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

STUDY OF BYPASS TRANSITION IN DENSE-GAS BOUNDARY LAYERS

Aurélien Bienner
Xavier Gloerfelt
DynFluid Laboratory
DynFluid Laboratory
Arts et Metiers Institut of Technology
Arts et Metiers Institut of Technology
151 Bd. de l’Hopital, Paris (75013), France 151 Bd. de l’Hopital, Paris (75013), France
aurelien.bienner@ensam.eu
xavier.gloerfelt@ensam.eu

Paola Cinnella
Jean Le Rond D’Alembert Institute
Sorbonne University
4 place Jussieu, Paris (75005), France
paola.cinnella@sorbonne-universite.fr

Leander Hake
Department of Mechanical Engineering
Muenster University of Applied Sciences
Stegerwaldstr. 39, Steinfurt (48565), Germany
leander.hake@fh-muenster.de

Stefan aus der Wiesche
Steffen Strehle
Department of Mechanical Engineering
Microsystems Technology Group
Muenster University of Applied Sciences
Technische Universität Ilmenau
Stegerwaldstr. 39, Steinfurt (48565), Germany Max-Planck-Ring 12, Ilmenau (98693), Germany
wiesche@fh-muenster.desteffen.strehle@tu-ilmenau.de

ABSTRACT

stream turbulence (FST) transition, the principal mechanismof laminar-turbulent transition for turbine blades, in dense
gases needs to be achieved. That is why the present study focuses on large-eddy simulations (LES) of FST transition forzero-pressure-gradient flat-plate boundary layers (ZPGFPBL)
of NovecTM 649. As part of a Franco-German collaboration,a joint experimental and numerical study is undertaken. The
experiments will be conducted in 2022 in the CLOWT windtunnel (Reinker et al., 2016) at the University of Muenster.
Boundary layer (BL) measurements will be carried out on a
sharp leading-edge silicon flat plate 2.5 mm thick, 6 cm longand 5 cm wide. The operating conditions for NovecTM 649
are given in table 1, corresponding to a Mach number M=0.9.
Contrary to most FST experiments (Fransson & Shahinfar,2020), the use of grid turbulence ahead of the flat plate is notdirectly possible due to the choking above M=0.5. Instead, theflow will be disturbed close to the leading edge using either
electrical or sound mode excitation. Moreover, a FST transition with 2% of turbulence intensity, obtained by removing themulti-screen system, is planned. The very thin BL, which constitutes a considerable challenge for the measurements, will
experience large-scale incoming turbulent structures. Miniaturized hot films will be inserted in the silicon wafer to follow
the evolution of the friction at the wall.

In a joint experimental/numerical effort to study the losses
associated with freestream turbulence (FST) boundary-layertransition on turbine blades in organic Rankine cycles, we
present the first large-eddy simulations of FST transition forthe dense gas NovecTM 649 at high subsonic condition. Dueto the small dimensions of the experimental apparatus, theboundary layer will experience relatively large-scale incoming
disturbances. The results for conditions similar to the wellknown T3A benchmark case are compared to cases with an
integral length-scale of FST multiplied by ten with a high andlow turbulence intensity. The size of the Klebanoff streaks,
forerunners of the appearence of turbulent spots, is doubled
and a relatively rapid onset of turbulence is observed even withthe low level of turbulence. The effect of the dense gas relies
essentially on its high heat capacity so that, even at high subsonic speeds, the transitional and turbulent states remains close
to those observed in the incompressible regime.

INTRODUCTION
Organic Rankine cycle (ORC) power systems have become a popular technology for waste-heat recovery andenvironmentally-friendly power generation but relatively little
is known regarding the impact of real-gas effects on loss mechanisms in ORC turbine expanders, which make use of molecularly complex organic fluids. In order to provide a deeper
understanding of these loss mechanisms, a new experimental
facility has been built at University of Muenster, which consists in a continuously running pressurized closed-loop windtunnel using NovecTM 649, an environmentally friendly working fluid, in the high subsonic speed range. To further increase
ORC turbine efficiencies, a better comprehension of free-

To characterize the disturbances ahead of the plate, preliminary experiments of the decay of grid-generated homogeneous isotropic turbulence (HIT) for NovecTM 649 are conducted in the CLOWT facility. Hot-wire measurements at low
speeds with a grid mesh size of 4 mm indicate a turbulencewith an integral length scale L11 ∼ 3 mm and a turbulence intensity Tu ∼ 2.8 %. This corresponds to large disturbances andto a very high Reynolds number based on L11 (ReL11 ≈ 9×105 )at the chosen operating conditions, to be compared for instance1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
A sponge zone combining grid stretching and a Laplacian filter is added at the oulet. Periodicity is enforced in the spanwise direction. Concerning the fluid, the NovecTM 649 is modeled with the Peng-Robinson-Stryjek-Vera equation of state(Stryjek & Vera, 1986) and the Chung-Lee-Starling model(Chung et al., 1988) for the transport properties. The MUSICAA solver has already been used in previous studies ofwall-bounded flows of a dense gas (PP11): compressible channel flows (Sciacovelli et al., 2017), supersonic boundary layers(Sciacovelli et al., 2019), ...

with the T3A case (Roach & Brierley, 1992), reproduced bynumerous numerical simulations using ReL11 of the order of1500. The aim of the present study is thus to investigate therole of large-scale disturbances on bypass transition for various Tu with the dense gas NovecTM 649 at M=0.9.

Table 1.

Thermodynamic and aerodynamic conditions.

U∞

c∞

p∞

T∞

ρ∞

µ∞

[kg/m3 ][µPa.s]

48.5

12.84

[m/s]

[m/s]

[bars]

[◦ C]

76.2

84.7

4

100

Generation of Freestream Synthetic Turbulence
To generate incoming freestream turbulence, we use asynthetic velocity field, based on Random Fourier Modes(RFM) (Gloerfelt & Le Garrec, 2008). The homogeneous
isotropic turbulent field is generated as the sum of N independent RFM:

The influence of the FST characteristics on transition
has been investigated experimentally and numerically for the
ZPGFPBL configuration in the incompressible regime. Roach& Brierley (1992) observed in their experiments that, for thezero pressure gradient, the transition occurred earlier as Tu is
increased. In the experiments of Jonas et al. (2000) at Tu = 3%,
it was found that the final stage of transition was advanced
by FST with large scales whereas the extent of the transition
region shortens with decreasing length scales. Brandt et al.
(2004) reported that in their numerical simulations, for a fixed
Tu , larger values of the integral length scale promotes earliertransition and noted that the spanwise scale of the streaks was
only slightly affected by the FST scales, at least for ReL11 between 750 and 2250. More recently, Fransson & Shahinfar(2020) obtained experimentally two behaviours depending on
the FST intensity: for low Tu (≤ 2.45%), the transition was
moved forward as L11 increased whereas the opposite was obtained with larger values of Tu (≥ 2.8%).
A preliminary study of modal transition of a NovecTM 649
boundary-layer flow has been carried out (Bienner et al., 2022)
by introducing a pair of oblique modes. A reference direct numerical simulation (DNS) database for turbulent BL of
NovecTM 649 has been generated and has enabled the validation of the implicit LES strategy retained in this paper, notably
the resolution in wall units and the use of an implicit time advancement scheme. Based on these results, the present paper
starts by recalling briefly the high-order numerical methods
and the generation of synthetic turbulence at the inlet. Then,the LES results for various Tu and integral scales are presented
and the transition patterns, specifically the generation of Klebanoff streaks, are analysed.

Nu0in (x,t) = ∑ ûn cos(kn .(x − ut) + ωn t + ψn )an

(1)

n=1

p
Their amplitude is prescribed as ûn = 2E(kn )∆kn , wherekn = |kn | is the wavenumber discretized using the logarithmic distribution ∆kn = (ln kmax − ln kmin )/(N − 1), with kmin
and kmax the minimum and maximum mode wavenumbers, respectively. We use here a von Kármán spectrum with Saffman
viscous dissipation function and a bottleneck correction:(u0rms )2 k4 /ke5
×exp −1.5cK (kη)2E(k) = 1.453
2
exp(17/6 log(1 + (k/ke ) )



1
1
arctan(10 log10 (kη) + 12.58) +(2)
× (1 + 0.522π2with ke = 0.747/L11 , cK = 1.613 and η the Kolmogorov viscous scale. In Eq.(1), ψn , kn /kn , an are a random variables
with given probability density functions. An unfrozen turbulent field is obtained by incorporating the convection velocity uand the pulsation ωn , accounting for the temporal evolution of
the perturbations. In the present turbulent simulation, N = 100
2/3
and ωn is deduced from Kolmogorov’s theory, ωn = ε 1/3 kn ,where ε is the the dissipation rate. The stochastic velocity
field u0in is entered using the Tam & Dong’s inlet boundary
condition (Gloerfelt & Le Garrec, 2008) and windowed by avan Driest type damping function to mimick the exponential
damping of continuous Orr-Sommerfeld modes in the boundary layer. We use the function proposed by Pinto & Lodato(2019), defined as:

NUMERICAL METHODS AND SET-UP
Flow Solver MUSICAA

σdamp (y) = (1 − e−y/(0.137×h) )1000

An in-house finite-difference code is used to solve thecompressible Navier-Stokes equations. The inviscid fluxes
are discretized by means of 10th-order standard centred differences whereas 4th-order is used for viscous fluxes. The
scheme is supplemented with a 10th-order selective filtering
to eliminate grid-to-grid unresolved oscillations and provide aselective regularization of subgrid-scales. A four-stage RungeKutta algorithm is used for time integration and a fourth-order
implicit residual smooting (IRS4) method (Cinnella & Content, 2016) is implemented to enlarge the stability and allow
the use of larger timesteps. Adiabatic no-slip conditions areapplied at the wall, and non-reflecting Tam & Dong’s conditions are imposed at the inlet, top and outflow boundaries.

(3)

where h corresponds to the height where the coefficient isequal to 0.5 and needs to be tuned by the user. This parameter has been shown to influence the transition location (Pinto& Lodato, 2019), as discussed later.

Simulation set-up
We select operating conditions representative of the future experimental campaign in CLOWT facility (see table 1)
corresponding to a flow of NovecTM 649 at Mach 0.9 in relatively dilute conditions. The fundamental derivative of gas

2

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

Figure 1. Damping coefficient applied close to the wall. The
cases B, C and D are superposed.

Figure 2. Initial kinetic energy spectra of inlet HIT. Cases A
and B are superposed

dynamics has a value below 1 so that the flow occurs in theso called dense-gas thermodynamic region, as used in ORC
applications. The flow properties are kept dimensional in thefollowing since they are representative of the CLOWT experiments. The timestep is fixed to ∆t = 1.67 × 10−9 s, whichcorresponds to a CFL of 4. In order to validate our numerical strategy, a first simulation, referred to as case A hereafter, is conducted to mimic the incompressible T3A experiment (Roach & Brierley, 1992). The Reynolds number at the
inlet is taken as Rex,in = 104 , which corresponds to a boundary
layer thickness δ99,in = 1.73 × 10−6 m. The injection height,
defined by Eq.(3), is set to h = 1.71δ99,in . In case B, keeping the same FST characteristics as in case A (see table 2), theonly changed parameter is h that is reduced to 1.21δ99,in . This
injection height is then kept fixed and two other LES simulations (C and D) are carried out with an integral length scale
L11,in 10 times greater and with two different turbulence intensities Tu . The size of large-scale incoming disturbances is thenmore representative of the ones which will be encountered in
CLOWT experiments at Mach 0.9.

spectra Eq.(1) are selected as follows. Since the peak kinetic
energy is localised around L11 , kmin is determined so that thecrossflow dimensions Ly and Lz are greater than 9L11,in . We
then choose kmax ≥ 64kmin , which yields a maximal value forthe grid spacings to accurately resolve every injected modes,
based on the numerical scheme used. The resolution of thesimulations is given in table 3 and the inlet spectra are plottedin figure 2. For cases A and B, the major constraint is givenby the freestream turbulence characteristics whereas, for cases
C and D, as the integral length scale is relatively large, thenear-wall resolution constraint is more restrictive.

Table 2.

FST characteristics for the LES simulations.

Name

ReL11,in

Tu,in (%)

h/δ99,in

A

1728

3.9

1.71

B

1728

3.9

1.21

C

17280

4

1.21

D

17280

2.5

1.21

Table 3.

Case

LegendComputational grid properties for FST simulations.

PointsResolution(Nx ×Ny ×Nz )+∆x+ ×∆y+w ×∆zA

1920×204×62

13×1.1×13

1100

B

1824×280×80

13×1.0×11

2950

C

1800×480×780

28×0.9×10

2200

D

1800×480×780

27×0.9×10

2050

INFLUENCE OF LARGE-SCALE
BANCES ON FST TRANSITIONDISTUR-Rθ ,endAs already pointed out, case A is carried out to mimic the
T3A experiments (Roach & Brierley, 1992). The FST characteristics are determined thanks to preliminary simulations ofspatially decaying HIT (not presented here), in order to matchthe FST evolution of the turbulence intensity in the T3A experiment, as recommended by Pinto & Lodato (2019), who
also used synthetic turbulence for this benchmark case. The
selected values are given in table 2. When L11 is increased or
decreased, the decay slope of the FST evolution is decreased
or increased, respectively. For case A, the integral length scale
L11,in = 6 × 10−6 m corresponds to ReL11,in = 1728, and the inlet Tu is 3.9%. These values are coherent with the ones in Pinto& Lodato (2019) (ReL11 = 1950, Tu = 3.5%) and comprised in
the range investigated by Brandt et al. (2004), where ReL11 is

The computational grid resolution needs to comply withtwo major constraints. The first one concerns the resolution of
the near-wall boundary layer flow. As mentionned in the introduction, a first study of NovecTM 649 BL transition by obliquemodes has been conducted (Bienner et al., 2022). This provides us a target resolution to achieve in the turbulent BL of+∆x+ × ∆y+w × ∆z ∼ 30 × 1.0 × 11. The second constraint is
the resolution of the freestream disturbances. As the synthetic
turbulence is injected by a limited number of modes, whichneeds to remain as small as possible in order to avoid excessive
computational overcost, the kmin and kmax of the inlet energy

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 3.

Figure 5. Streamwise evolution of the spectra kz Euu (kz )maximum for λz,1 and λz,2 . Linestyles as in tab. 2.

Evolution of the freestream turbulence intensity.

Figure 4.

case B is seen to perfectly match the one of case A in figure
3 since their initial energy spectra are superposed in figure 2.
The C f evolution in figure 4 indicates that a reduced h promotes a faster transition, which can be beneficial numericallyin term of the minimal streamwise extent to capture a fully turbulent state. This value of h has been chosen and kept constantfor cases C and D to allow the investigation of the influenceof large-scale disturbances on FST transition. The slope of the
C f rise is similar for the two injection heights in cases A andB but the value of u0rms,max in figure 7 is greater at the location
Rex = 67 × 103 since the onset of transition is already reachedat the following stations.
In order to observe the influence of a large L11 value ofthe incoming FST, the integral length scale is multiplied by afactor of ten in cases C and D, yielding a ReL11 of 17.28 × 103 .
For case C, the inlet turbulence intensity is kept close from theTu,in values of case A and B. As L11 is large, the FST decay isslow and its intensity remains high all along the computational
domain as seen in figure 3. Compared to case B, the slope of
the C f rise in the transition region is smoother in figure 4 and,even if the transition onset occurs earlier, the end of the transition region is slightly shifted downstream. A similar trend
has been observed in Fransson & Shahinfar (2020) for highturbulent intensity (Tu ≥ 2.8%). In case D, the Tu is reduced
to 2.5% to approximatively match the Tu obtained for case B
at the beginning of the transition region. The reduction of Tu
in case D causes the transition to move further downstream,with a slope of C f in the transition region slightly steeper withrespect to case C. Moreover, because of the slow decay rateof FST in cases C and D, an enhancement, more pronounced
for case C, of the turbulent BL skin friction is observed, witha C f slighty higher than in case B. An instantaneous view ofthe streamwise velocity for case D is depicted in figure 8. The
xy-slice clearly shows the large sizes of the energetic turbulent
scales in the freestream compared to the BL thickness. The
formation of the Klebanoff mode and the presence of turbulent
spots are clearly revealed in the top view.
Close-up views near the inlet are proposed in figure 9
for the four cases, with the same dimensional streamwise andspanwise extents, and provide a first qualitative comparisonof the Klebanoff modes. In cases A and B, we observe thatthe spanwise width and spacing of the streaks are very similar.
The comparison between cases C and D is less obvious, even if
it is clear that the scales associated with Klebanoff modes arevery different between the cases A-B and the cases C-D. To getfurther insights into these differences, spanwise wavenumber

Evolution of the friction coefficient.

varied between 750 and 2250. The freestream turbulence evolution is plotted in figure 3 along with the T3A experimental
data (•). The decay rate for case A is in reasonable agreementwith the reference. The distributions of the friction coefficientC f for all cases are plotted in figure 4, along with T3A experi√mental data (•), the laminar Blasius correlation 0.664/ Rex(), and the DNS of bypass transition of Wu & Moin(2009) (). The injection height h of the inlet turbulence has
been shown to be a sensitive parameter for the transition onset(Pinto & Lodato, 2019). The value h = 1.71δ99,in used in case
A yields a transition location in fair agreement with T3A. It isslightly higher than the one for which Pinto & Lodato (2019)better reproduced the T3A transition location (h = 1.5δ99,in )since their numerical methods are different. It is also worthy
to note that the present C f evolutions follow closely the ones
obtained in the incompressible regime despite the present highsubsonic Mach number of 0.9. As shown in Bienner et al.
(2022), the high heat capacity of NovecTM 649 reduces drastically the friction heating at the wall so that no compressibility
effects are observed on the velocity profiles. The mean streamwise velocity fluctuation profiles, scaled by the friction velocity uτ , are plotted in figure 7 for the different cases and theexperimental data. The profiles for case A are in good agreement with the experimental ones.
The second simulation (case B) is performed with thesame FST conditions but with a lower injection height h (seefigure 1). As there is no universal value for the injection heighth, the choice is made here to inject FST just above the edge ofthe inlet BL at 1.21δ99,in . As expected, the FST Tu decay for412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
transition and increase the spanwise scales of the Klebanoff
streaks. For the large cases, the decrease of Tu moves the transition downstream. In the turbulent state, the FST slighty enhances the wall friction in presence of large scales, due to theweak decay rate of FST along the streamwise direction. We
observed that the injection height at the inlet is a tunable parameter that influences the onset of transition. To get rid of that
artefact, we will include the leading edge in the future simulations to observe the shear sheltering effect. By varying thecurvature of the leading edge, we will be able to investigate theeffect of a favorale pressure gradient. This will constitute thenext step before tackling a blade configuration representativeof ORC turbines.

ACKNOWLEDGEMENTS

Figure 6. Streamwise evolution of the position of the spectra
maximum for λz,1 and λz,2 . Linestyles as in tab. 2.

This research has been funded by the Agence Nationale de la Recherche through the ANR-20-CE92-0019-02
project Regal-ORC. This work was granted access to the
HPC resources of IDRIS and TGCC under the allocation
A0092A01736 made by GENCI (Grand Equipement Nationalde Calcul Intensif).

premultiplied spectra kz Euu of the streamwise velocity fluctuations at successive locations along the boundary layer havebeen realised. The spectra are averaged over at least 1500 timesamples in case D and up to 3000 in case B, and the peaksin the crossflow plane λz -y indicate the emergence at a preferential height of several Klebanoff modes in the transition
region. The evolution of the intensity and wall-normal location of the two main peaks are reported in figures 5 and 6,
respectively. Mode 1, corresponding to the spanwise wavelength λz,1 , dominates first and the harmonic mode 2, withwavelength λz,2 = λz,1 /2, takes over more or less rapidly proportionately to the length of the transitional region. The wavelengths of the selected modes are given in table 4. Their mean
wall-normal height, plotted in 6, is determined by their size.
The first growth phase is remarkably similar for all cases. The
spanwise scales observed in the spectra are similar between
cases C and D, whereas they differ by a factor of approximately 2 with respect to the case B, which is coherent with
figure 9. More advanced statistics, based on streak identification (Nolan & Zaki, 2013), will be used to refine the present
analysis.

Table 4.

Values of λz,1 and λz,2 .

Name

A

B

C

D

λz,1 /δ99,in

9.6

9.6

18.0

18.0

λz,2 /δ99,in

4.8

4.8

9.0

9.0

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CONCLUSIONS AND FUTURE WORKIn the present study, we have investigated the bypass transition of a zero-pressure gradient flat-plate BL in a high subsonic organic vapor flow. At the chosen thermodynamic conditions, there is no peculiar non-ideal real gas effects. Dueto the high specific heat of NovecTM 649, the friction heating
at the wall is significantly reduced and the behaviour is close
to the incompressible regime. Given the dimensions involvedin the forthcoming experimental campaign in CLOWT facility, we are primarily interested by the influence of large-scale
freestream turbulence on transition. The LES results show thatthe high increase of the integral length scale tends to delay5

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

Figure 7.

Scaled streamwise fluctuating velocity: 0.2*(u0rms /uτ ) + Rex /105 .

Figure 8. Instantaneous slice xy (top) at z = 0 and xz (bottom) at y/δ99,in = 1.1 for case D shown for the full domain. The values areplotted between 0.9U∞ (red) and 1.1U∞ (blue) at the top and 0.3U∞ (red) and 0.9U∞ (blue) at the bottom.

Figure 9. Instantaneous slice of plane normal to the wall at the location y/δ99,in = 1.3 for case A and y/δ99,in = 1.1 for case B, C and
D. The values are plotted between 0.3U∞ (red) and 0.9U∞ (blue). From top to bottom: case A, B, C and D.

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Wu, X. & Moin, P. 2009 Direct numerical simulation of
turbulence in a nominally zero-pressure-gradient flat-plateboundary layer. J. Fluid Mech. 360, 5–41.

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Sciacovelli, L., Cinnella, P. & Gloerfelt, X. 2017 Direct numerical simulations of supersonic turbulent channel flows
of dense gases. J. Fluid Mech. 821, 153–199.
Sciacovelli, L., Gloerfelt, X., Cinnella, P. & Grasso, F. 2019
Numerical investigation of hypersonic boundary layers ofperfect and dense gases. Flow, Turbulence and Combustion
In redaction.

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