12th Workshop on Synthetic Turbulence Models 3rd-4th July 2017, Université Paris-Ouest, Nanterre La Défense, France
Synthetic ows for heat and mass transfer b
F. C. G. A. Nicolleau , D. Queiros Conde , A. F. Nowakowski
and T. Michelitsch
to investigate a wide range of two-component ow
The workshop was the 12th of the ERCOFTAC Special Interest Group on Synthetic Turbulence Models (SIG42).
It took place at Université Paris-Ouest,
Nanterre La Défense, France.
It was co-organised
with the SIG 14 dedicated to Multipoint Turbulent Structure and Modelling. The workshop particular theme was `Synthetic ows for heat and mass transfer'
problems. The robustness of the numerical approach was demonstrated using the cases of shock-bubble interaction representing media of non-uniform thermodynamic properties for which experimental data are available. The governing equations include non-conservative terms and therefore their numerical solution require a non-conventional approach. The numerical framework required a scheme ensuring conservativeness in
About 20 participants attended from dierent Eu-
a predictor-corrector and Godunov-type nite vol-
ropean countries (France, Germany, Russia, Spain,
United Kingdom) and beyond the European Commu-
methodology is the diuse interface treatment of the
nity (Columbia, Irak, Saudi Arabia) and 10 dierent
discontinuities and boundaries between ow compo-
institutions. It was an opportunity for the KS com-
nents. An ecient pressure relaxation procedure has
munity to strengthen the links with the energy en-
been implemented within the algorithm, to achieve
gineering community. Abstracts from the main con-
the equilibrium state, in the case of the pressure non-
tributions are reported below. An Ercoftac Book Se-
equilibrium model. 
An integral part of the applied
ries that will publish more detailed contributions is in preparation (to appear early 2018)
Abstracts of Talks
Instabilities and Pattern Formation in Mechanically Vibrating Thin Films
Helicity in the atmospheric dynamics and turbulence theory
O. G. Chkhetiani and M.V. Kurgansky [email protected]
An overview of the helicity concept and of its role
In a liquid layer with a free surface several hydrody-
in the atmospheric dynamics (including Nambu me-
namic instabilities may occur and may lead to self-
chanics) and the turbulence theory is given, also in
organized pattern formation.
relation to recent direct eld measurements of tur-
The patterns can be
seen as macroscopic motion of the uid, surface defor-
bulent helicity (Koprov,
mations, temperature or concentration distributions
In this contribution, the Faraday instability for thin lms was studied in detail.
Atmospheric and Oceanic
By considering a super-
position of the classic Ekman spiral solution and a jet-
The liquid layer is
like wind prole that mimics a shallow breeze circula-
thereby vibrated with one or more frequencies in nor-
tion over a non-uniformly heated Earth surface, a pos-
mal and tangential direction(s) with respect to its sur-
sible explanation is provided, why the measured mean
face. For a partially wetting substrate (small contact
turbulent helicity sign is negative. Whereas, the pos-
angle) a reduced theoretical description based on the
itive helicity is injected into the Ekman boundary
lubrication approximation is possible [2, 3].
layer in the northern hemisphere. A simple turbulent
stability as well as nonlinear results were presented
relaxation model is discussed that explains the mea-
and compared to ndings of the full set of hydrody-
sured positive values of the contribution to turbulent
namic basic equations. Recent results of a two-layer
helicity from the vertical components of velocity and
system consisting of two immiscible uids separated
by a deformable interface were discussed [4, 5].
A computationally ecient method for multicomponent ows
A. F. Nowakowski , F.C.G.A. Nicolleau and T. M. Michelitsch b
Large-eddy simulations of a wind turbine wake above a forest
J. Schroettle , Z. Piotrowski q,s
Since the pioneering large-eddy simulations of Shaw and Schumann (1992), the forest stands have been
This contribution focused on the developed numeri-
treated as a porous body of horizontally uniform
cal methods that constitute in house software used
(leaf ) area density with constant drag coecient.
This approach is sometimes called eld-scale ap-
A kinematic simulation was used to reconstruct the
Current ner scale applications and eld
missing-scale motions in isotropic turbulence  and
campaigns consider the heterogeneity of the canopies
turbulent shear ows . Yao and He  proposed
at the plant-scale (Schrottle and Dornbrack 2013).
to use a kinematic simulation (KS) to explicitly con-
Results from plant-scale simulations of ow through
struct the unresolved velocity elds with the required
resolved tree structures originating from laser scans
statistic properties in both space and time. The kine-
were presented in this contribution.
matic SGS model was used to calculate sound power
wake of one wind turbine, e.g., above a forest requires
spectra from isotropic turbulence and yielded an im-
a new computational approach.
For this purpose,
proved result: the missing portion of the sound power
2008) is modied to accom-
spectra was approximately recovered in the LES. We
modate two independent hydrodynamic solvers. The
discuss the procedure of implementation a kinematic
two solvers are integrated simultaneously.
SGS model in SOWFA code. The computational do-
EULAG (Prusa et al.
bulence structure above a forest is simulated in the
main as a box of length
rst solver at the eld scale and acts as inow for the
periodic boundary conditions were applied, was used
wind turbine wake ow.
for verication of dierent SGS models on dierent
LES and KS Applications of Wind Energy in the Atmospheric Boundary Layer
J.M. Redondo , J. Tellez-Alvarez , S. Strijhak f
The Large-Eddy Simulation (LES) became a powerful tool to simulate physical processes in Atmospheric Boundary Layer and aerodynamics of wind farm. The dierent sub-grid scale (SGS) models are widely used for simulation by dierent authors. The mathematical model was realized in SOWFA (Simulator for On/Oshore Wind Farm Application) code. SOWFA is an OpenFOAM-based incompressible atmospheric/wind farm LES solver, which is based on nite-volume method, that models wind turbine as actuator lines and actuator disk. The results of velocity magnitude's elds at dierent time steps are shown on Fig. 1.
on each side, where the
A non-local theory of turbulent pair diusion
N. A. Malik [email protected]
, [email protected]
In 1926, Richardson (1926)  proposed that the
is scale dependent with a single
power law over all turbulent scales, and that the diffusion process is local. He collected available data at
K(l) ∼ l4/3 , (which is hl2 i ∼ t3 ) although this has never been unambiguously veried. l is the pair separation, and h·i is the ensemble average. (It is usual p to evaluate K at typical values of, l, namely at σl = hl2 i, so this 4/3 scaling is replaced by, K ∼ σl .) the time, and assumed the t,
A re-examination of the original data set actually shows that
K(l) ∼ l1.564
is a much better t to the
data Malik (2016b). To date, experiments and DNS have not reached the high Reynolds numbers need to generate a large enough inertial subrange to test these ideas fully.  remark that, ...
there has not been an experiment
that has unequivocally conrmed R-O scaling over a broad-enough range of time and with sucient accuracy. A non-local theory for generalised power law spectra of the form
E(k) ∼ k −p , 1 < p ≤ 3,
features a novel calculation for the pair diusivity, Figure 1:
magnitude value at dierent time a) 150
s, b) 300 s, c) 500 s, d) 1000 s
K ∼ hl · vi, in terms of a Fourier decomposition of the relative velocity eld, v(l) = u(x + l) − u(x), where R u(x) = A(k) exp(ik · x)d3 k; then
The analysis of fractal dimension for turbulent wakes was performed with the results of numerical simulation by LES and Lagrangian-averaged scale-
Z K(l) ∼
independent dynamic Smagorinsky, One Eddy Equa-
exp(ik · x)id3 k
tion ABL turbulence models for a horizontal-axil wind single turbine and two turbines.
h(l · A)[exp(ik · l) − 1]
It is known
that such SGS models don't reproduce correctly the
Partitioning the integral in to local and non-local
energy spectrum for maximum wave number, the
ranges, and assuming a number of closures, leads to,
normalized time correlation coecients for veloc-
K(l) ∼ O(σl p ) + O(σl2 ),
ity modes and sound power spectra comparing with Direct Numerical Simulation (DNS) results.
stochastic SGS models, such as random forcing models,
represent alternatives that could correct the
nl is the locality scaling and γp scaling.
γpl = (1 + p)/2
is the non-locality
Now assuming a single power law t to
K(l) over p, and a
timescales of resolved velocity elds. Kinematic sim-
the inertial subrange of scales for any given
ulations that are limited to SGS motion (or kinematic
smooth and uniform transition between the asypm-
SGS models) can be used to represent unresolved velocity elds with imposed spatial-temporal statistics.
K ∼ σl2 ,
p = 1
K ∼ σl ,
p = 3
the observable scaling is intermediate be-
At the current time, we are carrying out a sys-
tween local and non-local scalings,
tematic parametric study of turbulent inertial parti-
K(l) ∼ σl p , with γpnl > γp > γpl
cle pair diusion for a wide range of Stokes' num-
for 1 < p < 3
p = 1.74, we obtain K ∼ σlγI , with γI > 1.37, and σl2 ∼ tχI , with χI > 3.2. The exact values of γI and χI can only be
For intermittent turbulence,
established through detailed experiments and DNS with extended inertial subranges of more than
This is not possible at the current time and probably not for many decades to come. However, Lagrangian models such as Kinematic Simulations (KS), , can indicate the scalings. KS with spectra
E ∼ k −p ,
over inertial subranges
γp of size 10 , yielded power law scalings for K ∼ σl . For intermittent turbulence, p = 1.74, KS produced K ∼ σl1.57 , which is within 2% of the revised data. 2 4.7 This is equivalent to σl ∼ t . 6
It has been shown that a non-local theory of pair diusion is at least as good an explanation of the observed and simulated results, and perhaps even a better one, than locality. However, only detailed experiments or observations in homogeneous turbulence with extened inertial subranges can give a decisive answer to this century old problem. The 1926 dataset is subject to signicant uncertainty in the length scales and bouyancies under dierent conditions, and although the overall sense is now leaning towards non-locality, the matter is far from certain.
new non-local theory, a number of assumptions and closures have been made, but all such theorie contain similar assumptions; locality makes the extra ad hoc assumption that the non-local term in equation is zero. The idea of non-locality could lead to important revision of our view of turbulence. The implications for modeling are equally important.
A theory of turbulent inertial particle pair diffusion
S. M. Usama and N. A. Malik [email protected] [email protected]
0 < St < 100, 102 ≤ kη /k1 ≤ 106 ,
and size of the inertial range and also for
1 < p ≤ 3.
method of in vestigation is numerical using Kinemataic Simulations (KS), Malik (2016a). Theoretical considerations suggest that inertial particle pair diusivity should follow a triple regime of diusion. For inertial pairs initially close together the pair diusion follows a ballistic regimes for short times, ity is
t < τp , such that the inertia pair diusivK(l) ∼ σl1 . At these short times, the energy
in the smallest turbulence scales is very small and therefore inertia dominates over the turbulence until the particles response time is comparable to the local tubulence time scale at the spearation
t∗ = t(l∗ ) ≈ τp .
After this time, the inertial particles will begin to feel more and more of the turbulent energies in the bigger scales as their speration increases.
diusion will therefore asyptote towards the non-local passive particle pair diusion regime in the limit that
t/τp → ∞
σl /η → ∞,
1.57 K(l) → σL
predicted in the non-local theory of Malik (2016b). This regime diers from the classical
4/3 − t3
Richardson (1926) and Obukhov (1941). In between these two asyptotic regimes, there may be a long period of transition between the ballistic and passive pair diusion regimes, long enough to constitute a third, transition regime. This is what we are observing in the nuermical results from KS. In the near future, we will complete the parametric study of inertial particle pair diusion. After that, in a second part of the study, we will investigate the inerial pair diusion process under gravity.
Eect of non Kolmogorov spectra on particle clustering
F.C.G.A. Nicolleau and N.M. Sangtani Lakhwani b
Clustering could be dened as the propensity of an initially uniformly distributed cloud of particles to accumulate in some regions of the physical space. This
It is natural to extend the ideas of non-locality,
is an important phenomenon to understand in or-
Malik (2016b), to inertial particles because most real
der to explore, identify and possibly monitor some
world applications concern inertial particle transport.
natural or hand-made mixing processes such as those
Although innumerabe studies have been carried out
causing rain formation sediments transportation, fuel
on single inertial paticle transport,
mixing and combustion.
literature survey found just one previous study of
In this contribution we study the clustering of
turbulent inertial particle pair diusion, the DNS
inertial particles using a periodic kinematic simula-
study by .
The systematic Lagrangian tracking of parti-
The parameters governing turbulent inertial parti-
cles makes it possible to identify the particles' clus-
cle pair diusion are, the size of the inertial subrange
tering patterns for dierent values of particle's inertia
(which is related to the Reynolds number), and the
and drift velocity. The main focus is to identify and
Stokes' number which is given by,
then quantify the clustering attractor - when it ex-
ists - that is the set of points in the physical space
where the particles settle when time goes to innity. Depending on gravity or drift eect and inertia values, the Lagrangian attractor can have dierent di-
mensions varying from the initial three-dimensional
particle relaxation time. The energy spectrum power
space to two-dimensional layers and one-dimensional
p, 1 < p ≤ 3,
attractors that can be shifted from an horizontal to
is the Kolmogorov time scale, and where
E(k) ∼ k −p ,
is an additional
parameter. In this part of the study, we will ignore gravity.
a vertical position. The particles initially uniformly distributed in the
Figure 2: Dierent Lagrangian attractors
ow eld are allowed to evolve until an asymptotic
ever passage probabilities fulll Riesz potential power
clustering pattern - also referred to as Lagrangian at-
law decay asymptotic behavior for nodes far from the
tractor - is achieved.
departure node [32, 41].
The shape of this cluster varies from clear onedimensional structures to three-dimension distributed structures or two-dimensional layer-like structures (Fig. 2). We quantify the variations in particle clustering in the presence of gravity with modied spectral power laws, from very steep (p
→ 2.5) to very at (p → 1.4)
energy distributions. Our main ndings are:
The spectral law can have a signicant eect on the Lagrangian attractor shape but for limited ranges of Froude or Stokes numbers,
ing. Without gravity (F r
random walk (α
Random Walks on Networks: Lévy Flights and Fractional Transport
A. Pérez Riascos
We study fractional random walks on networks deequation in graphs and their relation with Lévy walk navigation strategies on networks. We explore these processes for dierent structures; in particular, rings, circulant networks, n-dimensional lattices, complete graphs and random networks. From the spectra and
grangian attractor (1D ou 2D) whatever the
the eigenvectors of the Laplacian matrix, we deduce
∈ [1.4, 2]).
explicit results for dierent quantities that character-
With gravity for Stokes numbers large enough there is a `2D layered' structure whatever the spectral power.
is faster than a search strategy based on the normal
there is no La-
spectral power (p
a search strategy based on a fractional random walk
ned from the equivalent of the fractional diusion
in particular when a 2D Layer is achieved the spectral law has little or no eect on the cluster-
Our results conrm our recent ndings [32, 41] that
ize this dynamical process and their capacity to explore networks. We obtain analytical expressions for the fractional transition matrix, the fractional degree and the average probability of return of the random
If gravity is large
F r < 0.5,
there is no `quasi-
horizontal attractors'. Gravity tends to deform the attractor towards the vertical direction.
T.M. Michelitsch , B A Collet , A P Riascos , A.F. Nowakowski and F.C.G.A. Nicolleau d
Also, we discuss the Kemeny constant that
gives the average number of steps necessary to reach any site of the network.
Through all this work, we
analyze the mechanisms behind the fractional trans-
Fractional Random Walks on regular networks and lattices d
port on networks and how this long-range process induces dynamically the small-world property in dierent structures. [40, 41, 42, 43, 31, 32]
We establish a generalization of Polya's recurrence
Performance assessment of numerical modelling for hydraulic eciency of a grated inlet