Laizet - Imperial College London

Direct Numerical Simulations of
mutliscale generated turbulence
Sylvain Laizet, Christos Vassilicos
Department of Aeronautics, Imperial College London, UK
Eric Lamballais, Veronique Fortuné
Institut P', CNRS - ENSMA - Université de Poitiers, FRANCE

Turbulence generated by multiscale (fractal) objects

Fractal grid properties
!!DIFFERENT GRID CLASSES PRODUCE DIFFERENT SMALL-SCALE TURBULENCE!!
Protacted production and then decay of turbulence
SQUARE
GRIDS!
CROSS GRIDS I GRIDS SQUARE GRIDS
Kinetic energy dissipation rate decay ∼ u' 2 (rather than u' 3 )
Interscale energy transfers are severely modified
Appromixate exponential decay of turbulence
Taylor lenght-scale constant during decay after peak of turbulence
!!RESULTS WITH 4 and 5 FRACTAL ITERATIONS!!
(See Hurst & Vassilicos, Seoud & Vassilicos and Mazellier & Vassilicos in PoF)

Numerical strategy
Industrial codes
Good versatility BUT
poor accuracy AND/OR
not user friendly
INCOMPACT 3D
Academic codes
good accuracy BUT
poor versatility

Incompact3d
Incompressible Navier Stokes equations
Numerical methods
Compact finite difference schemes (sixth order)
Cartesian mesh (regular or stretched in one direction)
Explicit temporal discretization (AB2, RK3 or RK4)
Spectral methods in order to solve the Poisson equation
Immersed boundary method

Modified wave number
Physical space
Fourier space
equivalence
Modified wave number

Poisson stage
Modified wave numbers
Transfer functions
Staggered mesh
Only a single division (

Immersed boundary method
Forced incompressible Navier-Stokes equations
Ensuring
In the forcing region

2d domain decomposition
Also known as pencil decomposition
Derivation/Interpolation in one dimension at a time
Widely used in spectral codes, 1st time in FD code
Constraint Ncores < N2 for a N 3 DNS
(dCSE support from NAG 2009-->2012)

Scalability on Hector/Jugene

Fractal cross grid
EXPE
DNS

Fractal cross grid
Recirculation bubble
Comparison expe/DNS of the mean flow velocity along the streamwise
direction, on the centreline of the grid
1. -Good agreement expe/DNS
2. -Good agreement DNS1/DNS2
3. -Recirculation bubble with the DNS data, new insight provided by the
numerical approach (No expe closed to the grid)

Fractal cross grid
Comparison expe/DNS of the turbulence decay
along the streamwise direction, on the centreline
1. -Good agreement expe/DNS
2. -Intensity values a little bit more important in
the DNS data because of the Reynolds number
and the recirculation bubble but good agreement
after x/M eff
=20 (around 8%)

Fractal square grid
-765 millions mesh nodes
-3456 computational cores on HECToR
-3 fractal square grids, 1 regular grid, 2 Reynolds
numbers (2m/s and 10m/s as in wind tunnel) (6 DNS)

3D visualizations

Comparison regular/fractal N=3
-In average, fractal grids generate much more turbulence than regular grid
WITH THE SAME INPUT ENERGY
(Regular grid and square grid with Tr=8.5 → same blockage ratio)
strong influence of the shape of the grid

1
2
3
Enstrophy
4
5
6
1
4
2
5
3
6

Streamwise velocity 1
2
1
2

Streamwise velocity
1
2
1
2

Comparison Reynolds effect
Low Reynolds
High Reynolds
Umean
Umean
Umean
Umean
u'
u'
u'
u'

Comparison regular/fractal N=3
Streamwise evolution of
turbulent intensities on the
centreline
-Strong decrease for the regular grid
(same for the 3 components)
6%
2.5%
-2 regions downstream the fractal
grid (same as expe) : Streamwise
production of turbulence up to 10
Meff and then slow decay
-Much higher turbulence intensities
for the fractal grids
(2.5% regular and 6% fractal N=3
more expected with higher N)

Comparison regular/fractal N=3

Comparison regular/fractal N=3

Influence shape of the grid

Peak of turbulence

Energy spectra
E builds up from high wave numbers to small ones and then decays

Fractal square grid N=4
PASSIVE SCALAR INVESTIGATION

Fractal square grid N=4

Conclusion
Encouraging preliminary results
More data are currently under investigations
More Comparisons with experiments (3 fractal
iterations+PIV)
Passive scalar + Acoustic predictions
Bigger DNS with PRACE with 65k cores on Jugene