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HYBRID URANS-LES METHOD FOR INTERNAL COMBUSTION ENGINE APPLICATIONS
LES4ICE - RUEIL-MALMAISON 11-12 DECEMBER 2018
HASSAN AFAILAL
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PLAN
Introduction of common turbulence modeling approaches
Consistent hybrid turbulence model for ICE flows: HTLES
Validation on three cases
Attached boundary layer: Channel flow
Highly separated flow: Hill flow
Flow downstream a fixed valve: Steady Flow Rig
Conclusions and perspectives
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INTRODUCTION
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S U S T A I N A B L E M O B I L I T Y
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Huge interest to benefit from the simulation tools by developing accurate modeling approaches with affordable cost
DNS: Solve Navier-Stokes equations for all turbulent length & time scales => expensive
Solution: Limit the resolved scales by using turbulence modeling
2 commonly used approaches:
OVERVIEW OF COMMON MODELING APPROACHES
• All turbulent motions are modeled • Large framework • Affordable • Compatible with wall-functions • Provides only phase averages
• Explicit resolution of turbulent motions larger than the grid size
• Adapted for fully time-dependent ICE flows • Challenging for wall-bounded flows
Introduction Hybrid model: HTLES Results Conclusions & perspectives
Buhl et al. [1]
Possible solution
Use URANS near the wall and LES inside the domain
[1] Buhl, S. (2018). Scale-resolving simulations of internal combustion engine flows (Doctoral dissertation, Technische Universität). Affordable accurate scale resolving simulation
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HYBRID MODEL FOR ICE FLOWS
HYBRID TEMPORAL LARGE EDDY SIMULATION (HTLES)
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PRESENTATION OF THE HTLES METHOD
d
dtρktot = P − ρktotω + D (Eq. 1)
The original k-ω SST URANS model
where all turbulent motions are modelled ktot is the energy relative to integral scales
HTLES
d
dtρkm = Pm − ρ
km
T+ Dm (Eq. 2)
Scale resolving model adaptive to the grid resolution km is the energy relative to the grid resolution
By making the dissipation term in the energy equation sensitive to the temporal filter width T
𝜔 is replaced by 1/𝑇
Introduction Hybrid model: HTLES Results Conclusions & perspectives
T =r
1 +Cε2Cε1
− 1 1 − rCε1Cε2
×ktot
ε (Eq. 3)
T is the temporal filter width is computed from:
The ratio r is defined as km
ktot that has to be modelled
ktot = kres + km
HTLES transforms the k-𝜔 SST URANS model (Menter et al. [2]) to hybrid model
The model switches automatically between URANS & LES depending on the grid resolution
[2] Menter, F. R. Influence of freestream values on k-omega turbulence model predictions. AIAA journal, 30(6), 1657-1659.
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MODELING THE RATIO R
Introduction Hybrid model: HTLES Results Conclusions & perspectives
r = min 1,1
β
Uc ε
ktot3/2
23
ωc
−23
(Eq.4)
r varies between 0 and 1:
The ratio r is modelled using the multi-scale approach by comparing (Manceau et al. [3]):
the highest frequency that can be resolved by the grid resolution
and the frequency of the integral scales of the turbulence
The wall-distance is added to the model using the Elliptic Blending framework [4] which:
Forces the URANS mode near the wall
Guarantees a smooth transition between URANS and LES regions near the wall
0 1
DNS URANS Scale resolving mode
[3] R. Manceau et al. (2010) Recent progress in hybrid temporal LES-URANS modeling, V European Conference on Computational Fluid Dynamics, 1525–1532. [4] Fadai-Ghotbi et al.(2010). Temporal filtering: A consistent formalism for seamless hybrid URANS–LES modeling in inhomogeneous turbulence. International Journal of Heat and Fluid Flow, 31(3), 378-389.
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M O B I L I T É D U R A B L E
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PRESENTATION OF THE CFD SOLVER
Cell centered CFD code based on Finite Volume methods
Multiphysic solver: Turbulence – Diphasic flows – Combustion – Chemistry …
Automatic meshing for mobile geometries Hexahedral mesh with cut-cell Technique
Automatic mesh refinement (AMR)
Introduction Hybrid model: HTLES Results Conclusions & perspectives
(Converge CFD presentation video)
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• 𝑅𝑒𝜏 = 1 000 • Attached boundary flow
• 𝑅𝑒ℎ = 10 595 • Separated flows &
reattachment • Recirculation
• 𝑅𝑒𝐷 = 30 000 • Complex & industrial flow • Realistic engine configuration
Channel flow Steady flow rig Hill flow
HTLES PHYSICAL VALIDATION & COMPARISON WITH URANS/LES
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REMARKS:
All simulations use the same setup:
Focus only on the single impact of the models on the results.
Introduction Hybrid model: HTLES Results Conclusions & perspectives
Approach URANS Hybrid LES
Models k-𝜔 SST HTLES 𝜎-model
Numerics 2nd order temporal and spatial schemes
Grid resolution Same grid without AMR
Time resolution Same time step
Near-wall treatment Automatic wall function Werner & Wengle
wall function
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CHANNEL FLOW SETUP
Reference data: DNS data of Moser et al. [5]
𝑈𝑏𝑢𝑙𝑘 =28.32 m/s
𝑇 = 320 𝐾
𝑅𝑒𝐷 = 40 000
Introduction Hybrid model: HTLES Results Conclusions & perspectives
Case setup:
Height of the Channel Ly = D = 25 mm
Length of the Channel Lx = 10 × D
Width of the Channel Lz = 2 × D
Grid size is set to 0.5 mm in the 3 directions (500x50x100)
𝑦+~30
D
[5] Lee, M., & Moser, R. D. (2015). Direct numerical simulation of turbulent channel flow up to 𝑅𝑒𝜏 ≈ 5200. Journal of Fluid Mechanics, 774, 395-415.
Periodic
Slip wall
Wall (wall function)
Periodic + fixed axial momentum source
Q-criterion iso-surface given by HTLES simulation
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COMPARISON OF THE VELOCITY PROFILES
Velocity profiles along the altitude of the channel
Introduction Hybrid model: HTLES Results Conclusions & perspectives
LES combined with wall-function over-estimates the flow rate
URANS and HTLES give accurate flow rate compared with DNS-data
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HILL FLOW
COMPARISON OF HTLES TO URANS AND LES
Q-criterion iso-surface given by HTLES simulation
Introduction Hybrid model: HTLES Results Conclusions & perspectives
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2D slice
HILL FLOW SETUP
• Hill height h = 28 mm • Length of the domain Lx = 9h
• Height of the domain Ly = 3.035h
• Depth of the domain Lz = 4.5h
• 𝑅𝑒ℎ = 10 595 • Reference data: well-resolved LES data (Temmerman et al. [6])
Slip wall
Introduction Hybrid model: HTLES Results Conclusions & perspectives
Periodic Periodic
+ axial momentum
source
Wall: Wall function
Wall: Wall function 𝑦+ < 4
• 5.8 million cells
[6] Fröhlich, J., Mellen, C. P., Rodi, W., Temmerman, L., & Leschziner, M. A. (2005). Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. Journal of Fluid Mechanics, 526, 19-66.
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QUALITATIVE ANALYSIS: MEAN VELOCITY STREAMLINES
URANS: limited accuracy Recirculation length is overestimated
The center of the recirculation is shifted away from the hill
HTLES: close results to the reference
Recirculation length is close to the reference
Good location of the recirculation center
Introduction Hybrid model: HTLES Results Conclusions & perspectives
UR
AN
S R
efer
ence
W
ell r
eso
lved
LES
HTL
ES
x
x
x
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MEAN AXIAL VELOCITY PROFILES OVER THE ALTITUDE
URANS shows discrepancies with the reference data
HTLES gives accurate results in term of:
Separation location
Reattachment location
Farfield velocity profiles
Introduction Hybrid model: HTLES Results Conclusions & perspectives In
flo
w
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MEAN TOTAL TURBULENT ENERGY PROFILES ALONG THE ALTITUDE
URANS under-estimates the turbulent kinetic energy profiles
HTLES gives satisfactory kinetic energy profiles compared to the reference data
Introduction Hybrid model: HTLES Results Conclusions & perspectives In
flo
w
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STEADY FLOW RIG
Q-criterion iso-surface given by HTLES simulation
Introduction Hybrid model: HTLES Results Conclusions & perspectives
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STEADY FLOW RIG SETUP
Parameters Value
Fluid N2
𝑅𝑒𝐷 30000
Mass flow rate (Kg/s) 0.055
𝑈𝑖𝑛𝑙𝑒𝑡 (m/s) 65
Outlet pressure (atm) 1
References: LDA measurements [7]
Fixed valve
Inlet Fixed flowrate
Outlet: Fixed pressure
Velocity field of the HTLES simulation
Introduction Hybrid model: HTLES Results Conclusions & perspectives
[7] Thobois, L., Rymer, G., Souleres, T., & Poinsot, T. (2004). Large-eddy simulation in IC engine geometries (No. 2004-01-1854). SAE Technical Paper.
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MESHING STRATEGY
30 < 𝑦+ < 100 Total cells= 1M4
1 mm 2mm 8mm
Introduction Hybrid model: HTLES Results Conclusions & perspectives
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QUALITATIVE ANALYSIS: MEAN VELOCITY STREAMLINES
Close results between HTLES and LES
The first recirculation at the cylinder head is the same in the 3 simulations
The second recirculation length given by URANS is bigger than HTLES and LES predictions
Introduction Hybrid model: HTLES Results Conclusions & perspectives
UR
AN
S H
TLES
LE
S
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MEAN VELOCITY PROFILES ALONG THE RADIUS
20 mm
70 mm
velocity profiles are compared at two positions
(URANS) (LES) (HYBRID)
20
mm
• Good agreement with LDA measurements: velocity magnitudes are good located and well estimated
• LES and HTLES show the same radial profiles at 20 mm
• URANS simulations under-estimates
the radial velocity at 𝑟
𝑅∈ [0.6; 1]
• URANS over-estimates the axial velocity in the core region
• LES and HTLES show better assesment of the axial velocity at 70 mm
70
mm
Introduction Hybrid model: HTLES Results Conclusions & perspectives
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MEAN VELOCITY PROFILES ALONG THE RADIUS ARE BETTER PREDICTED BY HTLES AND LES
20 mm
Introduction Hybrid model: HTLES Results Conclusions & perspectives
20
mm
• All the simulations show good agreements of velocity magnitudes • LES and HTLES enhance slightly prediction of the radial velocity at 20 mm at
the recirculation region
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MEAN VELOCITY PROFILES ALONG THE RADIUS ARE BETTER PREDICTED BY HTLES AND LES
70 mm
Introduction Hybrid model: HTLES Results Conclusions & perspectives
70
mm
• URANS over-estimates the axial velocity in the core region • LES and HTLES show better results of the axial velocity at 70 mm than
the URANS
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20 mm
70 mm
20
mm
7
0 m
m
Introduction Hybrid model: HTLES Results Conclusions & perspectives
MEAN VELOCITY PROFILES ALONG THE RADIUS ARE BETTER PREDICTED BY HTLES AND LES
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PRESSURE PROFILES ALONG THE AXIAL DISTANCE
The head loss is over-predicted by LES simulation
The head loss is predicted correctly by HTLES and URANS simulations
ΔPLES ΔPHTLES
Introduction Hybrid model: HTLES Results Conclusions & perspectives
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CONCLUSIONS AND PERSPECTIVES
Introduction Hybrid model: HTLES Results Conclusions & perspectives
Consistent hybrid model was derived from k-𝜔 SST model
HTLES gave very good results compared to the reference data in three situations Attached boundary layers: channel fow
Highly separated flow: hill flow
simplified ICE configuration: steady flow rig
Results showed that HTLES combines the advantages of URANS and LES 1. Accurate prediction of the attached boundary layer flows by using URANS near the wall
2. Good predictions of separated flows by using the scale resolving mode far from walls
3. Fluctuation predictions as accurate as LES
Perspectives:
Explore the mesh dependency of the method
Extend the method to time-dependent flows and apply it to unsteady in-cylinder flows
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