Post on 07-May-2022
Numerical analysis of pressure fluctuations in shear layers at the rear of an Ahmed
body with a slant angle of 47°
28th November 2016
Stéphie EDWIGE – Yoann EULALIE – Philippe GILOTTE – Iraj MORTAZAVI
AUTO EXTERIOR DIVISION
Pressure fluctuations in shear layer : Outlines
Objectives :
Wake flow analysis of the 47° Ahmed Body drag reduction control strategy on SUV vehicle
Outlines :
Context : Generic SUV benchmark study
Wake characterization and correlation with pressure fluctuations
Dynamic and spectral analysis of shear layers
Vortex identification with Dynamic Modal Decomposition based on characteristic frequencies
Pressure drop mechanism in the near wake and flow control proposal
Conclusions
2
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AUTO EXTERIOR DIVISION
Pressure fluctuations in shear layer : automotive context
Aerodynamic force reduction on SUV vehicle
A growing market in SUV vehicle with important CO2 emissions (upper than 95 g/km)
Flow analysis around a generic shape and a Ahmed body with 47° slant angle (same rear angle than SUV)
Research of flow control solution at rear of a Ahmed body with 47° at 𝑅𝑒𝐻 = 400 000
28 NOVEMBRE 2016
3
50
126,7 201,6
20
47°
731
20
R=70
143
114
94 89
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CO2 emission for different SUV vehicles Generic SUV and Ahmed Body with 47° slant angle
30% due to aerodynamic losses on NEDC cycle
H
AUTO EXTERIOR DIVISION
Aerodynamic force distribution on SUV and Ahmed body :
PO SUV at full scale (VLES LBM solver)
Ahmed body at 47° at reduced scale (LES FEM solver cf.EULALIE,2014)
Pressure fluctuations in shear layer : automotive context
28 NOVEMBRE 2016
4
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-20% 0% 20% 40% 60% 80% 100% 120%
Side roof
front
rear
wheel
underbody
Total
Cx SUV Cx CA 47° 4 feet 30m/s Metka ASME 2014
Cx per surface
27 %
29 %
76 %
17%
AUTO EXTERIOR DIVISION
𝑥𝐺 [mm] 𝑦𝐺 [mm] 𝑧𝐺 [mm]
Wake pressure barycenter : 𝑥𝑖𝐺 = ∫ 𝑥𝑖 . 𝑃 𝑥 𝑑𝑥𝑖
PD
F[𝑧
𝐺]
PD
F[𝑦
𝐺]
PD
F[𝑥
𝐺]
Statistic wake characterization :
Quasi-torus iso-value of time average Cp
Pressure barycenter criteria : Gaussian distribution in the wake
Pressure minima criteria : Non Gaussian distribution for Y and Z coordinates
Pressure fluctuations in shear layer : Wake flow analysis
28 NOVEMBRE 2016
5
DIFFUSION RESTREINTE
𝑧𝑃𝑚𝑖𝑛 [mm]
Cp min
t [s
]
t [s
]
𝑥𝑃𝑚𝑖𝑛 [mm] 𝑦𝑃𝑚𝑖𝑛 [mm]
PD
F[𝑧
𝑃𝑚
𝑖𝑛]
PD
F[𝑦
𝑃𝑚
𝑖𝑛]
PD
F[𝑥
𝑃𝑚
𝑖𝑛]
Wake pressure minimum position
AUTO EXTERIOR DIVISION
Wake decomposition as a function of 𝑧𝑃𝑚𝑖𝑛
Presence of two independent minimum of pressure
Low pressure area are correlated to energetic pressure rms
Pressure fluctuations in shear layer : Wake flow analysis
28 NOVEMBRE 2016
6
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𝐶𝑝 [-] for 𝑍𝑃𝑚𝑖𝑛 in low part
𝐶𝑝 [-] for 𝑍𝑃𝑚𝑖𝑛 in top part
𝑃𝑅𝑀𝑆 [-] for 𝑍𝑃𝑚𝑖𝑛 in low part
𝑃𝑅𝑀𝑆 [-] for 𝑍𝑃𝑚𝑖𝑛 in top part
AUTO EXTERIOR DIVISION
Unsteady correlation between Pmin and P’ position
Pressure fluctuations : 𝐶𝑝′ 𝑥 , 𝑡 = 𝐶𝑝 𝑥 , 𝑡 − 𝐶𝑝 𝑥
Computation of : 𝐷 𝑡 = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐶𝑝𝑚𝑖𝑛 𝑡 ; 𝐶𝑝
′ 𝑚𝑎𝑥𝑡
𝐶𝑝𝑚𝑎𝑥′ always close to 250mm
Pressure fluctuations in shear layer : Correlation study 7
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Distribution of pressure minima colored by
distance to pressure fluctuation maxima
𝐷𝑡
[𝑚𝑚
]
𝑫
Cp RMS in the vicinity of the lower edge
𝑪𝒑𝑹𝑴𝑺𝒎𝒂𝒙
Time average pressure coefficient in the vicinity
of the lower edge
𝑫
𝑪𝒑𝒎𝒊𝒏
AUTO EXTERIOR DIVISION
Pressure fluctuations in shear layer : spectral analysis
Fluctuations analysis in an energetic RMS pressure region
Focus on the dynamic of the top and bottom shear layers
Monitoring point identification at 𝑥𝑚𝑜𝑛𝑖𝑡 from lower edge
Strictly periodic wave and perturbation at 𝑓𝑙 frequency
8
PSD of 𝐶𝑝′ 𝑥𝑚𝑜𝑛𝑖𝑡, 𝑡
Pressure fluctuations
on shear layer
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t = t2
Monitoring point
𝑥𝑚𝑜𝑛𝑖𝑡
t = t1
𝑥𝑚𝑜𝑛𝑖𝑡
t = t1 t = t2
𝑓𝑙
Pressure fluctuations at
monitoring point 𝐶𝑝′ 𝑥𝑚𝑜𝑛𝑖𝑡 , 𝑡
Strouhal 𝑆𝑡𝑙
AUTO EXTERIOR DIVISION
Shear layer fluctuations analysis
1D wave model along x : 𝛛𝟐𝐂𝐩𝐟
𝛛𝐱𝟐 =𝟏
𝐜𝟐
𝛛𝟐𝐂𝐩𝐟
𝛛𝐭𝟐 ⇒ 𝐶𝑝′ ∝ sin 2𝜋𝑓𝑡 . sin 2𝜋𝜆𝑥
Celerity in X direction at f=𝑓𝑙 : C = Vref/2
Shear layer is a source term 𝚫𝐏 = 𝐐𝐜𝐫𝐢𝐭 in the separated flow region
Wake pressure minima are transported by the wave celerity
Pressure fluctuations in shear layer : spectral analysis 9
𝑥𝑚𝑜𝑛𝑖𝑡
𝐿0
Pressure fluctuations at
monitoring point 𝐶𝑝′ 𝑥𝑚𝑜𝑛𝑖𝑡 , 𝑡
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𝝀
𝟏/𝒇
𝟏/𝒄
Pressure fluctuations
Cp′ x, t on line L0
AUTO EXTERIOR DIVISION
Shear layer fluctuations analysis
Feet shedding at 𝑓ℎ
Vortex pairing with phase shift
Pressure fluctuations in shear layer : spectral analysis 10
𝐿𝑦
Phase average of Vx’/Vref at high frequency 𝑓ℎ Phase average of Vy’/Vref at high frequency 𝑓ℎ
-W/4
+W/4
Velocity fluctuations on line Ly
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+W/4 -W/4
𝑉𝑥′ 𝑥, 𝑡 /𝑉𝑟𝑒𝑓
+W/4 -W/4
𝑉𝑦′ 𝑥, 𝑡 /𝑉𝑟𝑒𝑓
phase 0 2𝜋
phase 0 2𝜋
AUTO EXTERIOR DIVISION
Proper Orthogonal Decomposition : method description
Snapshots method (Sirovitch,1987)
Pressure decomposition
256 fields used, sampled at 1000Hz in the spectral domain [ 4Hz - 500Hz ]
Pressure fluctuations in shear layer : DMD analysis 11
DATE FOOTER CAN BE PERSONALIZED AS FOLLOW: INSERT / HEADER AND FOOTER
S[ ]
),(')(),( xtuxuxtu ii
N
k
ki
k
i xtaxtu )().(),(' )(xk
)( i
k ta
U∞
),('),('1
xtuxtuN
R ji
X
ij
iiiR
iik xtux
),(')( )(),(')( xxtut kiik
1/
2/
3/ are proper modes are modal coefficients
R is the correlation matrix ),( ii
are eigen values and eigen vectors of R
x
Proper mode Modal coefficient
= +
Average field Reconstructed field at time ti
ti
k
)(xk
)( i
k ta ),( xtu i
N modes
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AUTO EXTERIOR DIVISION
Dynamic Mode Decomposition combined with POD (Frederich,2011)
3D data of Vx,Vy,Vz and P in the wake with a sampling frequency range of [2.5Hz – 1000Hz]
Companion matrix construction 𝑈2𝑁 = 𝑈1
𝑁−1 . 𝐶 based on sample 𝑈1𝑁 = [𝑢1 𝑢2 … 𝑢𝑁]
Inversion : 𝐶 𝑣 𝑚 = 𝜆𝑚𝑣 𝑚 with 𝑐𝑗 calculated with 𝑅𝑖𝑁 = 𝑅𝑖𝑗 𝑐𝑗𝑁−1𝑗=1
- 𝜆𝑚 DMD eigenvalues 𝜆𝑚 = ||𝜆𝑚|| . 𝑒2𝜋𝑖𝑓𝑚 Δ𝑡 ∈ ℂ
- 𝑣 𝑚 = 𝑈1𝑁𝑣 𝑚 the DMD mode
- 𝑓𝑚 =ℑ ln 𝜆𝑚
2𝜋Δ𝑡 the associated frequency and 𝜎𝑚 =
ℜ 𝑙𝑛(𝜆𝑚)
Δ𝑡 the growth rate
Reconstruction : 𝑢𝑘 = 𝛼𝑚 𝑡 . 𝑣 𝑚 𝑁𝑚=1 with 𝛼𝑚 𝑡 = ℜ( 𝜆𝑚
𝑘.Δ𝑡)
Pressure fluctuations in shear layer : DMD analysis 12
S[ ] x
Dynamic mode 𝑣 𝑚(𝑥 ) Modal coefficient 𝛼𝑚 𝑡
= +
Average field Reconstructed field at time ti
𝑢 𝑥 , 𝑡𝑖
ti
k
N modes
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AUTO EXTERIOR DIVISION
Mode pressure fluctuations in the vicinity of the rear
DMD advantages :
– Periodic contributions can be easily separated
recirculation in the vicinity of the rear at 𝑓𝑙 mode
Pressure fluctuations in shear layer : DMD analysis 13
Velocity vectors and 𝐶𝑝′ based on DMD reconstruction
1. 𝑓𝑙 contribution : a. Ascending phase with high pressure; b : Descending phase with low pressure ;
2. 𝑓𝑙+𝑓ℎ contributions : a. Ascending phase with high pressure; b : Descending phase with low pressure ;
1a. Snapshot at t = t1 1b. Snapshot at t = t2
1a. Snapshot at t = t1 1b. Snapshot at t = t2
* *
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t = t2
Pressure fluctuations
at monitoring point
𝐶𝑝′ 𝑥𝑚, 𝑡
t = t1
AUTO EXTERIOR DIVISION
Modal energy transfer
𝑓𝑙 mode is more energetic than 𝑓ℎ
Strong interaction between shear layer wave and near wake flow : to be confirmed by growth rate analysis
Pressure fluctuations in shear layer : DMD analysis 14
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Flow control proposition :
Closed loop control based on 𝑓𝑙 measured at 𝑥𝑚𝑜𝑛𝑖𝑡 pressure fluctuations measurement
Objective : to force the ascending phase with active control energy source
𝑓𝑙 and 𝑓ℎ reconstructed snapshot
log 𝑓 lo
g𝑣
𝑖
Modes energy as a function of frequency
𝑓𝑙
𝑓ℎ
AUTO EXTERIOR DIVISION
Prospects :
Flow control at 𝑓𝑙 for pressure increase on the basis
Application on SUV Benchmark application
Experimental validation
Conclusions :
Identification of shedding and inner recirculation distinct
modes
Identification of a monitoring point capturing information
in a sensitive zone
Modal description of wake pressure flow thanks to DMD
analysis
Pressure fluctuations in shear layer : conclusions 15
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at t=t1
Questions ?