numerical analysis of pressure fluctuations in shear

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

DIFFUSION RESTREINTE 28 NOVEMBRE 2016


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

DIFFUSION RESTREINTE

CO2 emission for different SUV vehicles Generic SUV and Ahmed Body with 47° slant angle

30% due to aerodynamic losses on NEDC cycle

H


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


-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%


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


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


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


𝐶𝑝 [-] for 𝑍𝑃𝑚𝑖𝑛 in low part

𝐶𝑝 [-] for 𝑍𝑃𝑚𝑖𝑛 in top part

𝑃𝑅𝑀𝑆 [-] for 𝑍𝑃𝑚𝑖𝑛 in low part

𝑃𝑅𝑀𝑆 [-] for 𝑍𝑃𝑚𝑖𝑛 in top part


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


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


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


t = t2

Monitoring point

𝑥𝑚𝑜𝑛𝑖𝑡

t = t1


t = t1 t = t2

𝑓𝑙

Pressure fluctuations at

monitoring point 𝐶𝑝′ 𝑥𝑚𝑜𝑛𝑖𝑡 , 𝑡

Strouhal 𝑆𝑡𝑙

shear2.gif


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


𝐿0

Pressure fluctuations at

monitoring point 𝐶𝑝′ 𝑥𝑚𝑜𝑛𝑖𝑡 , 𝑡


𝝀

𝟏/𝒇

𝟏/𝒄


Cp′ x, t on line L0


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


+W/4 -W/4

𝑉𝑥′ 𝑥, 𝑡 /𝑉𝑟𝑒𝑓

+W/4 -W/4

𝑉𝑦′ 𝑥, 𝑡 /𝑉𝑟𝑒𝑓

phase 0 2𝜋

phase 0 2𝜋


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



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)


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



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


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

* *


t = t2


at monitoring point

𝐶𝑝′ 𝑥𝑚, 𝑡

t = t1


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



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

shear_plus_dmd_reconstructed.gif


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


at t=t1

shear_plus_dmd_reconstructed.gif

Questions ?

numerical analysis of pressure fluctuations in shear

Documents