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

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

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

Key Physical FeaturesMultiscale & Multiphyscis

Air-breathing scramjets

http://www.stanford.edu/group/fpc/cgi-bin/fpcwiki/Main/Research#hypersonic

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.)

Outlines

• Methodologies: DNS, LES, etc

• Sample project: DNS of high-speed boundary

layers over riblets

• Summary of other research

• Conclusions & Future work

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

• 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

• 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

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

12

0

( )

j

j

ii j ji

j j

j j ji j v

j

ji

j j

j

j

ut x

uu u p

t x x

EE p u q u c

t xQ

xD

( ) ( ') ( , '; ) ' 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

u u u u u u

D u u

LES of Compressible Turbulent FlowsGoverning Equations & SGS Terms

• 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)

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

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

Outlines

• Methodologies: DNS, LES, etc

• Sample project: DNS of high-speed boundary

layers over riblets

• Summary of other research

• Conclusions & Future work

RibletsLongitudinal Microgrooves

Sketch of Riblet Geometry(Robert, AGARD-R-786 1992)

Example from Nature

silky shark(Bechert & Bartenwerfer, JFM 1989)

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

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

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

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

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

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%

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%

Case: M25

Spanwise Distribution of Mean Wall Shear

TipValley

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)

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

Drag Reduction MechanismsInstantaneous Flow Fields

Extensive area affected by downwash motion

iu

n u

M25_s40: Drag Increase

x i

u

Drag Reduction MechanismsTurbulence Statistics

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

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◦

Case: M72 Spanwise Distribution of Mean Wall Shear and

Temperature Gradient

Tip ValleyValley Tip

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%

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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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

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

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

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

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

Summary of Past ResearchHypersonic Flow over a Deformed TPS Panel

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

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A

A

A2

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Desorption

Surface Processes

Outlines

• Methodologies: DNS, LES, etc

• Sample project: DNS of high-speed boundary

layers over riblets

• Summary of other research

• Conclusions & Future work

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

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/

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

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

Thank you!

Questions?