Presentation of my Ph.D. work on the Improvement of the Near Wall Treatment in Large Eddy Simulation for Aeroacoustic Applications

1. Improvement of wall treatment
in Large Eddy Simulation
for aeroacoustic applications
Chaofan Zhang
Université de Sherbrooke, Canada
16/04, 2019

2. 2
/ Introduction
Jet
Low
speed
fans
Turbine
blades
Landing
gears
High lift
devices
others
Noise sources of a long-haul aircraft
during approach phase1
Landing
gears
An A380 approaching in Heathrow
Motivation
1. Sengissen, Airbus EEA6, 2006

3. 3
• Bluff-body features:
- Boundary layer transition, separation, pressure gradient
• Reynolds numbers of main parts: 2 × 105 to 5 × 106
/ IntroductionLanding of an A380
Q criteria of a modeled landing gear 2
Landing gears
2. Sengissen et al. AIAA, 2015
Motivation

4. 4
• LAnding Gear nOise database for computational aeroacoustic validatiON
• 0.4 scaled Airbus A320 nose landing gear
Aerodynamic measurement Noise measurement
Lagoon project
Sideline microphones
Flyover microphones
~ 1m
𝑅𝑒 𝐷
= 1.5 × 106

5. 53. Piomelli & Balaras, ARFM, 2002
/ IntroductionLanding of an A380
Numberofpoints
wr-LES
wm-LES
Current Capacity
• RANS, DES, LES with limited resolution
• LBM + wall model
• NO Wall-modeled LES !!!
LAGOON project
Methodology
Landing
gear
setup

6. 6
Wall
models:
𝛻𝑃
Implementations
Development
Wall model review
Application
Application
1 LES
3 wm-LES
Validations
Cylinder
Rod-Airfoil
1 wr-LES
3 wm-LES
2 wm-LES
Verifications
Hybrid grid
A priori validation
18 test cases
1 RANS
Proposed methodology

7. 7
Wall-stress
model LES
LES domain extends
down to the wall
Hybrid
RANS/LES
Predefined interface
grids
LES domain exists only
above the interface
exchange
information
at interface𝜏 𝑤
𝑢1
𝑞 𝑤
𝛻𝑃
2D: TBL equations wall model
Solves TBL equations in the
boundary layer
• Can include more physics
• Separate refined embedded grid
• Expensive to have more physics
• Limited to attached flows
Wall models for LES
1.5D Integral wall model
• Cost friendly
• Limited to attached turbulent flowIntegrate the TBL
equations vertically using
given velocity profiles
1D: Analytical wall law
• Simple, negligible cost
• Limited to attached turbulent flowRelates 𝑢1 from LES to the
wall shear stress
• Afzal’s law
- Simple, negligible cost
- Tested in LBM solver LaBs

8. • Wall-law accounting for APG (Afzal)
84. Afzal, IUTAM, 1996; 5. Lee & Moser, JFM, 2015
𝑢+ = 𝜅−1[ln 𝑦+ + 𝜅𝐵 − 2 ln
1+𝛽𝑖 𝑦++1
2
+2 1 + 𝛽𝑖 𝑦+ − 1 ]
𝛽𝑖 =
𝜈
𝜌𝑢 𝜏
3
𝑑𝑝
𝑑𝑥
log-law pressure gradient terms
Eq.(2)
• Near wall generalization
𝑢 𝑔
+
= 𝑢+ × [1 − 𝑒−
𝑦+
𝐶 ]
5
ONLY FOR
TURBULENT BOUNDARY LAYER
Afzal’s law and continuous formulation
Eq.(1)

9. 9
• Laminar region: mean incompressible BL equation
Convection Diffusion
• Subgrid-scale model: wall adapting local-eddy viscosity (WALE)
− zero in pure shear flow as in laminar state BL
− sensor ∶ 𝑟 =
𝜇 𝑡
𝜇
f(r):
blending
function
• Wall-shear stress in the transition region
Integration × 2
neglected
Afzal’s law with transition (LAF)

10. • Prismatic/Tetrahedral elements
• 2 convection directions
• 3 different irregularities
• 3 convection schemes: LW, TTGC, TTG4A
• No artificial viscosity applied
• 2Δ diffusion scheme
10
Simulation domain
Mesh
regular
perturbation
centaur
Verification case

11. 11
LW TTGC TTG4A
Integrated on the
computational domain
Verification case: centaur hybrid grids

12. • Separate 2D resolved RANS simulation
- Turbulence model: 𝑘 − 𝜖 (two−layer model), 𝑦 𝑚𝑒𝑎𝑛
+
= 0.9
• Extraction of BL wall-normal profiles in the APG region:
- Input of the wall-model equations to predict 𝜏 𝑤𝑎𝑙𝑙
12
NACA0012 airfoil, 𝑅𝑒 𝐶 = 480𝐾
APG region
Wall-law equations:
Log-law and Afzal’s law
𝜏 𝑤𝑎𝑙𝑙
Verification case

13. 136. Drela, Springer, 1989; 7. Garcia-Sagrado & Hynes, JFS, 2012
Mean pressure and skin coefficient
6
7

14. 14
• Velocity profiles in good agreement with experimental results
Mean velocity profiles

15. 15
• APG increasing advancing towards the trailing edge
• Wall-stress properly recovered by the continuous Afzal’s law
Wall law predicted shear stress

16. CASE Wall BC Max 𝒚+
Cell No. 𝚫𝐭
WR No-slip wall 3.5 160M 2 × 10−8
𝑠
WM-LOG Log-law 41
23M 2 × 10−7
𝑠WM-AF Afzal’s law 41
WM-LAF Laminar + Afzal’s law 33
16
• Critical regime: 𝑅𝑒 𝐷 = 2.43 × 105
• Wall resolved & modeled LES
• AVBP solver, WALE + TTG4A
𝐿𝑥, 𝐿𝑦, 𝐿𝑧 = 44𝐷, 40𝐷, 3.5𝐷
24𝑘
1.2𝑀
= 2%CPU time on NIAGARA 1.2M hours (Intel Skylake cores, 2.4GHz)
Cylinder: simulation setup

17. 17
Tripping lines at 72∘and 288∘
𝐻 = 0.04%𝐷
10 prisms
30 prisms
10
times
refined
at wall
2∘
2∘
160M cells
23M cells
Cylinder: grids

18. Cylinder: flow regime
18
• All the simulations in the range of the critical regime
Drag Vortex shedding frequency

19. 19
RESO LOG
AFZAL LAF
• Similar global flow topologies are predicted by all the simulations
Cylinder: flow visualisation

20. 20
Cylinder: flow phenomenology
Kelvin-Helmholtz instabilities
Shear layer transition
Vortex pairing and Von Karman shedding
street
𝑆𝑡 𝐾𝐻𝑆𝑡 𝑉𝐾

21. 21
Cylinder: flow phenomenology
laminar
separation
bubble
final
separation
turbulent
reattachmenttransition

22. 22
𝑆𝑡 𝑉𝐾
2𝑆𝑡 𝑉𝐾
0.64
Far-field pressure PSD
Cylinder: noise
𝑆𝑡 𝐾𝐻

23. 23
• Highest peaks on the cylinder
surface around 107.5∘
• Slightly lower peak levels in the
near-field shear layer from 1.0D to
1.8D.
Far-field/wall correlation
Far-field/near-field correlation
D 2D
Cylinder: noise sources

24. 24
• 𝐶 𝑝 of WR and WM-LAF in good
agreement with reference data
• 𝐶 𝑝,𝑟𝑚𝑠 of LAF slightly higher than
the reference
𝐶 𝑝
𝐶 𝑝,𝑟𝑚𝑠
Cylinder: wall pressure coefficients

25. 25
RESO LOG
AFZAL LAF
90∘
0∘ 180∘
| | [pa]
• AF&LOG: over-prediction after 50°
and delayed separation
• WR and LAF: good agreement with
reference data
• Marginal difference between LOG&AF
Mean skin frictionInstantaneous wall shear stress
Cylinder: wall-shear stress

26. 26
WR-LES: separation bubble
first off-wall grid-point
of the corase mesh
• Improved velocity profiles by LAF
• Marginal difference between LOG
and AF in the APG region
Cylinder: velocity profiles

27. 27
90∘
100∘
110∘
• At 100∘ , wm-LES complete the transition to turbulence
• LAF shows slightly higher peak levels at 90∘
and 100∘
than LOG and AF
Cylinder: wall-pressure spectra

28. 28
• wall modeled simulations predict similar far-field spectra in the wr-LES
• LAF shows slightly higher sound level
90∘
, 50D OASPL, 50D
Cylinder: far-field noise

29. 29
CASE Wall BC
Mean
𝒚+
Physical
Time
Cell
No.
𝚫𝐓
NS No-slip 35
0.24s 75M
3
× 10−7
𝑠
LOG Log-law 57
AF Afzal’s law 56
LAF
Laminar+
Afzal’s law
52
Simulation domain Mesh
Mesh cut-off frequency for TTG4A
Lagoon

30. 30
Lagoon: flow phenomenology (LAF)
• Transitional boundary layers
• Massive separations
• Complex interactions
• Presence of wheel cavity

31. 31
Lagoon: flow phenomenology (LAF)
wake
Inboard/outboard sides flow mixing
wheel inboard side
Wheel cavity vortex &
flow solid surface interaction
wheel outboard side
Flow solid surface interaction
Outboard side flow
separation
bottom
Fully 3D flow
features

32. 32
• NS: transition after the flow separation after 90∘
• LOG and AF early transition
• LAF: delayed transition compared with LOG and AF
90∘
60∘
Lagoon: flow around the wheels

33. 33
• Symbols are computed from the
integration of the pressure PSD
• LAF improves the transition to
turbulence compared with LOG/AF
Wall-mean pressure
Cprms
Lagoon: wall-pressure coefficients – wheel

34. 34
• LAF improves the
pressure fluctuations in
the front region
• LAF yields improved wall
shear stress
𝐶 𝑝
𝐶𝑓
𝐶 𝑝𝑟𝑚𝑠
Lagoon: wall coefficients – high leg
𝑅𝑒 𝐷 =
3.55𝑒5
𝑅𝑒 𝐷 =
3.50𝑒5
𝑅𝑒 𝐷 =
2.43𝑒5

35. 35
𝑢 𝑤 𝑤𝑟𝑚𝑠
• All the simulations recover the mean and rms streamwise velocity from
experiment
• LAF shows improved crosswise velocity component 𝑤
𝑤
3𝑐𝑚
𝑢
3𝑐𝑚 after the wheel
Lagoon: near wake velocity profiles
𝑢 𝑟𝑚𝑠

36. 36
K5 K9
K1
K4: 90∘
K2
Lagoon: wheel-surface pressure PSD

37. 37
NS LOG
AF LAF
K24 K25 K26
Lagoon: flow around the main leg
K25

38. 38
Flyover, 90∘ sideline, 90∘
OASPL, flyover OASPL, sideline
Lagoon: far-field noise
1500Hz

39. 39
1500Hz1000Hz
Lagoon: cavity modes
Flyover 90∘ Flyover 90∘

40. 40
Log-law, SMAGO
Log-law, WALE
Lagoon: sensitivity to SGS model

41. 41
K5
K9
K1
K4
K2
Lagoon: sensitivity to SGS model

42. 42
K25
NS
• SGS model has
important effects
• SMAGO too dissipative
K26: in the turbulent wake
Lagoon: sensitivity to SGS model

43. 43
• Verification
− Evaluation of the performance of different schemes on the hybrid meshes
− A priori verification of Afzal’s law
/ Introduction
• Validations
− Validation of the new wall-models on two different configurations
− First compressible wall-resolved LES of the cylinder flow in the critical regime
− Pressure gradient effect second order; transition first order
• Development and implementation
− Implementation of Afzal’s law and sliding temporal average
− Extended model for the laminar and transitional boundary layer
• Application
− First wall-modeled LES on the LAGOON configuration
− Improved results from LAF model
− Strong influence of SGS model
Conclusions

44. 44
• Wall-modeling
- Investigation of the influence of coupling with SGS model
- Sensor using TKE
TKE computation can be achieved by using the running average which has been
implemented for the pressure gradient
- Integral model: from 1D to 1.5D
Perspectives

45. 45
Thank you

46. 46
• C. Zhang, M. Sanjosé, and S. Moreau, “Improvement of the near wall
treatment in large eddy simulation for aeroacoustic applications,” in 2018
AIAA/CEAS Aeroacoustics Conference (AIAA Paper, 2018-3795, Atlanta,
Georgia) pp. 1–17
/ Introduction
• C. Zhang, S. Moreau, and M. Sanjosé, “Turbulent flow and noise sources on
a circular cylinder in the critical regime”, submitted to Physics of Fluids, 2019
• C. Zhang, M. Sanjosé, and S. Moreau, “Wall-modeled Large Eddy
Simulation with adverse pressure gradients: Application to bluff bodies,” in
Proceeding of 26th Annual Conference of the CFD Society of Canada
(Winnipeg, Manitoba, Canada, 2018).
• C. Zhang, M. Sanjosé, and S.Moreau, “Aeolian noise of a cylinder in the
critical regime”, submitted to The Journal of the Acoustical Society of America,
2019
Publications

47. 47
• SGS has important effects
• SMAGO too dissipative
WR-LES
LOG-WALE
LOG-SMAGO
Wall-friction Cprms
Cylinder: sensitivity to SGS model

48. 48
Lagoon: pressure gradient distribution

49. 49
Lagoon: noise radiation

50. 50
Lagoon: noise source separation
LAF-sideline, 90∘
LAF-flyover, 90∘
LAF-sidelineLAF-flyover

51. Compute wall shear stress
Wall model
Convective flux, 𝐹(𝑤)𝐼
Viscous flux, 𝐹(𝑤) 𝑉
Viscous flux at wall cells, 𝐹(𝑤) 𝑉
𝑤
Advance in time
LES solver
iteration n
Extraction of:
LES variables:
Wall model correction
converged
yes
no
∆𝑦, 𝒏
𝛻𝑝1,||
Afzal’s law
𝜏 𝑤
𝒖 𝟏,||
Compute tangential
velocity
Compute smoothed
longitudinal pressure
gradient
𝐹(𝑤) 𝑉
𝑤,||
=
0
𝜏 𝑤 ∙ 𝒙||
𝑞 𝑤 = 0
𝒖 𝟏, 𝜵𝒑 𝟏
grid parameters:
Implementation in AVBP 2

52. 52
Implementation in AVBP 2
• Slip velocity
y u
Δy
11
𝑢0
𝜏 𝑤 =
𝑢1 − 𝑢0
Δ𝑦
× (𝜇 𝑡 + 𝜇)
From wall-model From sgs model
estimated by this equation

53. 53
• Example of Instantaneous model:
- 𝜏 𝑤 : assumed to be aligned with the first off-wall tangential velocity
- Assumption: correlation between the velocity at the first off-wall grid points and 𝝉 𝒘
through an analytical model
1D: analytical model

54. 54
• Turbulent boundary layer equation
- Separate embeded grid with refinement in the wall normal direction
- dependency of the viscosity model for the TBLE: lot of work concern how to adjust the
viscosity model to improve the precision
- Convection terms must be retained to consider the pressure gradient
2D: TBL model

55. 55
• Principles:
- Integration of the momentum equation in y direction using an assumed velocity profiles
- Sliding averaged filtered LES velocities: upper boundary conditions
- Resulting in an ordinary differential equation in time for the wall stress
1.5D: integral model

56. 56
• Principles:
- Integration of the momentum equation in y direction using an assumed velocity profiles
- Sliding averaged filtered LES velocities: upper boundary conditions
- Resulting in an ordinary differential equation in time for the wall stress
1.5D: integral model
Use wall-law at one position - Use integrated wall-law velocity profile
- 𝜈𝑡 is also considered as an average value
of the mixing length model

57. 578. Jacob et al., TCFD, 2005; 9. Giret et al. AIAAJ, 2014
• Experimental study: Rod-Airfoil (NACA0012) (Jacob et al.)
- 𝑅𝑒 𝐷 = 48𝐾, 𝑅𝑒 𝐶 = 480𝐾, spanwise Lz=0.3C
- Validation: WMLES for aerodynamic and acoustic prediction
- Wall-resolved LES (Giret et al.) using the same solver available: reference simulation
Inflow
C C
D=0.1C
Vorticity magnitude
Validation case 2: rod-airfoil

58. 58
Extra-Coarse (XC)Coarse (C)Fine (F)
Case Airfoil: BC & mean y+ Cell
No.
Time step Physical
Time
CPU hours
(for 0.02s)
NS-F no-slip 4 90M 2 × 10−8
𝑠 0.02 s 192K
NS-C no-slip 16 32M 1.5 × 10−7
𝑠 0.1 s 7.4K
LG-XC log-law 40 22M 1.5 × 10−7
𝑠 0.1 s 4.8K
AF-XC afzal’s law 40 22M 1.5 × 10−7
𝑠 0.1 s 4.8K
LE zoom views
• TTG4A scheme
• WALE sgs model
• Wall modeled LES: LOG and AF
4.8𝑘
192𝑘
= 2.5%
Simulation parameters

59. 59
Inflow
Section A
• Similar inflow conditions for the airfoil at section A
Velocity profiles before airfoil

60. 60
Pressure coefficients

61. 61
Slope of −𝑪 𝒇
• Wall-shear improved by using wall-laws
• Slope of the wall resolved LES better recovered by Afzal’s law
Mean skin-friction coefficient

62. 62
Porous FWH surface
• Peak value improved using wall-model compared with NS-C
• Slight improvement using Afzal’s law compared with log-law
4dB
𝜃
Far-field noise at 𝜃 = 120∘

63. 63
Solids FWH surfaces
• Peak value improved using wall-model compared with NS-C
• Slight improvement using Afzal’s law compared with log-law
0.2 0.3
4dB
𝜃
Far-field noise at 𝜃 = 120∘

64. White’s: extention of log-law into compressible and with heat
64
compressibility
Heat flux
Following White: viscous fluid flow, 2nd edition, page 547, 548

65. White’s extension of wall-law
65
Reformulation Restatement of the
incompressible adiabatic
law-of-the-wall*
*Nichols and Nelson, AIAAJ 2005