Farhad JaberiDepartment of Mechanical Engineering

Michigan State UniversityEast Lansing, Michigan

A High Fidelity Model for Numerical A High Fidelity Model for Numerical Simulations of Complex Simulations of Complex

Combustion/Propulsion SystemsCombustion/Propulsion Systems

Objectives Develop a high-fidelity numerical model for

high-speed turbulent reacting flows Study “laboratory combustors'' of interest to

NASA for various flow and combustion parameters with the new model

Improve basic understanding of turbulent combustion in supersonic and hypersonic flows

Technical Approach LES/FMDF: A hybrid (Eulerian-Langranian)

model, applicable to subsonic and supersonic turbulent combustion in complex configurations

DNS data are used together with experimental data for validation and improvement of LES/FMDF submodels

Progress New high-order numerical schemes are

developed/validated for supersonic turbulent flows,

Compressible subgrid stress and energy flux models are implemented and tested,

Scalar FMDF model is extended and applied to compressible (supersonic) reacting flows,

LES/FMDF predictions are compared with experimental data,

DNS data for supersonic mixing-layer are generated. LES results are compared with the DNS data.

Impact Numerical Simulations of a scramjet combustor

is now possible but reliability and accuracy of predictions are dependent on compressible models

Numerical experimental: A systematic and detailed study of various flow/reaction parameters on combustion stability and efficiency

Better understanding of supersonic combustion Feedback to experimentalists and designers

DNS of Supersonic Mixing Layer

LES of Supersonic Co-Annular Jet

Publications: (1) Z. Li, A. Banaeizadeh, F. Jaberi, Large Eddy Simulation of High Speed Turbulent Reacting Flows, International Symposium on Recent Advances in Combustion., 2008. (2) A. Banaeizadeh, F. Jaberi, LES of Supersonic Turbulent Flows with the Scalar FMDF, APS-DFD, 2009, (3) Li and F. Jaberi, Numerical Investigations of Shock-Turbulence Interactions in Planar Mixing Layer, AIAA Annual Meeting, 2010.

Eulerian: Transport equations for the SGS moments

- Deterministic simulations

Lagrangian: Transport equation for the FMDF- Monte Carlo simulations

Coupling of Eulerian & Lagrangian fields and a certain degree of “redundancy”

COCO22 andand CC77HH1616 Mass FractionsMass Fractions

Pressure IsolevelsPressure Isolevels

Nozzle

Wall

Vorticity Contours & Monte Vorticity Contours & Monte Carlo ParticlesCarlo Particles

Monte Carlo Particles

Kinetics: (I ) reduced kinetics schemes with direct ODE or I SAT solvers, and (I I ) flamelet library with detailed mechanisms or complex reduced schemes.Fuels: methane, propane, decane, kerosene, heptane, J P-10

Filtered continuity and momentum equations via a generalized multi-block high-order finite difference EulerianEulerianscheme for high Reynolds number turbulent flows in complex geometries

Various closures for subgrid stresses

GasdynamicGasdynamicFieldField

Scalar Field Scalar Field (mass fractions(mass fractionsand temperature)and temperature)

Filtered Mass Density Function (FMDF) equation via LagrangianLagrangianMonte Carlo method - I to Eq. for convection, diffusion & reaction

ChemistryChemistry

COCO22 andand CC77HH1616 Mass FractionsMass Fractions

Pressure IsolevelsPressure Isolevels

Nozzle

Wall

Vorticity Contours & Monte Vorticity Contours & Monte Carlo ParticlesCarlo Particles

Monte Carlo Particles

Kinetics: (I ) reduced kinetics schemes with direct ODE or I SAT solvers, and (I I ) flamelet library with detailed mechanisms or complex reduced schemes.Fuels: methane, propane, decane, kerosene, heptane, J P-10

Filtered continuity and momentum equations via a generalized multi-block high-order finite difference EulerianEulerianscheme for high Reynolds number turbulent flows in complex geometries

Various closures for subgrid stresses

GasdynamicGasdynamicFieldField

Scalar Field Scalar Field (mass fractions(mass fractionsand temperature)and temperature)

Filtered Mass Density Function (FMDF) equation via LagrangianLagrangianMonte Carlo method - I to Eq. for convection, diffusion & reaction

ChemistryChemistry

LES/FMDF of Complex Turbulent Reacting Flows LES/FMDF of Complex Turbulent Reacting Flows A Hybrid Eulerian-Lagrangian Mathematical/Computational MethodologyA Hybrid Eulerian-Lagrangian Mathematical/Computational Methodology

Filtered LES Equations -> Eulerian

0ˆ

i

iu

t

J

tJ

j

ie

jj

je

iij

jii

i uuPuu

t

Ju

t

uJ

ˆˆˆˆˆ

ˆ

/ˆ and ,ˆ_____

ffxdxxGtxff

NS

MWRTRTP

1

0^

ˆ)(

FMDF Equation -> Lagrangian

xdxxGtxtxtxPL

)()),(,(),(),;( Subgrid scalar

FMDF:

LLLmi

lLt

iLLi

i

L PSPx

P

xPu

xt

P)(

/~~

Reaction termReaction term

Reaction termReaction term

SJ

quuPuE

t

JE

t

EJ

ij

i

i

i

i

i

ˆˆˆˆˆˆ

ˆ

)(/ LPS Dt

DP

1Added to FMDF

equation as a source/sink term

Dt

Dp

1

For non-reacting flows: internal energy/enthalpy equation obtained from

FMDF-MC is consistent with LES-FD equation

For reacting flows: reaction terms are closed in FMDF

Total derivative of pressure in enthalpy equation

LES of High Speed Turbulent Reacting LES of High Speed Turbulent Reacting FlowsFlows• In LES, large-scale variables are correctly calculated when reliable and accurate

numerical methods+BC , SGS models and chemical kinetics models are provided.

• For LES and DNS of non-reacting supersonic/hypersonic turbulent flows, high-order numerical schemes have been developed and tested.

• Compressible (Dynamic) Gradient, Similarity, Mixed and MKEV models have been employed for subgrid stresses and scalar fluxes. Better subgrid turbulence models for supersonic and hypersonic flows are needed.

• Compressibility effects are included in the scalar FMDF for supersonic turbulent combustion. Efficient Lagrangian Monte Carlo methods have been developed for flows with shock waves in complex geometries. Consistency/accuracy of LES/FMDF is established. Better mixing and SGS convection models for FMDF are desirable.

• DNS data for non-reacting supersonic mixing layer are generated and are being used for evaluation/improvement of subgrid models. DNS data for supersonic reacting (hydrogen-air) mixing-layer are being generated.

• Comparison of LES results with experimental data for supersonic reacting flows is essential.

• Reliable and efficient reduced chemistry models and solver are needed. However, no serious problem is expected in the implementation of chemical reaction in LES/FMDF.

Rapid Compression Machine – LES/FMDF Predictions

In-CylinderIn-Cylinder

pistonpiston

Piston groovePiston groove

TemperatureTemperatureContoursContours

Hydraulic Chamber Driver ChamberMain Ignition Chamber

Spark Plug

Fuel Injector

Optical Access

piston

piston

piston

Non-Reacting RCM Simulations

Temperature

Pressure

FD: finite-difference (LES) MC: Monte Carlo (FMDF)

FDFD

MCMC

MCMC

FDFD

Temperature ContoursTemperature Contours

Fuel Mass Fraction ContoursFuel Mass Fraction Contours

Rapid Compression Machine - LES/FMDF Predictions

Reacting Simulations - Consistency between finite-difference (LES-FD) and Monte Carlo (FMDF-MC) values of Temperature and Mass Fractions

3D Shock Tube Problem– LES/FMDF Predictions3D Shock Tube Problem– LES/FMDF Predictions

3D Shock Tube3D Shock Tube

pp22/p/p11=15=15

pp11

pp22

Two-Block GridTwo-Block Grid

5 MC per cell5 MC per cell 20 MC per cell20 MC per cell 50 MC per cell50 MC per cell

• Compressibility effects are included in FMDF-MC. Without Compressible term FMDF-MC results are very erroneous.• By varying the initial number of MC particles per cell, the

filtered temperature does not noticeably change.• By increasing the initial particle/cell number, MC particle number density becomes smoother and nearly the same as

filtered density.

Particle Number Particle Number DensityDensity

Particle Number Particle Number DensityDensity

Particle Number Particle Number DensityDensity

63.5 mm

diam

cen

ter jet

CARS/ Rayleighbeams

M=2 vitiated air jet

Burner/ nozzle

CARS/ Rayleighbeams

M=2 vitiated air jet

Burner/ nozzle

Coflownozzle

Facility flange

M=2 setup M=1 setup

SiC liner

Watercooled shell

Small-scale facilityNozzle (SiC)

Water-cooled combustion chamber

Spark plug

H2 fuel tube

Air+O2

passage

Coflownozzle

Water-cooled injector

10 mm

diam

eter C

enter jet

Supersonic Mixing and Reaction - Co-Annular Jet Experiments Supported by NASA’s Hypersonic Program

LES/FMDF of Co-Annular JetMixing and combustion

Grid System for LES Grid System for LES

Cutler et al. 2007Cutler et al. 2007

Large-scale facility

3D LES 3D LES

Calculations with Calculations with Compact SchemeCompact Scheme

Iso-Levels of Mach Number

Iso-Levels of Mach Number

Vorticity Magnitude

LES/FMDF of Supersonic Co-Annular Jet Mixing Case – No Combustion

Pressure Temperature

LES of Supersonic Co-Annular Jet Mixing Case – No Combustion

ExperimentSmagorinsky

MKEV 0.02MKEV 0.03

LES/FMDF of Supersonic Co-Annular Jet – Mixing Case

ExperimentSmagorinsky

MKEV 0.02MKEV 0.03

Instantaneous ScalarInstantaneous Scalar

LES-FD

FMDF-MC

Experiment

Instantaneous Scalar Mean Scalar

LES - FD

FMDF - MC

LES/FMDF of Supersonic Co-Annular Jet – Consistency of FD and MC

DNS and DNS and LES of LES of

Supersonic Supersonic Turbulent Turbulent

Mixing LayerMixing Layer

DNS Without Incident Shock DNS Without Incident Shock WaveWave

Vorticity ContoursM2=1.8

M1=4.2

Pressure Contours

-10 0 101

1.5

2

2.5

3

3.5

4

x=222

x=275

x=347U

y

Re=400

-10 0 10

-0.5

0

0.5

x=222

x=275

x=347

(U-U

c)/(

U1

-U2

)

(y-y )/0

-10 0 10

-0.5

0

0.5 Re=300

Re=350

Re=400

Re=500

(U-U

c)/(

U1

-U2

)

(y-yo)/ (x)

amp=0.08

-10 0 10

-0.5

0

0.5

amp=0.04

amp=0.08

(U-U

c)/(

U1

-U2

)

(y-yo)/ (x)

Re=400

Vorticity Contours

Vorticity

LES of Supersonic Turbulent Mixing-Layer - No ShockLES of Supersonic Turbulent Mixing-Layer - No Shock

0 100 200 300 400-0.5

0

0.5

1

1.5

2

2.5

3

DNS

NOMODEL

LES-MKEV

LES-MIXED

LES-Smag

x

0 100 200 300 400-0.5

0

0.5

1

1.5

2

2.5

3

DNS

NOMODEL

LES-MKEV

LES-MIXED

LES-Smag

x

-10 0 10

1.5

2

2.5

3

3.5

DNS

NOMODEL

LES-MKEV

LES-Smag

X=347

y

U

d=2h

-10 0 10

0

0.5

1

DNS

LES-MKEV

LES-Smag

X=275

y

-10 0 10

0

0.5

1

DNS

LES-MKEV

LES-Smag

X=347

y

LES of Supersonic Turbulent Mixing-Layer - No LES of Supersonic Turbulent Mixing-Layer - No ShockShock

-10 0 10

0

0.5

1

DNS

LES-MKEV

LES-Smag

X=347

y

M

ean

Sca

lar

Mea

n A

xial

Vel

ocit

y

-10 0 10

1.5

2

2.5

3

3.5

DNS

NOMODEL

LES-MKEV

LES-Smag

X=275

y

U

-10 0 10

1.5

2

2.5

3

3.5

DNS

NOMODEL

LES-MKEV

LES-Smag

X=347

y

U

d=2h

Vorticity Contours

DNS of Supersonic Turbulent Mixing-Layer with ShockDNS of Supersonic Turbulent Mixing-Layer with Shock

-10 0 100

0.04

0.08

0.12

X=300

ek

-10 0 100

0.04

0.08

0.12

X=340

No-ShockShock-Angle 16o

Shock-Angle 18o

Shock-Angle 20o Shock-Angle 22o

-10 0 100

0.04

0.08

0.12

X=340

-10 0 100

0.1

0.2

0.3

X=380

Imposed Shock

LES of Supersonic Turbulent Mixing-Layer with ShockLES of Supersonic Turbulent Mixing-Layer with Shock

Pressure Scalar

-10 0 101

1.5

2

2.5

3

3.5

U

y

X=340

-10 0 101

1.5

2

2.5

3

3.5

DNS

LESSmag

LESMKEV

U

y

X=380

-10 0 10

0

0.2

0.4

0.6

0.8

1

DNS

LESSmag

LESMKEV

y

x=380

-10 0 10

0

0.2

0.4

0.6

0.8

1

y

x=340

Mea

n A

xial

Vel

ocit

y

Mea

n S

cala

r

LES of High Speed Turbulent Reacting LES of High Speed Turbulent Reacting FlowsFlows• In LES, large-scale variables are correctly calculated when reliable and accurate

numerical methods+BC , SGS models and chemical kinetics models are provided.

• For LES and DNS of non-reacting supersonic/hypersonic turbulent flows, high-order numerical schemes have been developed and tested.

• Compressible (Dynamic) Gradient, Similarity, Mixed and MKEV models have been employed for subgrid stresses and scalar fluxes. Better subgrid turbulence models for supersonic and hypersonic flows are needed.

• Compressibility effects are included in the scalar FMDF for supersonic turbulent combustion. Efficient Lagrangian Monte Carlo methods have been developed for flows with shock waves in complex geometries. Consistency/accuracy of LES/FMDF is established. Better mixing and SGS convection models for FMDF are desirable.

• DNS data for non-reacting supersonic mixing layer are generated and are being used for evaluation/improvement of subgrid models. DNS data for supersonic reacting (hydrogen-air) mixing-layer are being generated.

• Comparison of LES results with experimental data for supersonic reacting flows is essential.

• Reliable and efficient reduced chemistry models and solver are needed. However, no serious problem is expected in the implementation of chemical reaction in LES/FMDF.

Future PlansFuture Plans

Further improvement and validation of LES/FMDF: - DNS of supersonic turbulent reacting (H2) mixing layer - LES/FMDF of co-annular reacting (H2) jet - Improved SGS turbulence models for supersonic flows - Implementation/testing of reduced kinetics models

Reliable and accurate subgrid models for turbulence-shock-combustion interactions in strongly compressible reacting flows ‘Correct’ implementation of boundary/initial conditions Efficient kinetics solver Limited well-defined, detailed experimental data and DNS data for supersonic turbulent combustion

Critical ChallengesCritical Challenges