Improvement of DNS tools for Air-assisted

Improvement of DNS tools for
Air-assisted Primary Atomization
Simulations
A. BERLEMONT1, J.L. ESTIVALEZES 2, S. ZALESKI 3
CNRS-CORIA1, ONERA 2, UPMC 3
T2.2.1
FIRST Project Spray and Soot Workshop
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FIRST Project Spray19-20
and Soot
Workshop,
19-20
November
November
2014,
Derby,
UK 2014, Derby, UK
General context
Atomization: a multi-scale problem
Atomization is a complex multi-scale phenomenon
Example: air-blast atomization of a liquid
sheet
Injector width ≈ 4 cm

Finest droplets ≈ 10 µm
A thin liquid sheet is injected between
two parallel high-velocity air flows
 Growing aerodynamic instabilities
triggered by the shearing effect induce
the sheet disintegration
Sheet thickness ≈ 0.3 mm
channel length ≈ 30 cm
A. Cartellier, A. Delon, J.P. Matas, LEGI
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General context
Atomization: a multi-scale problem
• Some orders of magnitude:
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Liquid sheet thickness : between 300 and 600 microns
Mean break-up length : between 5 mm and 25 mm ( depending on velocity ratio)
Size of primary atomization zone : around 5 cm x5 cm x 5 cm
Smallest droplet diameter : 10 microns
Minimum droplet resolution needed for DNS : 10 to 15 grid points/ diameter
High liquid-gas density ratio
conservation problems
High shear at liquid gaz interface
• Uniform grid : 125 1012 grid points
• AMR grid : 125 109 grid points
primary atomization
secondary atomization
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General context
Atomization: a multi-scale DNS approach
• Fully resolved DNS are still out of reach even with AMR
alone
• Solutions:
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Parallel computing (High Performance Computing)
AMR ( Adaptive Mesh Refinement)
Improvement of mass and momentum conservation
Multi-scale simulations
(Euler-Lagrange coupling)
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Coria Contribution-code ARCHER:
Introduction
Objective
• Numerical simulations are known for becoming unstable for atomization
processes with large density ratios coupled with large shear.
Development of a new consistent mass and momentum flux computation using
Rudman type technique in ARCHER code (coupled Level Set / VOF / Ghost fluid
methods )
Simulations are performed on air assisted atomization on experiments from LEGI
(T3.1) and presented in T4.1.4
A. Cartellier, A. Delon, J.P. Matas, LEGI
A. Cartellier, A. Delon, J.P. MATAS, LEGI
A. Berlemont, T. Ménard, G. Vaudor, CORIA
• Development of adaptive mesh refinement algorithm for incompressible two
phase flows
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Work Description and Results
• Problem description
NS formulation
•
V
 .( V V)  p  .( D)  g
t

 .V   0
t
Incompressible NS
•
 V

 (V .)V   p  .(  ( ) D)   ( ) g •
 t

V
. 0
 ( )
In incompressible NS, we lost
consistency between mass flux and
momentum flux at the interface: the
V flux must be the same in both
equations in NS equation, but
disappears in Incompressible
formulation.
This induces numerical instabilities in
simulations, or wrong results.
We thus need to ensure consistency in
ARCHER algorithms.
G. Vaudor, A. Berlemont, T Ménard, M. Doring A Consistent mass and momentum flux computation
using Rudman type technique with a CLSVOF solver, FEDSM2014, Chicago, USA, August 3-7, 2014
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Work Description and Results
•
Objective : Use VoF (=Mass) flux to compute
momentum flux.
•
Mass fluxes are known on the faces of the
black cell (A,B,C,D)
•
Problem: Faces for momentum equation are
not in the same place (staggered grid) (orange
and purple cells). We need fluxes A’,B’,C’,D’
•
Flux A’ and C’ are unknown ( B’ and D’ not
directly but easy)
Two approaches:
Rudman technique with a dual grid for CLSVOF (twice smaller)
Our approach: mass balance on a half cell
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Work Description and Results
•
Validation on turbulent round jet experiment (Sedarski et al): measurements of
interface velocities
1
2
1
3
4
250
Simulation
•
Experiment
Velocity [m.s-1]
200
150
4
100
50
0
0
200 Radial distance
400 [µm] 600
800
Good agreement for
Interface velocities
Sedarsky D., Idlahcen S., Rozé C. Blaisot J.B., 2013, Velocity measurements in the near field of a diesel fuel
injector by ultrafast imagery. Experiments in Fluids, Vol. 54:2, 1-12.
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Work Description and Results
• Adaptive Mesh Refinement
Done :
 Data structure
 Adaptive mesh
 Convective term
Very difficult work developed by
 Poisson Solver
M. Doring (moved in June 2014)
 Navier-Stokes equation
Now developed by T. Ménard
 Coupled VOF – Level Set
 Validations
Last developments
 Parallelisation
 Load balancing …
 New discretization of N-S (Consistent fluxes)
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Work Description and Results
• 3D axi-symetric jet (CNRS LEGI) ( see WP 4.1.4)
8 mm cylindrical water jet (0,27 m/s)
surrounded by a
1.7mm thick air flow (22,6m/s)
with new convection scheme is introduced
AMR with load balancing
• Example of Domain MPI cutting
Refinement blocks
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One level refined grid
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Work Description and Results
Adaptive Mesh Refinement
•
•
•
A. Cartellier, A. Delon, J.P. Matas, LEGI
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642x128 +1 level – 64 procs
642x128 +2 level – 64 procs
642x128 +2 level – 128 procs
A. Berlemont, T. Ménard, G. Vaudor, CORIA
FIRST Project Spray and Soot Workshop, 19-20 November 2014, Derby, UK
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Onera contribution-code DyJeAt: AMR and
lagrangian tracking
 Coupled LS/VOF method is based on Sussman and Puckett (JCP
2000), Menard et al. (IJMF 2007)
 VOF : mass conservation
 Level-set : good description of the interface
 Geometrical computation of the fluxes [VOF Tools, Hernández and
López 08]
 Adaptive Mesh Refinement
 Oct-tree block refinement
 “Near interface” refinement criterion
 Droplets generation
 Small liquid inclusions:
 Under resolved by CLSVOF (2-6 cells)
 Local mesh refinement triggered
 the spray would create an everywhere-refined mesh
 Lagrangian tracking of stable droplets
 mesh de-refinement, dilute flow hypothesis satisfied!
 Problem
 Dispersed phase models definitely not satisfied at the droplet
creation!
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Droplets detection procedure
1)
Tag cells where C > 0.5 (“liquid cell”): integer index
2)
Propagate the minimum index among all the tagged neighbour liquid cells
3)
Extension of the tag to the neighbouring cells : C< 0.5
4)
Parallel propagation of the tags
5)
Size criterion
6)
a)
Ni number of liquid cells contained in an inclusion
b)
if Ni < 2m (m=ndim)  point lagrangian particle  small droplets
c)
For 2m < Ni < 6m  medium droplets (volumic particle)
d)
In the others cases eulerian treatment is done (CLSVOF)
Shape criterion (medium droplets)
Droplet generated if
a)
Sphericity
b)
Volume
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Medium droplets treatment
“Medium” droplet treatment (kind of penalty method)
1)
Mass and momentum projection on the Eulerian grid:
2)
Two-phase N.S. solve +
3)
Averaging the new velocity inside the droplet:
4)
Move the droplet according to :
(0) Old position
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(1) Projection
(2) NS solve
(3) Lag transport
FIRST Project Spray and Soot Workshop, 19-20 November 2014, Derby, UK
(4) New position
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Small droplets treatment and reimpact
“Small” droplet treatment : EulerLagrange two-way coupling (DPS-DNS)
•
Interpolate gas velocity @ particle location :
•
Solve the following equations for the point particle (Runge-Kutta 2):
•
With
,
,
Droplet impact
•
Reimpact allowed if :
•
Level-set and VOF reconstruction inside the droplet
•
Momentum coupling :
•
Level-set redistance
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Numerical tests: droplet splashing, We = 272
Mesh Δx
Euler
Mesh 2Δx
Euler+Lagrange
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Numerical tests: surface impact
Classical treament
Lagrangian projection ( medium droplet reimpacttreatment)
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Numerical tests: impact on a pool
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Atomization of a 3D liquid sheet, ambiant
conditions
Ug = {40, 60, 80} m.s-1
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Ul = 2 m/s
P = 1 bar
M = 2.6
Air-water
Liquid sheet thickness 2a =300 m
Splitter plate thickness=150 m
AMR-CLSVOF-Eul-Lag calculation
Dxmin = a/6
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Atomization of a 3D liquid sheet, engine
conditions
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Ul = 2 m/s
Ug = 17 m/s
P = 10 bar
M = 2.62
Air-Kerosene
Liquid sheet thickness =300 m
Splitter plate thickness=850 m
Air boundary layer thickness=1.5 mm
AMR-CLSVOF-Eul-Lag calculation
Dxmin = a/10
(see WP 4.1.4)
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UPMC Contribution-code Parissimulator
•
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•
•
•
•
•
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New UPMC code
previous results obtained with Gerris
Gerris does not perform well on large numbers of processors (> 64)
write a new code, Paris Simulator, with the following features:
Free code under the GPL. Written in Fortran 90/95
Use a regular structured grid and finite volume discretisation.
Uses MPI and a regular array of subdomains for parallelisation.
Momentum : QUICK, ENO, Verstappen or a momentum-conserving method
Implicit viscous terms.
Either Volume-Of-Fluid or Front-Tracking may be used to follow interfaces.
VOF uses either CIAM or Weymouth-Yue scheme for advection.
Height function method for curvature estimation and surface tension.
Parallelized Lagrangian Point Particles (LPP) with VOF to LPP and LPP to VOF
conversion
• Second order in time and space with projection method.
• Uses either hypre or internal Poisson solver.
• Immersed solid boundaries
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Parissimulator performances i):
Parissimulator
Speed issues
• Facing scalability
problems with Gerris
code
• Rewriting of a new
code Parissimulator
• Vof method +
lagrangian coupling
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Parissimulator performances ii):
Perfect scalability on massive HPC (IDRIS Turing)
Normalized Speed
16
8
4
2
1
1024
IBM BlueGene Turing
Ideal
2048
4096
8192
16384
# of cores
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Point Lagrangian coupling i)
• Add Lagrangian Point Particles (LPP) that obey a point-particle equation
du p
dt
= Fp éë u p ,u f (×) ùû
• The force is determined by the surrounding carrier fluid velocity field: u f (×)
• It reacts on the Navier-Stokes equation through a smoothing Kernel G
r Du / Dt = -Ñp + Ñ ×(2mD) + skd S n - Fp *G
• where the strain-rate tensor D is
1 æ ¶u j ¶ui ö
Dij = ç
+
.
÷
2 è ¶xi ¶x j ø
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Point Lagrangian coupling ii)
The choice of resolved interface or LPP modelling depends
on the type of simulation and on grid resolution
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Point Lagrangian coupling iii)
VOF to LPP conversion - High Reynolds – CORIA (Berlemont) jet
time
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Atomization of a plane sheared liquid film
• Legi experiment (Descamps, Matas & Cartellier)
• Reδ = 1000, density ratio 100
• Simulation 64 x 256 x 512
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Results
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PDF of droplet diameters
(a) t = 0.4s, (b) t = 0.41s, and (c) t = 0.42s.
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Conclusions
• Improvements of DNS codes
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AMR : Archer and DyJeAt codes
Parallel Euler-lagrange coupling : Parissimulator and DyJeAt
codes
Mass conservation improvement : Archer, DyJeAt, Paris codes
Momentum conservation : Archer, DyJeAt codes
IBM : Parissimulator, Archer codes
• First cross comparisons with experiments : see WP 4.1.3
and WP 4.1.4
This project has received funding from the European Union’s Seventh Framework Programme
for research, technological development and demonstration under grant agreement no 265848.
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