

0.6

0.7

0.8

0.9

1

Figure 4: Probability of separated flow along the upper

0.025

IDDES, Mesh4
0.02 IDDES, Mesh5
IDDES, Mesh6
DNS, Mesh2
0.015
0.01
0.005
0
0

0.1

0.2

wing surface.

Figure 5: Boundary layer displacement thickness δ ∗ /calong the upper side of the wing.

Shape Factor H [-]DDES on Mesh 4 clearly behaves different as the eddy viscosity is far higher than in the other cases. Here the model goes
into URANS mode suppressing resolved turbulent structuresby high eddy viscosity.
The other configurations from Mesh 1 to Mesh 4 show
very similar levels of eddy viscosity with a slight maximum
in the region of the greatest displacement thickness before reattachment and where the separation bubble becomes thinner.
Within the separation bubble eddy viscosity also gets convected upstream leading to the pattern which can be seen in
the plots. In Mesh 5 the eddy viscosity is slightly higher as
significantly more structures need to be covered by the model.
Finally, Mesh 6 brings the IDDES to its limits. The eddy viscosity drops rather low and, as will be shown below, the prediction of the turbulent boundary layer becomes less accurate.
The key feature of this flow is the flow separation which
initiates the entire process. In ideally laminar freestream conditions as they can be found in the present setup, the separation occurs in a straight line which is hardly affected by processes further downstream. The re-attachment, however, takes
place in turbulent flow and therefore appears very unsteady.
In the following turbulent boundary layer, also local separation is present. It can be seen best in the plot from Mesh 6 inFigure 2 as the separated spots are covered but still present in
the other plots. Investigating the separation in the mean flow
field may become misleading. Instead, Figure 4 shows thetime-averaged probability to encounter separated flow along
the chord. The initial separation produces a steep rise. Its
location varies significantly depending on the configuration.
This is not an effect of the turbulence model as it occurs in
the laminar region. Actually, this behavior is purely affectedby the mesh resolution and, in comparison with DNS, by thediscretization scheme, which both change the capability to resolve gradients of pressure and velocity.
After the initial separation, a range of fully separated flow
appears in all cases. The first stage of re-attachment is thencaused by the growing diameter of the shear layer vortices
leading to a decrease of the mean separation probability. Oncea vortex breaks up into smaller scales, the trend to re-attach
stops, instead the fraction of separated flow increases. When

8
7 SST, Mesh1
SST, Mesh2
6 SST, Mesh3
5 SST, Mesh4
4 DNS, Mesh2
3
2
1
0
0
0.2

0.4

0.6

0.8

1

Shape Factor H [-]Shape Factor H [-]x/c [-]
8
7 DDES, Mesh1
DDES, Mesh2
6 DDES, Mesh3
5 DDES, Mesh4
4 DNS, Mesh2
3
2
1
0
0
0.1
0.2

0.3

0.4

0.5
x/c [-]

0.6

0.7

0.8

0.9

1

8
7 IDDES, Mesh4
IDDES, Mesh5
6 IDDES, Mesh6
5
DNS, Mesh2
4
3
2
1
0
0
0.1
0.2

0.3

0.4

0.5
x/c [-]

0.6

0.7

0.8

0.9

1

Figure 6: Boundary layer shape factor H = δ ∗ /Θ along

the upper side of the wing

the turbulent boundary layer forms, the probability of separation decays to a every low level but above zero as embedded
patches of separated flow are still present. Towards the trailingedge, the trend to separation slightly increases.
This process is produced by most cases. Only the DDES
on Mesh 4, which remains in URANS mode, does not predictthe dip of separation probability as the breakup into resolved
turbulence is missing. Mesh 1 produces a curve closer to the
DNS. The other cases up to Mesh 4 show a quantitatively very4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
similar behavior with the onset of the re-attachment processslightly upstream of the DNS. Also breakup takes place sooner
but the turbulent boundary layer is reached in accordance with
the DNS. The coarsest Meshes 5 and 6 also show the process
but the quantitative deviations are stronger. Mesh 6 shows asignificantly higher rate of separated flow within the turbulent
boundary layer. The general trend of the *DES cases to predict
the onset of re-attachment sooner is supposed to be connectedwith the observation that the shear layer vortices remain moreplanar than observed from the DNS. Therefore, they can growslightly faster and initiate re-attachment before breaking up.
A closer look to the properties of the boundary layer isprovided by Figures 5 and 6 showing displacement thickness
δ ∗ and shape factor H = δ ∗ /Θ along the upper side of thewing. Besides results from the turbulence resolving cases,
also results from 2D URANS are plotted to give an indication
how far the underlying RANS model in the hybrid simulations
could provide reasonable results. As long as the flow remains
in a mostly two-dimensional structure, the results are in good
agreement. Towards the rear part the prediction becomes lessaccurate. The shape factor of the turbulent boundary layer issignificantly mispredicted by URANS. Further can be seen,that with Mesh 4 the URANS is not at all capable of producing the flow process, for which reason no results from coarser
meshes have been considered.
In the turbulence-resolving simulations a coarser meshresolution appears applicable since three-dimensional effects
are covered. Even the DDES with Mesh 4, which effectively
is close to a 3D URANS, provides better results - of course
at a far higher total cell count than all 2D RANS meshes presented here. The general trend in Figure 5 is an overprediction of displacement thickness by *DES compared to the DNS.
This, again, is expected to be attributed mainly to the spatial
discretization as it already appears far upstream of the model
activation. In terms of the shape factor, the attached parts of
the laminar and turbulent boundary layers are captured very
well. The increase of the shape factor prior to transition occurs slightly upstream of the DNS as could be expected fromthe sooner separation. The drop towards the turbulent attachedpart occurs similar to the DNS. The finer meshes tend to show
this process further downstream than the coarser ones.
As seen from the quantities discussed above, the transition
takes place at slightly different stream-wise locations in the
different cases. For a closer investigation of the resolved transition process in a more isolated way, it appears useful to compare the cases with respect to the transition onset point. Several criteria are common in the literature for example based on
Reynolds shear stress or boundary layer thickness. Here the lo-

0.08

DDES, Mesh1
DDES, Mesh2
DDES, Mesh3
DDES, Mesh4
DNS, Mesh2

0.07

k/U02 [-]

0.06
0.05
0.04
0.03
0.02
0.01
0
-0.1

0

0.1
0.2
(x-xδ*max)/c [-]

0.08

0.4

IDDES, Mesh4
IDDES, Mesh5
IDDES, Mesh6
DNS, Mesh2

0.07
0.06
k/U02 [-]

0.3

0.05
0.04
0.03
0.02
0.01
0
-0.1

0

0.1
0.2
(x-xδ*max)/c [-]

0.3

0.4

Figure 7: Resolved turbulence kinetic energy hki along
the displacement thickness. Stream-wise coordinate
shifted with respect to location of maximal displacement
thickness.

0-0.005<u'v'>/U02 [-]-0.01-0.015-0.02-0.025

DDES, Mesh1
DDES, Mesh2
DDES, Mesh3
DDES, Mesh4
DNS, Mesh2-0.03-0.035
-0.04
-0.1

0

0.1
0.2
(x-xδ*max)/c [-]

0.3

0.4

0

<u'v'>/U02 [-]-0.005-0.01-0.015-0.02-0.025IDDES, Mesh4
IDDES, Mesh5
IDDES, Mesh6
DNS, Mesh2-0.03-0.035
-0.1

0

0.1
0.2
(x-xδ*max)/c [-]

0.3

0.4

Figure 8: Resolved turbulence shear stress hu′ v′ i along

the displacement thickness. Stream-wise coordinate
shifted with respect to location of maximal displacement
thickness.

Table 2: Stream-wise coordinate x/c of maximal dis-placement thickness.
DNS
Mesh 1

DDES

IDDES

2D-URANS

0.5461

0.5482

0.5572

0.5360

Mesh 30.52670.5435

Mesh 4

0.5285

Mesh 2

0.53640.4894

Mesh 50.5038Mesh 60.4920cation of maximal displacement thickness has been selected asa reference point. It is typically located slightly downstream ofthe maximum bubble thickness and marks the onset of a steep
increase of turbulence. In the following plots, the stream-wisecoordinate has been shifted by this length. Table 2 provides
the exact locations.
Figure 7 shows the resolved turbulence kinetic energy
along the displacement thickness. From the DNS, it can beseen that onset of the steep rise coincides well with the maximal displacement thickness. The levels of fluctuation energy

0.50405

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
0.08

0.06
L11/c [-]

the turbulent boundary layer, the resulting integral length scaleis higher. All other cases produce the same L11 as the DNS besides some deviation of unclear origin on Mesh 2 towards thetrailing edge.

DDES, Mesh1
DDES, Mesh2
DDES, Mesh3
DDES, Mesh4
DNS, Mesh2

0.07

0.05
0.04
0.03
0.02

CONCLUSIONS

0.01

Simulations of laminar separation on a planar airfoil havebeen performed using hybrid RANS-LES on a set of six differently fine meshes in order to investigate the effect of meshresolution on the flow with a particular focus on the transition.
In comparison with DNS, it could be shown that not only meshresolution but also the discretization scheme have a strong influence on the key aspects of the flow, namely separation andtransition. The turbulent boundary layer towards the rear partof the wing, however, requires a less fine mesh resolution andallows to apply stability-oriented discretization schemes stillobtaining accurate results in terms of resolved turbulence intensity and integral scale of the structures. On the other hand,the front part of the wing needs to be refined very well andshould also be treated with accurate schemes.
For future applications this provides chances to increase
the efficiency in the simulation of wings at low Reynolds numbers where laminar separation is to be expected. The mesh canbe adapted locally to fulfill the required resolution for the different stages of the flow process. It also appears feasible toperform the spatial discretization in a hybrid way to provide
best accuracy for the laminar flow and increased stability inthe turbulent zones as this is often required especially for more
complex geometries.

0
-0.1

0

0.1
0.2
(x-xδ*max)/c [-]

0.08

0.4

IDDES, Mesh4
IDDES, Mesh5
IDDES, Mesh6
DNS, Mesh2

0.07
0.06
L11/c [-]

0.3

0.05
0.04
0.03
0.02
0.01
0
-0.1

0

0.1
0.2
(x-xδ*max)/c [-]

0.3

0.4

Figure 9: Integral length scale L11 /c along the displacement thickness. Stream-wise coordinate shifted with respect to location of maximal displacement thickness.

prior to the reference point are predicted already significantly
higher by the *DES than seen from the DNS. The resultsfrom Mesh 1 appear slightly better than those from the coarser
meshes. Once the flow becomes turbulent, most cases producea very similar level of resolved fluctuation energy. The DDES
Mesh 4 case clearly does not resolve much turbulence. But
also from Meshes 5 and 6 a reduction of resolved fluctuations
can be seen. Especially Mesh 6 fails as the produced profile
appears rather different from the other cases.
A similar view is given by the shear stress hu′ v′ i in Figure 8. It is noteworthy that here all cases start with a value ofnearly zero. Besides those cases which do not appropriately
resolve the process, all *DES cases first produce a slightly
sooner rise of hu′ v′ i towards the greatest magnitude than the
DNS. The magnitude then is predicted very well. Finally, thedecaying phase is predicted slightly too weak.
From a technical point of view, the small turbulent structures within the boundary layer after transition might be ofless interest as long as intensity and size of the larger scales
are captured well. A quantity to measure this is the integral
length scale. Utilizing the homogeneity of the span-wise direction, the integral length scale L11 on the displacement thickness has been computed. Figure 9 shows the resulting profiles
with the coordinate conditioned to the maximal displacement
thickness as above. Again, the DDES on Mesh 4 produces significantly different results as discussed before. All *DES results exhibit a large length scale in the beginning which drops
strongly during transition. The DNS prescribes a similar behavior, but due to its less diffusive discretization and the consequence that the shear layer flow is less planar, the length scaleis significantly smaller. It starts dropping once the maximal
displacement thickness is reached. This behavior is produced
different by the DDES, which at the reference location justreaches the final value of L11 . The breakup process towards
smaller scales appears to occur later and steeper on the finer
grids. The IDDES seems to perform slightly better as at least
for the Meshes 4 and 5 the breakup starts further downstream
and ends with the DNS. Meshes 5 and 6 are not capable of resolving the scales seen on the finer meshes any more. Within

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