Interaction of Turbulence, Chemistry, and Interaction of Turbulence, Chemistry, and Radiation in Strained Nonpremixed FlamesRadiation in Strained Nonpremixed Flames

Chun Sang Yoo, Hong G. ImDepartment of Mechanical Engineering

University of Michigan

Yi Wang, Arnaud TrouvéDepartment of Fire Protection Engineering

University of Maryland

Sponsored by the DOE SciDAC Program

http://purl.org/net/tstc

Outline of PresentationOutline of Presentation

Introduction

Role of DNS in Combustion Science (a brief version)

Overview: Terascale High-Fidelity Simulations of Turbulent Combustion with Detailed Chemistry (TSTC)

Research Highlights* (work led by U. Michigan)

Computational: Improved Navier-Stokes Characteristic Boundary Conditions (NSCBC)

Science: Counterflow Diffusion Flames with Soot and Radiation Models

Ongoing/Future Work

*More TSTC Research Highlights: Poster SessionWED21: Trouvé and Wang (Maryland)WED22: Rutland and Wang (Wisconsin)

DNS: A Computational MicroscopeDNS: A Computational Microscope

A diagnostic tool to study the fundamental physics of turbulent reacting flows Full access to temporally/spatially

resolved information. Allows identification of key paths

for relevant phenomena, such as turbulence-chemistry interaction

A benchmark tool to develop and validate physical submodels used in macro-scale simulations of engineering-level systems (LES with embedded DNS)

DNSPhysicalModels

Engineering-levelCFD Codes

A KIVA-3V engine simulation

Formation of edge flames in a turbulent counterflow

. S3D0: F90 MPP 3D

. S3D1: GrACE-based

. S3D2: CCA-compliant

Software architecture

. IMEX ARK

. IBM

. AMR

Numerical algorithms

. Thermal radiation

. Soot formation

. Spray dynamics

Physical modelsSciDAC

CCA

Post-processors: In-situ visualization Feature tracking

SciDAC

CMCSSDM

MPP S3D

Hong G. Im, University of MichiganArnaud Trouvé, University of Maryland Chris Rutland, University of WisconsinJackie Chen, Sandia National Labs

TTerascale High-Fidelity erascale High-Fidelity SSimulations of imulations of TTurbulent urbulent CCombustion with Detailed Chemistry (TSTC)ombustion with Detailed Chemistry (TSTC) http://purl.org/net/tstc

SciDAC

CFRFS

S3D: MPP DNS CodeS3D: MPP DNS Code

S3D code characteristics: Compressible reacting Navier-Stokes, total

energy, species equations Fortran 90, MPI domain decomposition Highly scalable and portable on all modern

architectures Numerical algorithms:

8th order non-dissipative spatial finite difference, 10th order dealiasing filter

4th order explicit RK integrator with error monitoring

Additive 4th order RK integrator for stiff chemistry

Improved boundary conditions to allow transverse velocity, flame passage through boundary, or solid walls*

Physical models: Lewis number, mixture averaged, or

multi-component transport Detailed gas-phase chemical

kinetics(Chemkin-compatible)

All thermodynamic properties are functions of T, p, and Yi

Radiative heat transfer (discrete ordinate / discrete transfer method)*

Soot formation* Lagrangian spray model*

*Recent Contributions from the SciDAC TSTC Project

Characteristic Boundary Conditions Characteristic Boundary Conditions

A “pre-requisite” issue for high-quality turbulent combustion DNS

Historical Development General nonreflecting outflow boundary conditions

(Engquist and Majda 1977, Hedstrom 1979) Pressure damping for Navier-Stokes equations

(Rudy & Strikwerda 1980, 1981) Inviscid characteristic theory for Euler equations

(Thompson 1987,1990) Navier-Stokes characteristic boundary conditions (NSCBC)

- Viscous conditions (Poinsot & Lele 1992) Multi-component reacting flows (Baum et al. 1994)

Applications to turbulent and reacting flows have revealed problems of spurious pressure waves, numerical instabilities. Reaction source terms (Sutherland & Kennedy 2003)

Characteristic WavesCharacteristic Waves

x

vL

33

x

wL

44

x

uc

x

pL

21

1

x

p

xcL

222

x

uc

x

pL

25

5

x

vL

23

x

wL

44

x

uc

x

pL

21

1

x

p

xcL

222

x

uc

x

pL

25

5

inflow outflow

• Li : characteristic wave with i

(wave velocities, 1= (uc), 2=3=4=u, 5= (u+c))

Computational

domain

flow

Locally One-Dimensional Inviscid (LODI) Locally One-Dimensional Inviscid (LODI) RelationsRelations

Neglecing transverse convection, viscous, and reactive terms

The incoming Li’s can be determined at both inflow and outflow boundaries using LODI relations

Hard inflow boundary conditions yield large spurious wave reflections : nonreflecting conditions are needed

0

0

0

0

0

0

5

15

4

3

15

2152

xi

xx

x

x

xx

xxx

i L

LL

L

L

cLL

cLLL

Y

p

w

v

u

t

5 and ,4 ,3 ,2 ),(

determined is 1

iffL

L

iiix

i

x

• Inflow boundary

determined are ,,,

)(

5432

target11

xxxx

x

LLLL

ppL • Outflow boundary

Generalized NSCBC for Transverse, Generalized NSCBC for Transverse, Viscous, Reacting FlowsViscous, Reacting Flows

LODI relations are no longer valid: transverse, viscous, reaction terms must be considered in Li’s

ii Y

p

w

v

u

Y

p

w

v

u

itt

tttt

tt

tt

tt

tttt

xi

xx

x

x

xx

xxx

i s

s

s

s

s

s

d

d

d

d

d

d

Y

pp

zpw

ypv

u

L

LL

L

L

cLL

cLLL

Y

p

w

v

u

t

v

vv

v

v

v

vv

1

1

5

15

4

3

15

2152

ppppL x11

)(1

)(1

)(1

)(112

1 xxx SVppt

uc

t

p

Conventional LODI Improved BC

Outflow boundary conditions (at x = lx)

Spatial :

Temporal :

Low-Ma asymptotic expansion yields: Ma

)(1

)(1

)(11

)(1

xxxx SVppL

ppt

uc

t

p12

1

)(1

)(1

)(1

)(exact,11

)(1 1 xxxxx SVaappL

2

1 )(exact,1

)(11

xxappt

uc

t

p

Test 1: Vortex-ConvectionTest 1: Vortex-Convection

Incompressible inviscid vortex

Conditions

Three different boundary conditions

BC1 : conventional LODI with

BC2 : keep all the transverse terms (a = 0.0)

BC3 : improved BC with pressure and transverse

damping (a = M= 0.05)

2

20

200

2exp ,

1

0 cR

yyxxC

x

yu

v

u

2

20

20

2

2

2exp

cc R

yyxx

R

Cp p

0025.0 ,1.0 ,05.0Ma 0 xxc clClRcu

0)(exact,1 x

Vorticity and PressureVorticity and Pressure

LODI Improved BC (a = 0.05)BC2 (a = 0.0)

P

VelocitiesVelocities

LODI Improved BC (a = 0.05)BC2 (a = 0.0)

v

u

Temporal Pressure VariationTemporal Pressure Variation Examine how the solution approaches the steady state The L2-norm :

2

2

0,,

,,

pyxp

ptyxp

Temporal variations of the L2-normsof pressure difference

10-5

10-4

10-3

10-2

10-1

100

101

0 50 100 150 200 250

BC1BC2BC3

||p(x

,y,t

)-p in

f||2

/ ||p

(x,y

,0)-

p inf||

2

Time [sec]

Three test cases Case A: conventional LODI Case B: include source terms in incoming Li’s (Sutherland

& Kennedy 2003)

Case C: improved BC with a = 0.125 (scaling analysis)

Test 2: Ignition HTest 2: Ignition H22-O-O22 Mixture Mixture

Stoichiometric H2-O2 mixture diluted with 50% N2 by volume

2mm 2mm (200 200 grid points)

Initial temperature and pressure, 300K and 1atm

Initial Gaussian temperature peak

)(1

)(112

1 xx Vppt

uc

t

p

)(11

)(1

xx SppL

Temperature and HOTemperature and HO22

Case A (LODI)

Case B(Sutherland & Kennedy)

Case C (Improved BC)

YHO2

T

Test 3: Poiseuille Flow Test 3: Poiseuille Flow (Isothermal Wall)(Isothermal Wall) Viscous terms must be considered Test cases

Case A: conventional LODI B.C. with 1,exact

Case B: including only pressure damping term (a = 0.0) Case C: improved B.C. with a = 0.1

0.990

0.995

1.000

1.005

1.010

1.015

1.020

1.025

1.030

0.0 0.5 1.0 1.5 2.0

Case ACase BCase C

Pre

ssur

e [a

tm]

Time [msec]

Max. pressure

Min. pressure

Temporal variation of pressure

The pressure level of Case A is increased because 1,exact does

not cancel out all the viscous and heat flux effect

The velocity at the outflow boundary in Case B is not accurate: transverse damping term is needed

Test 4: Turbulent Reacting Test 4: Turbulent Reacting CounterflowCounterflow

Transverse terms cannot be ignored

a = 0.01

Use the steady laminar H2air nonpremixed counterflow flame as the initial condition

Turbulence inflow condition

Velocity fluctuations are superimposed on the mean inlet velocities.

Homogenous turbulence

xx

xx

tyvvL

tyuuL

3033

5055

,

,

20

24 2exp~

k

kkkE

(a) temperature (b) vorticity

Strained Nonpremixed Flames with Strained Nonpremixed Flames with Soot and RadiationSoot and Radiation Motivation

Predictive tools for pollutant formation (soot, NOx)

Thermal radiation plays an important role, but has not been incorporated in high-fidelity simulations

Need better understanding of interaction between flow, chemistry, and heat transfer

Objectives

To develop high-fidelity DNS capabilities with advanced physical submodels for soot and radiation

Validate and assess the impact of the advanced physical models in a canonical configuration (flame-vortex)

Perform laboratory-scale simulations to answer science questions on turbulence-chemistry-radiation interaction (future work)

Radiation Models in S3DRadiation Models in S3DBased on gray gas assumption

Radiative heat flux:

Optically thin model (OTM)

Discrete ordinate method (DOM)RTE solved in n discrete directions (ordinates)

Sn approx. number of equations = n(n+2)/2 (2-D) S2: 4 eqs., and S4: 12 eqs.

Discrete transfer method (DTM)RTE solved for n rays (ray-tracing)

,,,1, niSIy

I

x

Iii

ii

ii

s

sn

j

jijjbi ,IΦwIS

4

11

4

rad 4),( bIdSSrIq

44rad 4 TTq

iYT ,

,0),(4

dSSrI

nieIeII nn KSib

KSip

ip ,,1,11

Performance of DOM/DTMPerformance of DOM/DTM

MPI Scalability

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140

DOMDTM

Spee

d-up

Number of processors

Cheetah

Seaborg

Ideal speed-upbased on DOM in Cheetah

Ideal speed-upbased on DTM in Seaborg

Total radiative power

Relative error

DOM is found to be overall superior for the desired accuracy.

Soot Model (Two Equation Model)Soot Model (Two Equation Model)

A semi-empirical two-equation model based on a flamelet approach (Young and Moss, 1995)

Soot number density

Soot volume fraction

200

NnN

n

dt

d

Nucleation Coagulation

Sndt

dfox

vs

Surface growth

OxidationNucleation

)/19778exp(

10085.1

36

exp

exp

2/15

3/23/12

C2/1

2/1

C2/12

2

T

TX

fnndS

c

TTXTc

Tc

TTXTc

Oox

v

• Parameters

Computational ConfigurationComputational Configuration

Calculation procedure

1. Generate 1-D diffusion flame profile (Oppdif)

2. Establish steady diffusion flame in counterflow

3. Superimpose initial vortex pairs

Velocity profile for a vortex

]1[2

)(3)/(2

2

max,

rer

C

u

ru

Lx=2.48cm

Ly=

2.4

8c

m

Ethylene Air

u0 uL

ParametersParameters

Parameter Case A Case B Case C

u,max [cm/s] 100 300 500

u0 [cm/s] 78 78 78

uL [cm/s] 78 78 78

Three different vortex strength casesWeak vortex : flame and soot are not extinguishedMedium vortex : extinguishes soot only Strong vortex : extinguishes both flame and soot

Weak vs. Strong Vortex CasesWeak vs. Strong Vortex CasesTemperature Nsoot fv

CaseA

CaseC

Vorticity

CaseB

Integrated NIntegrated Nsoot soot andand ffv v (Case B)(Case B)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.000 0.005 0.010 0.015 0.020

total fvfv (T < 1300K)

fv (T < 1000K)

fv (T > 1000K)

No

rma

lize

d s

oo

t vo

lum

e f

ract

ion

, f v

Time [sec]

Volume-integrated fv in different temperature regions

Volume-integrated Nsoot and flame volume

Soot number density depends strongly on the high-temperature flame volume

Soot volume fraction increases by surface growth at low temperature, fuel-rich regions

0.2

0.4

0.6

0.8

1.0

1.2

0.000 0.005 0.010 0.015 0.020

total ns

Vflame ( T > 1300K)

Vflame ( T > 1600K)

Vflame ( T > 2000K)

No

rma

lize

d v

alu

es

Time [sec]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Case A (u,max=1.0m/s)

Case B (u,max=3.0m/s)

Case C (u,max=5.0m/s)

Inte

gra

ted

f v

Vortex turn-over time (2r/u,max)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Case A (u,max=1.0m/s)

Case B (u,max=3.0m/s)

Case C (u,max=5.0m/s)

Inte

gra

ted

ns

Vortex turn-over time (2r/u,max)

Comparison of integrated fv for Cases A-C

Comparison of integrated Nsoot for Cases A-C

Effects of the Vortex StrengthEffects of the Vortex Strength

As vortex strength increases, more soot particles are convected into fuel rich zone Case A: fv is more directly affected by the soot nucleation.

Case C: fv does not change much even the the soot nucleation (Nsoot) is turned off.

Comparison of Radiation ModelsComparison of Radiation Models

0.20

0.40

0.60

0.80

1.00

1.20

0.000 0.005 0.010 0.015 0.020

OTMDOM

No

rma

lize

d r

ad

iativ

e h

ea

t lo

ss

Time [sec]

Total radiative heat loss with

OTM and DOM for Case B

Radiative heat loss During transient period,

OTM overpredicts the radiative heat loss by up to a factor of two compared to DOM

Fidelity of radiation model is important in DNS

Ongoing/Future Work Ongoing/Future Work

Terascale Computing: 3D Turbulent Nonpremixed CounterflowFlames with Radiation, Soot, and Water Spray

Integration of all the developed physical submodels Test bench for numerical algorithms: boundary conditions, acoustic

speed reduction (ASR) Science issue: partial/total extinction and pollutant formation due to

water spray interaction

Further To-Do List Computational Development

Immersed boundary method Adaptive mesh refinement Chemistry reduction strategies

Physical Models Detailed soot model Radiation model (spectral) Catalytic surface reaction

Enabling Technologies Data-mining and visualization Object-oriented code architecture

for efficient management

DOE INCITE Project: 3D DNS of turbulent nonpremixed jet flame,J. H. Chen et al.Sandia National Labs

AcknowledgmentsAcknowledgments

SciDAC TSTC Program Hong G. Im (Michigan)

Chunsang Yoo, Ramanan Sankaran (SNL)

Christopher J. Rutland (Wisconsin) Yunliang Wang

Arnaud Trouvé (Maryland) Yi Wang

Jacqueline H. Chen (Sandia National Laboratories) Scott Mason, Chris Kennedy, James Sutherland, Evatt Hawkes

Pittsburgh Supercomputing Center Ravishankar Subramanya, Raghurama Reddy

DOE Computing Resources National Energy Research Scientific Computing Center Oak Ridge National Laboratory Pacific Northwest National Laboratory

University of Oregon (the Tau Project) Sameer Shende, Allen Malony