Thermal and mechanical non ... - · PDF fileAEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Thermal and mechanical non-equilibrium effects on turbulent flows: fundamental studies

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY

Thermal and mechanical non-equilibrium effects on turbulent flows: fundamental studies of energy

exchanges through direct numerical simulations, molecular simulations and experiments

Diego A. Donzis1 Rodney Bowersox1 Simon North2 William Hase3

1Department of Aerospace Engineering, Texas A&M University

2Department of Chemistry, Texas A&M University 3Department of Chemistry and Biochemistry, Texas Tech University

AFOSR Review – July 2015 Tullahoma, TN

BRI - FA9550-12-1-0443


Research Team

• Diego Donzis – Fundamental and numerical simulations

– Agustin Maqui, Aditya Konduri, Daniel Chen (PhDs); Sualeh Khurshid (UG)

• Rodney Bowersox – Nonequilibrium transport modeling and experimentation

– Chi Mai, Brianne McManamen (PhDs), Evan Marcotte (UG)

• Simon North – Chemical kinetics and experimentation

– Rodrigo Sanchez-Gonzalez (post-doc); Wade Eveland, Nic West (PhDs)

• William Hase – Chemical kinetics and molecular simulations

– Amit Paul, Swapnil Kohale, Subha Pratihar (post-docs)


Outline

• Motivation

• Turbulence and thermal non-equilibrium (TNE) – Stationary and decaying flows

– Diagnostic Development in TNE

• Turbulence and mechanical non-equilibrium (MNE) – Shock-turbulence interactions

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Air Force Motivation


Turbulence-TNE interaction: motivation

• Only few studies: clear link between internal molecular structure and turbulence processes

• But coupling is insufficiently understood (e.g. to affect control)

• Improving understanding and modeling of these mechanisms are scientific challenges that can lead to new opportunities to extract fluid energy


Turbulence + TNE/MNE

• Long term objective: Control of turbulence across the spectrum via TNE and MNE – Vibrational modes: large-scale prod/diss

(Fuller etal JFM 2014)

– Rotational modes: small-scale dissipation (numerical study, Liao etal PRE 2010)

– MNE: shock-turbulence interactions (Donzis PoF 2012a,b, IUTAM 2013; Bowersox 2013)

• Quantify and understand turbulence response to TNE and MNE in canonical flows: – decaying/stationary homogeneous – shock-turbulence interactions

Amplification factor

K = δ/η

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Project Scope


• Theory and direct numerical simulations: Donzis, Hase • Details of molecular energy transfers: North, Hase • TNE turbulence experimentation: Bowersox, North

– Diagnostics development in TNE • Experimental techniques: North, Bowersox

• Turbulence and mechanical non-equilibrium (MNE) – Shock-turbulence interactions in TE

• Theory and direct numerical simulations: Donzis • Experiments at M=6: Bowersox, North

– TNE effects • Theory and numerical simulations: Donzis, Hase • Experiments in TNE: Bowersox, North

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Approach

• DNS: isotropic, normal shocks, channels, BL • resolve all spatial/temporal scales • systematically vary temp., relaxation times, . . . • impossible-to-measure quantities

• Experiments: mesh, channel, BL • Rotational/vibrational photo-excitation • Mechanical non-equilibrium: shock turbulence

interactions

• Molecular simulations: collisional transfers • accurate potential energy functions • different molecular systems: NO2, C6F6, Cl2

• Internal modes: relaxation and diffusion processes

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Direct Numerical

Simulations

• Direct Numerical Simulations: – Incompressible: spectral in space, RK2/4 in time – Compressible: compact (spectral-like) in space, RK3/4 in time – Steady state with solenoidal and dilatational forcing – TNE effects: transport equation for ev (Landau-Teller)

• Substantial effort on massively parallel codes – Scaled to more than 0.5M cores – Challenges in most subsystems at Peta (and Exa) scales – New paradigm at Exascale: exploit asynchrony (Donzis etal JCP 2014)

• Large database – Resolutions up to 20483

– Turbulent Mach number Mt = 0.1 - 0.8 – Taylor Reynolds number Rλ = 24 – 400

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Experimental Approach

• Apparatus - Actively Controlled Expansion (ACE) hypersonic tunnel

Shock turbulence interaction with varying freestream turbulence

- Repetitively Pulsed Hypersonic Test Cell 1: Thermal energy exchange and characterizing the LINE concept

- Repetitively Pulsed Hypersonic Test Cell 1: Shock turbulence interaction with thermal NE

- Instrumentation VENOM (discussed later), fast response Kulite Pitot probes, Hot-wire anemometry

Facility Mach No. Re/m (million/m)

Test Section Run Time

Duty Cycle

ACE Tunnel 5.0 – 8.0 0.3 – 7.0 9” x 14” 45 s 2 h

RPHT Cell 1 2.9, 3.8, 4.6, 6.2 *** 0.5” – 2.0” 10 ms 1 s

RPHT Cell 2 3.0 – 6.0 0.3 – 10.0 4” x 4” 250 ms 30 s


Actively Controlled Expansion Tunnel

• Flow Conditions – M = 5 – 8 (Continuous) – Re/m = 0.2 – 7.0 million – 9”x14” Nozzle Exit – Run Time = 40 sec

• BRI Role: Shock-Disturbance Interaction Studies


Repetitively Pulsed Hypersonic Test Cell 1

• Flow Conditions – M = 2.9, 3.8, 4.6, 6.2

– 0.5 – 2.0” exit diameter

– Pulsed at 1 Hz

– Run Time = 10 msec

– Synchronize with lasers

• Experiments – Diagnostic Development

– Energy Exchange 0.7% rms


Repetitively Pulsed Hypersonic Test Cell 2

• Flow Conditions – M = 3.0 – 6.0

– 4” x 4” pulsed facility

– Run Time = 200 msec

– Synchronize with lasers

• Experiments – Shock interaction studies

– Thermal non-equilibrium studies


Outline


AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Laser Induced Non-Equilibrium

(LINE) Turbulence

• Perturbation can be tuned: molecular system, number of lines, mode specificity

– Cl2 at 355 nm: > 2000 m/s; C6F6 at 266 nm: all vibration

• Can we generate and control turbulence using TNE? Can we generate turbulence in TNE?

• LINE concept: photodissociation of e.g. NO2 at 355nm; fragments with velocities ∼ O(1000) m/s

5% NO2/N2 • ~Double the

temperature • M = 4.6, T = 58K

DNS

Background


time

<ε>

τ*

• When is realistic turbulence established? – Incompressible simulations with LINES as ICs – Critical time scale τ* – Small difference lead to long distances at high speeds

• New results – Radial statistics around lines: spreading rates – Vorticity production mechanisms: enstrophy production – Spatial distribution of energy in time: stages of evolution – More realistic setup: compressible spatially evolving LINEs…

REl: Reynolds number based on IC

τ*El/ν

τ*~(ν/El)REl1.4

• Can predict time to reach fully turbulent flow and Re

• Higher Re requires longer times: challenge for experiments

Laser Induced Non-Equilibrium (LINE) Turbulence

Distance between lines

time

w(r

)


New results: compressible LINEs


• Trigger turbulence using TNE (photoexcitation) – Translation, rotation, vibration excitation: depending on molecular system – Possible macroscopic perturbation in temperature, density, velocity,… – Experimental conditions

• Relevant non-dimensional parameter ∆K: additional KE, ∆e: additional internal energy

• Qualitative differences: – Low Q: narrow influence; turbulence is not established – High Q: high spreading rate of perturbation; realistic turbulence

KQe

∆=

∆

LINEs

Flow direction

Low Q High Q


New results: compressible LINEs


• Low Q: large T increase relative to TKE, leads to high dissipation rates (of TKE) – turbulence is quenched

distance downstream

Width of perturbation: b

Q

Q

Mach line

Spreading rate: db/dx Mach line

Normalized dissipation

Q

Skewness of du/dx

fully turbulent


• Equilibrium

• But T has random fluctuations:

• Thus, , instead:

(KT=θv/T; gT, gM: universal functions)

• Mean vibrational energy in TE: higher than laminar flow at same mean T

• Similar results for Ev*=ρ ev

*

• Are results independent on forcing scheme?

Turbulence-TNE interaction: stationary flows

Background: fundamentals of energy distribution *

exp( / ) 1v

v vv

Re eT

θθ

= ≡−

2 4' tT M

* *( )v ve e T≠

( )( )

* * 24

2*

'( ) ( )v vT T M T t

v

e e T Tg K Ag K Me T T

−= ≈

(θv: charact. vib. temp.)

22' /T T

Mt

(Donzis & Jagannathan JFM 2013)

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Turbulence-TNE interaction:

stationary flows

New results: universality of effects of turbulence in TNE

Mt 22' /T T

22' /T T

* * *[ ( )] / ( )v v ve e T e T−* * *[ ( )] / ( )v v vE E T E T−

• Extended and implemented new forcing schemes: • solenoidal (SF), dilatational (DF), energy (EF)

KT

Symbol colors: SF, DF, SF+EF, DF+EF Dashed lines: analytical results

* * *[ ( )] / ( )v v ve e T e T−


stationary flows


Κτ

• Out of equilibrium: • Landau-Teller exchange: relaxation towards equilibrium

• Important parameter: Kτ = τv/τη (τη: Kolmogorov time scale) • Statistically stationary state always out of equilibrium - depends on Kτ

*/ ( ) ( ) /v v v v vDE Dt D e E E τ= ∇ ⋅ ∇ + −

Κτ

Fully developed turbulence at Rλ~60, Mt~0.3. IC: vibrationally cold

<Ev>

t/τη t/τη


stationary flows


• Can obtain analytical expressions for ratio of mean vib. energy to mean trans-rot. energy, <Ev>/<E> in the limits: – : frozen turbulence – : frozen TNE

<Ev>/<E>

22' /T T

ΚΤ

• Strong turbulence: more energy into the vibrational mode

• Effect stronger for slow relaxation (high Kτ)

• Fundamental change in energy distribution

Mt

Kτ → ∞0Kτ → Kτ → ∞ 0Kτ →


decaying flows

• Decaying flows (spatially or temporally) are found in practice • How do they change when TNE is present? Can use TNE to

modify/control turbulence?

t/τv0 Sv0 t/τv0

Dissipation K

E

Ev K

p.d (Ev*- Ev)/τv

<ε>

Energy flow • Relative importance of TNE and

turbulence cascade:

• Sv0>>1: TNE dominates • Sv0<<1: turbulence unaffected

*| |v vv

v

E ESτ ε

−=

< >

Peak of dissipation

Ev0/E0

Ev0/E0

SK=(Ev0+Ev0*)/K

Dashed: theoretical limits

Low Sv0: turbulence unaffected

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Bridging experiments and

DNS: molecular simulations

• Molecular simulations (VENUS): classical trajectory chemical dynamics simulations – photo excited C6F6 surrounded by a bath of gas (Paul etal JCP 2014)

– relaxation, diffusion, transfer/collision, V-R/V, effect on bath

• Bi-exponential energy decay: • Are k’s (τv’s) the same for initially vibr. cold states?

[ ] )()exp()exp()]()0([)( 2211 ∞+−+−∞−= EtkftkfEEtE

Background


New results: “Hot” vs “Cold” C6F6

[ ]1 1 2 2( ) [ ( ) (0) ] 1 exp( ) exp( ) (0)E t E E f k t f k t E= ∞ − − − − − +

Average energy of C6F6 versus time for N2 different bath densities

Each of these curve is fit to a bi-exponential:

C6F6 <E(0)>

(kcal/mol) ρ

(kg/m3) E(∞)

(kcal/mol) f1 f2 k1 (ps-1) k2 (ps-1)

hot 109 20 20.0 0.240 0.760 0.01384 0.00409 cold 5 20 20.6 0.143 0.857 0.0155 0.00127

Initial C6F6 Vibrational Energy (kcal/mol)

Temperature (K) Corresponds to Initial C6F6 V. Energy

Average Total Initial C6F6 Energy (kcal/mol)

N2 Bath Temperature (K)

107.4 (“hot”) 1800 109.2 298

2.98 (“cold”) 50 4.80 298

Comparison with “Hot” C6F6 Simulation

Bridging experiments and DNS: molecular simulations

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY TNE Energy Exchange

C6F6: Initial Model System Well-studied energy transfer system (Troe, Flynn, Mullin, Sevy, Mori, and others)

o UV absorption (266 nm)results exclusively in internal conversion to form highly vibrationally excited ground state molecules (Evib~37,000 cm-1)

o Low frequency out-of-plane vibrations is more efficient vibrational energy transfer than C6H6.

o Initial estimates suggest substantial perturbation of high speed cold (30-70K) flows even at modest seed ratios

Establish experimental timescales and magnitude/mode of flow energy following laser excitation of seeded C6F6 (and other molecular systems) as a function of flow temperature and composition o Initial work at 300 K using a static/slow-flow apparatus with future work in pulsed high speed

flows down to 38 K

x500

Wavelength (nm)

⌠266nm=2.7x10-19 cm2 Absorption Spectrum Providing direct comparison to the

Molecular Dynamics simulations of Hase et al for implementation in the numerical calculations of Donzis


Outline

• Turbulence and thermal non-equilibrium (TNE)

– Diagnostic development in TNE


• Vibrationally Excited NO (laser induced) Monitoring/2 – Two-line Thermometry & Molecular Tagging Velocimetry

• Laser excitation of NO X2Π - A2Σ (0,0) with subsequent relaxation to X2Π(v = 0, 1,…)

– Or use photolysis (355 nm) of NO2 to produce NO X2Π(v=1)

• Low temperature (T < 70K) NO quenching characterization

• Uncertainties: Velocity – 1%, Temperature – 3-5%

• BRI Role: Characterize energy transfer in thermal non-equilibrium flows

VENOM Laser Diagnostic

1 2

1

2


Outline

• Turbulence and mechanical non-equilibrium (MNE) – Shock-turbulence interactions


Shock-turbulence interactions

Background

• Interest: effect on turbulence and on the sock • Developed an alternative to Ribner’s 54

• Unable to capture Rλ and Mt effects • Shock structure neglected

• Amplification factors, shock structure, regimes of the interaction (Donzis PoF 2012a,b)

• But data mainly from shock-capturing simulations:

• Need experiments and shock-resolving simulations • Test theories • Study details of the interaction

• No study of STI with TNE

Mt/(M-1)

Mt2/(M2-1)

rms-to-mean ratio of dilatation at the shock

Scaling suggested in literature (Lee etal PoF 1993)

Proposed analytical scaling

3-1/2 Mt/(M-1)

Regimes: wrinkled, transition, broken


(ρu)’ Re/m = 4e6

Pt2’

Shock-turbulence Interaction

0.0

1.0

2.0

3.0

0 10000 20000 30000

A Pt2

f (Hz)

Mai and Bowersox 2014, Barre et al 1998

New results: experiments at M=6

Re effect

• Kulite Pt2’ Re > 3.5 x 106: Acoustic disturbances Re < 2.5x106: Vortical disturbances Spectral data follow Barre et al

• Hot-wire (ρu)’ – Aρu’ ~ 1.25 (Re/m = 4 x 106)

• Switching to MTV in the RPHT Cell 2

0.90

1.00

1.10

1.20

1.0E+06 3.0E+06 5.0E+06

A Pt2

Re/m

Re effect

Vortical Acoustic

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Shock-turbulence interactions

• Shock-resolving DNS: – Resolve turbulence and shock: computationally

very expensive – Range of Reynold and Mach numbers: especially

unexplored regimes (high K)

New DNS results

S1: random forcing

Recycle

S2: sponge

back pressure

S3: sponge accele-ration

shock

M>1 inflow downstream distance

Longitudinal amplification factor, G (stars: new results)

M-1

Scaling of Ribner 1953 Scaling of Donzis

PoF 2012

K = Rλ−1/2 Mt/(M-1)

Long. Reynolds stresses

Mt

S1 S3 S2

• Pt2: similar behavior as Reynolds stress

• G: better collapse under proposed scaling

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Summary

• Objective: Understand thermal and

mechanical NE turbulence coupling • Accomplishments:

– Turbulence and TNE • Stationary and decaying flows

– Fundamental understanding of energy distribution and governing parameters

– Constructed massive DNS database – Evaluated LINE concept

• Energy exchange mechanism – Performed molecular dynamic simulations and

experiments to quantify vibrational relaxation • VENOM development

– Invisible Ink (NO excitation for v = 1) – Quantified low-temp NO quenching

– Turbulence and MNE • Shock-turbulence interactions in TE

– Developed new scaling laws: collapse data – Performed shock-resolving DNS – Performed hypersonic experiments – Constructed new facility for coupled TNE/MNE

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Next Steps and technical

challenges

• DNS (Donzis, Hase) – Characterize macroscopic parameters for DNS

(vibrational characteristic times, diffusion, etc.)

– Understand and quantify effect of TNE in amplification factors, shock structure, etc.

• Experiments (Bowersox, North) – RPHT Cell 2

• Operate at M = 4.0 (avoid liquefaction) • Shock generators

– LINE with NO2 and C6F6

– VENOM, Hot-wire and Kulite-Pitot diagnostics

– Quantify the effects of laser induced TNE on shock turbulence interactions

• Extend theories (Ribner, Donzis) to include TNE

Shock Turbulence Interaction with TNE

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Publications

1. Donzis D.A., “Shock structure in shock-turbulence interactions” Phys. Fluids, 24, 126101, 2012.

2. Donzis D.A., “Amplification factors in shock-turbulence interactions: Effect of shock thickness” Phys. Fluids, 24, 011705, 2012.

3. Sanchez-Gonzalez, R., Srinivasan, R., Hofferth, J., Kim, D., Tindall, A., Bowersox, RDW, and North, S., “Repetitively Pulsed Hypersonic Flow Apparatus for Diagnostic Development,” AIAA Journal, 50, 691-697, 2012.

4. Donzis D.A. and Jagannathan S., “On the relation between small-scale intermittency and shocks in turbulent flows” Procedia IUTAM, 9, 3-15. 2013.

5. Donzis D.A. and Jagannatham S., “Fluctuations of thermodynamic variables in stationary compressible turbulence'' J. Fluid Mech. 733, 221-244. 2014.

6. Paul A. K., Kohale S. C. , Pratihar S. , Sun R. , North S. W. and W. L. Hase, “A Unified Model for Simulating Liquid and Gas Phase Intermolecular Energy Transfer. N2 + C6F6 Collisions”, J. Chem. Phys. 140, 194103, 2014.

7. Mai, C. and Bowersox, R.D.W., “Experimental Examination of the Effect of Normal Shock Waves on Freestream Turbulence at Mach 6,” AIAA-2014-2641, AVIATION 2014 Conference, Atlanta GA, June 2014.

8. Sánchez-González, R. Bowersox, R.D.W and North, S.W., “Vibrationally excited NO tagging by NO(A2Σ+) fluorescence and quenching for simultaneous velocimetry and thermometry in gaseous flows,” Optical Letters, 39, 2771-2774, 2014.

9. Sánchez-González, R., Eveland, W.D., Mai,* C.L., Bowersox, RDW and North, S.W., “Low temperature collisional quenching of NO(A2Σ+) (v’=0) by NO(X2∏) and O2 between 34 and 109K,” J. Chem. Phys., 141, 074313, 2014.

10. Paul A. K., Kohale and S., Hase W. L. , “A Bath Model for N2 + C6F6 Gas-Phase Collision: Detail of Intermolecular Energy Transfer Dynamics”, J. Phys. Chem. C, DOI: 10.1021/jp512931n

11. Jagannathan S. and Donzis D. A. “Reynolds and Mach Number scaling in stationary compressible turbulence using high resolution direct numerical simulations”, J. Fluid Mech. (under review).

12. Donzis D. A. and Maqui A.F. “Stationary states of turbulence in thermal equilibrium and non-equilibrium ”, J. Fluid Mech. (under review)


Backup


Business Update

• Spending Status • Total awarded $2,223,000 • Total expended $1,680,438.47 • Total encumbered $182,000.29 • Remaining available balance $172,354

• Reporting status • Annual progress report: 15 Sep 15 • Final Technical report: 14 Feb 16 • Vouchering: done monthly

AEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Low-Temperature Quenching

TkTkT

B

iNOiqiq 8

)()( ,,,

πµσ =

Sanchez-Gonzalez et al 2014a

• Collisional Quenching of NO(A2Π+, v’=0) by NO and O2 at Low-Temperature Results

– Low-temp measurement of fluorescence decay rates for different quencher molecule mole fractions – Long-range multipole interactions between NO(A2Π+, v'=0) and the collision partner provides a better

description of the quenching cross-section temperature dependence

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Thermal and mechanical non ... - · PDF fileAEROSPACE ENGINEERING & CHEMISTRY TEXAS A&M UNIVERSITY Thermal and mechanical non-equilibrium effects on turbulent flows: fundamental studies