direct numerical simulation and large eddy...
TRANSCRIPT
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Direct Numerical Simulation and Large Eddy
Simulation of High-Speed Turbulent Flows
Lian Duan
National Institute of Aerospace
Hampton, VA 23666
December 13th, 2011/NIA
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Space Shuttle
Orion
(CEV/CRV)
http://chimeracfd.com/professional/research-images/capsule/schlieren.png
MotivationSpace Access and Planetary (re)entry (Space Shuttle,
CEV/CRV, MSL, etc.)
http://www.nasa.gov/centers/ames/images/content/146600main_sts1anni
v-AC76-1713.jpg
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NASA X-43
Boeing-AF X-51http://www.aerospaceweb.org/question/investigations/q0116.sht
ml
http://trendsupdates.com/boeing-x-51a-waverider-takes-maiden-test-ride-aboard-b-52-
stratofortress/
MotivationAtmospheric Hypersonic Flight External and Internal Flows
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Key Physical FeaturesMultiscale & Multiphyscis
Air-breathing scramjets
http://www.stanford.edu/group/fpc/cgi-bin/fpcwiki/Main/Research#hypersonic
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High-Speed Turbulent FlowsChallenges & Research Approaches
• Grand challenges
(Roy & Blottner Progress in Aero. Sci, 2006, Wright et al. NASA TM 2009-
215388)
– Limited flight-test data with large uncertainties
– Mismatch in energy levels, Reynolds numbers, and Mach numbers for
ground facilities
– Missing data on real-gas effects, heat transfer, and reactions
– Unjustified turbulence models and model parameters
• DNS and LES of high-speed turbulent flows
– provide high-fidelity 3D space and time-accurate turbulence field
– allow for exploration studies
– understand fundamental processes (Compressibility , wall cooling,
catalysis, high enthalpy, shock interactions, etc)
– improve predictive capabilities
– assess techniques for flow control (drag, surface heating, pressure
loading, combustion etc.)
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Outlines
• Methodologies: DNS, LES, etc
• Sample project: DNS of high-speed boundary
layers over riblets
• Summary of other research
• Conclusions & Future work
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BackgroundDNS and LES for Compressible Turbulence
• DNS/LES were well developed for incompressible flows
– Not for compressible flow
• Conflicting requirements for numerical schemes
– Shock capturing requires numerical dissipation
– Turbulence needs to reduce numerical dissipation
• Starting a simulation from a laminar/random initial
condition
– very costly
– hard to control final flow conditions
• Require continuous inflow conditions
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• Weighted Essentially Non-Ocillatory (WENO) Scheme(Jiang & Shu JCP 1996, Martin et al. JCP 2007, Taylor et al. JCP 2007)
– shock-capturing capability
– high-order accuracy (up to 7th order)
– good bandwidth efficiency
DNS of Compressible Turbulent FlowsNumerical Methods
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• Mean flow: Large-domain RANS calculation (DPLR
Code, NASA Ames)
– Prescribe Mach and Reynolds numbers
• Locally transform velocity fluctuations using
Morkovin’s scaling
• Locally compute thermodynamic fluctuations from
Strong Reynolds analogy
DNS of Compressible Turbulent FlowsInitialization Procedure (Martin, JFM 2007)
' '
1 1( 1998)
i i
w wM M Spalart
u u
u u
' 2
' '
'( 1)
uT M T
u
T
T
Initial flow field resembles true flow mean, statistics, structure and spectra
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DNS of Compressible Turbulent FlowsInflow Conditions (Xu & Martin, PhysFluids 2004)
• Periodic boundary condition‒ Isotropic homogeneous turbulence
‒ channel flows
• Generalized rescaling method
‒Flat-plate turbulent boundary layers
•Auxiliary simulation ‒ boundary layer with surface roughness
‒ compression ramp
‒ etc
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12
0
( )
j
j
ii j ji
j j
j j ji j v
j
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ut x
uu u p
t x x
EE p u q u c
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( ) ( ') ( , '; ) ' D
ff x f x G x x dx f
( ) SGS stresses
( ) SGS heat flux
( ) SGS turbulent diffusion
SGS viscous diffusion
ij i j i j
j i i
j j k k j k k
j ji i ji i
u u u u
Q u T u T
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LES of Compressible Turbulent FlowsGoverning Equations & SGS Terms
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• SGS Stresses: Mixed Model (Speziale et al. 1988)
• SGS Heat Flux: Mixed Model (Speziale et al. 1988)
• SGS Turbulent Diffusion (Knight et al. 1998)
• SGS Viscous Diffusion Negligible
• Dynamical Evaluation of Model Coefficients
– Ensemble average along spatial directions (Moin et al. 1991 , Lilly 1992)
– Lagrangian average along the fluid particle paths (Meneveau et al. JFM 1996)
2
32
( )
ij
ij ij ij
ij ij kk
ij i j i j
C A
S S S
A u u u u
2
Prj j j
T j
S TQ C u T u T
x
j k jku
LES of Compressible Turbulent FlowsSGS Models (Martin, Piomelli & Candler 2000)
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DNS and LES for Compressible Turbulence Constitutive Relation (Duan & Martin AIAAJ 2009)
• Conservative form of mass, momentum and energy equation‒ Thermodynamic Properties
‒ NASA curve fits for high-temperature air species ( Gordon & McBride 1994)
‒ Perfect-gas air model for low-enthalpy air ( Roy & Blottner 2006)
‒ Transport Properties
‒ Gupta-Yos mixing rule for high-temperature air mixture (NASA RP-1232)
‒ Power law or Keyes model (Keyes 1952) for low-enthalpy air
‒ Chemical Reaction Mechanisms for Earth Atmosphere
‒ 5 species-air-reaction mechanism (N2, O2, NO, N, O) (Park, 1990)
‒ 11 species-air reaction mechanism (N2, O2, NO, N, O, N2+,O2
+, NO+, N+, O+, e)
‒ Diffusion Model
‒ Fick’s diffusion model
‒Self-consistent binary diffusion (SCEBD) model (Ramshaw, 1990)
‒ Species Boundary Conditions
‒ Simple Models: assuming constant recombination efficiency
‒Supercatalytic
‒Noncatalytic
‒ Material Dependent Catalytic Recombination Model (Natsui et al., JTHT 1996)
,
0s w
Y
n
, ,s w sY Y
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DNS/LES Validation• For turbulent boundary layers against experiments at the same conditions
– Me = 2.32, Reθ = 4450 (Martin JFM 2007)
– Me = 2.9, Reθ = 2300 (Wu & Martin AIAAJ 2007)
– Me=7.2, Reθ=3300 (Sahoo, Schultze & Smits AIAA 2009)
• In the presence of shock waves against experiments
– Wu & Martin AIAAJ 2007
– Ringuette, Wu & Martin JFM 2008
– Ringuette, Wu & Martin AIAAJ 2008
• For high-temperature phenomena
– Duan & Martin AIAAJ 2009
• SGS models for LES
– Martin CTR, 2000,Martin et al. AIAA 2000
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Outlines
• Methodologies: DNS, LES, etc
• Sample project: DNS of high-speed boundary
layers over riblets
• Summary of other research
• Conclusions & Future work
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RibletsLongitudinal Microgrooves
Sketch of Riblet Geometry(Robert, AGARD-R-786 1992)
Example from Nature
silky shark(Bechert & Bartenwerfer, JFM 1989)
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MotivationViscous Drag Reduction
• Viscous drag accounts for a significant portion of total drag
– up to 1/2 for a transonic transport aircraft
– up to 1/3 for a supersonic aircraft
• Two major strategies for reducing skin friction drag
– Delay laminar-turbulent boundary layer transition
– Modify turbulent structures of a turbulent boundary layer
• Riblets for turbulent drag reduction
– “Premier approach for turbulent drag reduction” (Bushnell 1990)
– Drag reduction potential of 8%10% for subsonic flows
(Reviews by Walsh 1990, Coustols 1994, Vishwanath 2002)
– Extra benefits of film riblets (Walsh 1988)
• Reduced fuselage drag due to leakage from pressurized cabin
• Lower roughness drag
• corrosion resistance
• substitute for paint
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Examples of Practical Applications
Swimsuits Racing YachtsAirliners
• Airbus 320: 2% reduction in overall fuel burn (Szodruch, 1991)
• Speedo racing swimsuits: Sidney Olympic Games in 2000
• Stars and Stripes: Winner of America‟s Cup in 1987
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Background
• Riblets extensively investigated for subsonic applications
– Drag reduction potential established via wind tunnel experiments, flight
tests, and channel flow simulations (Walsh, 1990, Choi et al., 1993,
Goldstein et al. 1995, Mayoral & Jimenez, 2011)
– Drag reduction mechanism not well understood
• Measurements challenging in the close vicinity of the grooves
• Lack of detailed near-wall turbulence data
• Few studies in supersonic regime, none for hypersonic flows
– Experiments
• Wind Tunnel:
M =2.97 (Robinson 1988), M=1.5 (Gaudet 1989), M=1.6, 2.0, 2.5 (Coustols & Cousteix,1994)
• Flight test:
M=1.2-1.6 (Zuniga, et al, NASA Tech. Memo 4387)
• Maximum skin friction drag reduction up to 8% has been reported
– No numerical studies
– Unknown effects on heat transfer
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Objectives
• Evaluate riblet effects on turbulent, high-speed boundary
layers using DNS
– Assess the effectiveness of riblets in reducing drag at M>1
– Investigate alteration of flow characteristics due to riblets
– Elucidate the physical mechanism by which riblets reduce drag
and influence heat transfer
• Identify differences, if any, between the drag reduction mechanisms
for incompressible and high-speed boundary layers
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Flow Conditions and DNS Setup
• 7th order WENO (Jiang & Shu JCP 1996, Martin et al. JCP 2007)
• Auxiliary inflow simulation with rescaling (Xu & Martin, PhysFluids 2004)
• Principal simulation
• Lx ≈ 14δi , Lz ≈ 11δi
• 20 riblets in the spanwise direction with L+y ≈ 400
• Nx x Ny x Nz = 400 x 640 x 120 (Total: ≈30 M)
• M∞=2.5, ρ∞=0.1kg/m3, T∞ = 270 K, δi = 4.58 mm
• Reθ=1719, Reτ = 321
• Adiabatic wall
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Computational ParametersRiblet Spacing
Case M∞ s+ h+ α
M25_s20 2.5 21.4 9.7 45◦
M25_s40 2.5 45.3 19.6 45◦
Effects of rib spacing on skin friction
(from Bechert, et al., JFM 1997)
Drag-reducing Configuration
Drag-increasing Configuration
• 32 grid points for each riblet surface
• Grid clustering near the riblet tips
• Tip rounded with R/s < 4%
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Effects of Riblets on Skin Friction Drag
Case Cf x 103 ΔCf/Cf
M25_Clean 2.506 NA
M25_s20 2.331 -7.0%
M25_s40 2.616 +4.4%
212
wfC
u
r w x y
uD dA L L
n
Drag reduction
Drag Increase
• Sensitivity Analysis‒ Grid convergence and domain extent
‒ 32 & 64 points per riblet (≈ 0.7%)
‒ 10 & 20 riblets (≈ 1.0%)
‒ Statistical convergence (≈ 0.4%)
• Maximum numerical uncertainty in total drag ≈ 2.0%
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Case: M25
Spanwise Distribution of Mean Wall Shear
TipValley
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Drag Reduction MechanismsHypotheses
• The universal presence of „streaks‟ (streamwise
counter-rotating rolls) in the wall region (Kline et al. JFM 1967, Kim et al JFM 1987, Karniadakis & Choi
Annu. Rev. Fluid Mech. 2003)
– Average diameter d+≈30
– Undergo cycle of events, known as „bursts‟
• Ejection: slow-moving wall fluid entering the outer region
• Sweep: fast-moving outer fluid entering the wall region
• account for a significant portion of wall drag
• Riblets interact with near-wall streamwise vortices
– Inhibit or restrict the spanwise meandering so as to
weaken the bursting events(Choi JFM 1989, Bechert & Bartenwerfer JFM 1989,
Schwarz et al. IUTAM Symp. 1990, Karniadakis & Choi
Annu. Rev. Fluid Mech. 2003)
– shield the vortices away from the wall so as to expose
only limited surface area to downwash of high-speed
fluid (Choi et al. JFM 1993, Lee & Lee, Exp. Fluids 2001)
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x i
u
Limited area affected by downwash motion
Very similar to incompressible simulations by
Choi et al. (1993)
Drag Reduction MechanismsInstantaneous Flow Fields
M25_s20: Drag Reduction
iu
n u
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Drag Reduction MechanismsInstantaneous Flow Fields
Extensive area affected by downwash motion
iu
n u
M25_s40: Drag Increase
x i
u
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Drag Reduction MechanismsTurbulence Statistics
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BackgroundHeat Transfer
• Reynolds analogy
– Similarity in turbulent transport of momentum and heat
– Reynolds analogy factor nearly constant with RA=2Ch/Cf >1
– Experiments: 1.1 < RA < 1.3 for flat-plate turbulent Boundary Layers
(Hopkins & Inouye, AIAAJ, 1971)
• Controversial findings for riblet effects at subsonic speeds
‒ Reynolds analogy violated (Walsh & Weinstein 1979, Lindemann 1985, Choi &
Orchard, 1997)
• ΔCf < 0 while ΔCh > 0
‒ Reynolds analogy holds with increased heat transfer efficiency relative to
drag (Maciejewski & Rivir 1994, Stalio and Nobile 2003)•
• consistent with RA>1
• No studies on riblet effects on heat transfer for high-speed flows
212
wfC
u
( )
wh
p r w
qC
u C T T
/1
/
h h
f f
C C
C C
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Effects of Riblets at Hypersonic Conditions
Case Cf x 103 Ch x 103 RA=2Ch/Cf ΔCf/Cf ΔCh/Ch
M72_Clean 1.054 0.618 1.17 NA NA
M72_s20 0.983 0.568 1.15 -6.8% -8.1%
• RAriblet ≈ RAflat
• /1
/
h h
f f
C C
C C
Drag Reduction Heat Reduction
• M∞=7.25, ρ∞=0.071 kg/m3, T∞ = 66 K
• Reθ=6735, Reτ = 398
• Cold wall with Tw/Tr = 0.5
• Triangular riblets with s+=19.5, h+=9.5, α=45◦
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Case: M72 Spanwise Distribution of Mean Wall Shear and
Temperature Gradient
Tip ValleyValley Tip
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Summary
• DNS of turbulent boundary layers over riblets in supersonic (M=2.5, adiabatic) and hypersonic (M=7.2, cold wall) regimes
• For riblets with symmetric V-grooves, skin friction drag reduction of approximately 7% is achieved under both regimes
• Flow statistics and visualizations of near-wall structures support the earlier hypothesis that riblets with small enough spacing reduce the viscous drag by restricting the location of streamwise vortices above the wetted surface so that only a limited area is exposed to the vortex induced downwash of high-speed fluid
• For the hypersonic cold wall condition, Reynolds analogy holds. Triangular riblets with s+≈20 reduce surface heat transfer by approximately 8%
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Outlines
• Methodologies: DNS, LES, etc
• Sample project: DNS of high-speed boundary
layers over riblets
• Summary of other research
• Conclusions & Future work
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| |0.8exp
"Numerical Schli
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NS
Summary of Past ResearchCompressibility Effects
(Duan, Beekman & Martin JFM 2011)
“eddy-shocklets”: shocks produced by the
fluctuating fields of the turbulent eddies
DNS of zero pressure gradient adiabatic boundary layer with freestream
Mach number from 0.3 to 12
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Summary of Past ResearchWall Cooling Effects
(Duan, Beekman & Martin JFM 2010)
'
( ) ' '
,
'( , , )w
wu
w rms rms
u x y zR
u
VLSM model, Kim & Arian PoF 1999
Adrian et al. JFM 2000
DNS of zero pressure gradient boundary layer at Mach 5 with
Tw/Tr from 0.18 (cold wall) to 1 (adiabatic wall)
M5, Tw/Tr=0.18
M5, Tw/Tr=1.0
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Summary of Past ResearchHigh-Enthalpy Effects
(Duan & Martin JFM 2011)
DNS of zero pressure gradient boundary layer with high and low
enthalpy levels representative of hypersonic flight (ht,∞≈20 MJ/kg)
and ground based facilities (ht,∞≈0.8 MJ/kg)M∞=21
T∞=226.5 K
P∞=1196 Pa
Tw/Tr≈0.13
M∞=21
T∞=226.5 K
P∞=1196 Pa
Tw/Tr≈0.13
' '
Pr
' 't
Tu w
zu
w Tz
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Summary of Past ResearchTurbulence-Chemistry Interaction
(Duan & Martin AIAAJ 2011)
( , ) ( , )s sw T c w T c
' '''' '
1 1
( , ) ( ) ( ) ( )i i
ns ns
s s s s f i b i
i i
w T c M k T c k T c
M∞=21
T∞=226.5 K
P∞=1196 Pa
Tw/Tr≈0.13
M∞=21
T∞=226.5 K
P∞=1196 Pa
Tw/Tr≈0.13
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Summary of Past ResearchTurbulence-Radiation Interaction
(Duan, Martin, Sohn, Levin & Modest AIAAJ 2011)
Orion Exploration Crew Vehicle (CEV) at peak heating during Earth entry:• Velocity: 9.5 km/s
• Altitude: 53 km
• Angle of attack: 18◦
( , ) ( , )R s R sq T n q T n
( , )R R sq q T n
Turbulence-Radiation Interaction
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Summary of Past ResearchHypersonic Flow over a Deformed TPS Panel
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Advances in Hypersonics, Bertin, Periaux, Ballmann, 1992
Summary of Past ResearchSurface Catalytic Recombination
(Pejakovic, Marschall, Duan & Martin JTHT 2008, 2010)
Quartz Diffusion-Tube Side-Arm ExperimentsExperimental calibration (measurement techniques)
Code Validation (diffusion models and boundary conditions)
Investigation of NO formation at material surface
PA PB
PMT1 PMT2 PMT3 PMT4
Partially-dissociated
gas flow
V1 V2
Titration
port
Pt
As,m
Adsorption Eley-Rideal Langmuir-Hinshelwood
A
A
A
A
A2
A
A
A
A2
A
Desorption
Surface Processes
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Outlines
• Methodologies: DNS, LES, etc
• Sample project: DNS of high-speed boundary
layers over riblets
• Summary of other research
• Conclusions & Future work
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Conclusions• Newly developed DNS and LES methodologies have been
introduced, which include– numerical methods
– initialization procedure
– inflow boundary condition
– SGS models
• The DNS and LES tools have been successfully applied to study multiple critical phenomena in hypersonic flows, including the effects of
– high compressibility
– wall cooling
– high enthalpy
– turbulence-chemistry interaction
– turbulence-radiation interaction
– turbulence-surface interaction
• The numerical tools have been applied to assess techniques for controlling turbulence drag and heat
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Ongoing/Future ResearchMultiscale/multiphysics Simulations
• Environmentally friendly vehicle– Viscous drag reduction
• Laminar-to-turbulent transition prediction and control
• Turbulent drag reduction by surface roughness
– Emission reduction (CO2, CO, NOx, hydrocarbons, soots)• Turbulent combustion
• Turbulence-chemistry interaction
• Reactive flow modeling
Supersonic business aircraft
with natural laminar flow wing
(Kroo, VKI lecture series, 2005)
http://www.standford.edu/group/ctr/
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Future ResearchMultiscale/multiphysics Simulations
• Airbreathing scramjet propulsion system– Shock wave/turbulent boundary layer interaction
– Supersonic combustion , turbulence-chemistry interaction
– Thermal management and heat transfer
Flow inside a generic scramjet engine
Courtesy of Mike Holden, CUBRC
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Acknowledgment• My Ph.D. advisor
– M.P. Martin
• Current NASA Sponsor
– Meelan M. Choudari (for transitional model and turbulence flow control)
• Collaborators
– M. F Modest, D.A. Levin, A.M. Feldick & I. Sohn (for radiation modeling)
– J. Marschall & D.A. Pejakovic (for surface catalytic modeling)
– A.J. Smits & D. Sahoo (for high Mach number experimental data)
– R. Gosse (for fluid-structure interaction study)
• Funding Agencies
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Thank you!
Questions?