Computational Transport Phenomena Laboratory

S.L. Yılmaz Department of Mechanical

Engineering and Material Science

Ph.D. ProposalDecember 5th 2007

APPLICATION OF RANS/PDF & LES/FDF METHODS TO PREDICTION OF PREMIXED TURBULENT FLAMES

Outline•Objectives summary•PDF/FDF methodologies•Flame configurations•Preliminary Results•Scalable parallelization•Tasks summary

Concluding remarks [Drozda 2005]• Sandia Flame DSandia Flame D and and Sydney/Sandia bluff-body stabilized flamesSydney/Sandia bluff-body stabilized flames are are

simulated via the LES/SFMDFsimulated via the LES/SFMDF• Transport equation for the FDF is solved via the Transport equation for the FDF is solved via the hybrid Eulerian-hybrid Eulerian-

Lagrangian methodLagrangian method. . • MKEVMKEV and and SmagorinskySmagorinsky models are considered for the SGS stresses and models are considered for the SGS stresses and

fluxes.fluxes.• Flamelet chemistry modelFlamelet chemistry model relates the thermo-chemical variables to the relates the thermo-chemical variables to the

mixture fraction.mixture fraction.

Future/Ongoing workFuture/Ongoing work• Prediction of non-equilibrium flames via scalar FMDF Prediction of non-equilibrium flames via scalar FMDF

and ISAT.and ISAT.• Prediction of turbulent flames via joint velocity-scalar Prediction of turbulent flames via joint velocity-scalar

FDF and FMDF.FDF and FMDF.• Optimization of the solver to reduce computational

requirements.

Objectives• Extend the boundaries of two novel

methodologies for prediction of turbulent flames,

• Predict a bluff-body burner with a RAS/PDF methodology,

• Predict a pilot-stabilized burner with a LES/FDF methodology,

• Employ non-equilibrium kinetics,• Develop scalable LES/FDF

computational code.

DNS, LES, and RAS

Large Eddy Simulation

(LES)

Reynolds Average

Simulation (RAS)

Direct Direct Numerical Numerical Simulation

(DNS)(DNS)

Starting Equations

Averaging versus Filtering• Statistical description: Turbulent fields are

Random Signals in time and space. • RANS: Define one-point, one-time joint-PDF

• LES: Define spatial low-pass filter

Transported PDF Methods• Solve the one-point one-time Joint PDF

directly• Closed quantities

• Unclosed quantities

PDF Transport Equation• From full-set of NS equations:

• Solves for

LHS closed, RHS needs model

RANS Connection• Ensemble-mean equations derived from JPDF

transport equation:

• Define Favre averages:

Filtered Density Function (FDF)• Formal definition:

• Satisfying the properties of PDF

Transport of FDF• Identically to PDF transport:

Scalar FDF• Transport equation of the marginal FDF of

scalars

Lagrangian PDF Models• Closure via Stochastic Differential Equations • e.g. The Velocity-Scalar-Frequency SDEs

Modeled PDF Transport Equation• Corresponding Fokker-Planck equation

Lagrangian FDF Model• SDEs for closure

• Fokker-Planck equation

Simulation Procedure• Monte-Carlo simulation of the SDEs• Finite Difference solution of Eulerian Filtered

or Averaged equations

Bluff Body Lean Premixed Flame• Pan (1991);

Velocity measurements

• Nandula (2007); Temperature, species concentrations measurements

• Re = 43,400• Φ = 0.59

Simulation Details• Axisymmetric, adiabatic walls, uniform inlet.

Comparison of Mean Velocities

Mean and RMS Velocities

Temperature and Major Species

Temperature and Minor Species

Premixed Bunsen Burner• Y.C. Chen 1996. Velocity, temperature,

species measurements.• Three Flames of Re = 24K, 40K and 52K• Φ = 1.0

Cold Flow Computations• Using only FD solver with MKEV turbulence

model

Parallelization

Monte Carlo solver consumes 95% of total time.

Load Balancing Problem

Region of High Activity

Region of Low Activity

Stiff Term

Load Balancing Problem

Uniform Partitions

Balanced Partitions! (with METIS)

3D Arbitrary Partitions

Task Summary• Modify RAS/PDF computational code for

Bluff Body configuration• Perform RAS/PDF simulation of the Bluff

Body• Implement detailed kinetics into LES/FDF

solver• Implement scalable FDF computational code• Perform LES/FDF simulation of the Bunsen

Burner

Also thanks to, • CTPL members!• Cornell Combustion• NETL• PSC

THANK YOU.