Tesi

1
University of Rome La Sapienza Dept. of
Mechanics and Aeronautics
Analysis of Small Scale Turbulence-Combustion
Interaction for LES Modeling
Valerio Parisi, Claudio Bruno DMA, University
La Sapienza, Rome, ITALY Eugenio Giacomazzi
ENE-IMP, ENEA C. R. Casaccia, Rome, ITALY At
present Graduate Student at Georgia Tech. 43rd
AIAA Aerospace Sciences Meeting and Exhibits -
Reno, USA, 10-14 January, 2005 -
2
Aims

• Analyze turbulence-chemistry interaction in LES
  SGS
• Focus on modeling kinetic energy production (or
  destruction) by combustion
• Propose new SGS model alternative to ?t
• Test new model using numerical simulation of
  Sydney University experiments Masri et al., 2002

3
Contents

• Conceptual approach
• SGS Fractal Model (FM)
• KE equation and its modeling at the SGS scale
• ROM analysis
• Testing of the KE equation model
• Conclusions

4
Conceptual Approach (1/2)

• Develop new LES SGS model not based on ?t
• Test its realism / plausibility
• compare ROM of terms
• simulate U. Sydney burner using this group FM
  SGS model (based on ?t)
• compare source term in new SGS model with from
  simulations
• draw conclusions

5
Conceptual Approach (2/2)

• SubGrig Scale Model
• energy cascade from ? (macro) to ? (dissipation
  scale) modeled by means
• of the Fractal Model (FM) Giacomazzi et
  al., 2000
• combustion is assumed to take place inside fine
  structures
• modeled by Eddy Dissipation Concept (EDC)
• Magnussen, Hjertager e Lilleheie, 1989
• fine structures are assumed to behave
• as local tubular PSR (Perfectly Stirred
  Reactor)
• with characteristic sizes ? and ? (? gtgt?)

PSR
?
surrounding fluid
Reference system centered along the axis
6
Simulations based on Fractal Model (FM) SGS

• FM is an algebric subgrid scale eddy viscosity
  model
• Giacomazzi et al., 2000
• In each computational cell the inertial cascade
  is modeled by means of fractal theory
• The dissipative scale ? estimated as
• Number of dissipative scales locally produced
• Eddy viscosity (being ?? the molecular viscosity)

length scale velocity scale time scale
? The FM model estimates eddy viscosity by means
of characteristic quantities at the dissipative
scale
7
Kinetic Energy Equation (1/3)
Dot product Velocity ? Crocco-Vazsonyi
equation (variable density)
Effect of chemical reactions
Viscous dissipation
? Viscous stress tensor
This equation links the material derivative of
kinetic energy to spatial gradients due to
chemical reactions and viscous dissipation ? may
extract ?(V2/2) / ?t, rate of KE change!
8
ROM Analysis (2/3)

• Substitute entropy transport equation inside
  KE equation,
• obtain the source S ?(V2/2)/?t

?

• Estimate importance of terms nondimensionalize
  with reference quantities associated to the
  dissipative scale
• Characteristic numbers

RED BOX combustion-driven
BLUE BOX viscosity-driven
9
Conclusions from Nondimensionalization (3/3)

• Combustion related terms on the RHS of ?(V2/2) /
  ?t
• have the same order of magnitude
• ? subgrid reactor must be non adiabatic,
  and
• 
  include diffusive mass transport
• are larger than viscous terms

• Any new SGS model must account for chemical heat
  release effects on KE

• SGS based on ?t instead
• account only for turbulence fluidynamic
  properties
• do not include effects of combustion
  thermodynamics (dilatation, ...)

Nondimensional analysis shows the importance of
developing new SGS models (not based on eddy
viscosity)
10
Kinetic Energy Equation Application to Fine
Scales (1/5)

• LES ? split KE equation into filtered and
  subgrid variables

Local quantity
filtered
subgrid (These are not fluctuations)

• Model this source, term by term, to account for
  the effects of turbulencechemistry
• interaction on resolved scales
• Subgrid (spatial) gradients modeled by means of
  FM and EDC

11
EDC Modeling the SGS Steady PSR Reactor (2/5)

• Mass transport equation

• chemical reactions
• convection
• diffusion

Ficks law (for the time being)

• Energy transport equation

• chemical reactions
• conduction
• convection

Fouriers law

• Weighed average between reactor and
  surrounding fluid 0 quantities

and inside the reactor
Function of known quantities (from cell and FM)
and in the surrounding fluid
12
Modeling the Kinetic Energy Equation Assumptions
(3/5)

• Perfectly Stirred Reactor uniform fields inside
• Characteristic velocities
  with and
• 
  0 at the center of reactor
• Spatial gradients
• The operator has only the radial
  component
• Second derivatives
  (negative, dissipate energy)
• Neglect kinetic energy contribution to total
  enthalpy (Mach ltlt 1)
• Entropy

13
Modeling Vr (4/5)

• Vr is the instantaneous rate of change of
  dissipative scale
• reactor volume
• Density change due to combustion
• combustion

?
14
Modeled Kinetic Energy Equation (5/5)


SGS Source modeled as
15
Testing of Model
Goal validate new source S by numerical
simulations of flame experiments done
at University of Sydney Masri et al.,
2002
16
CFD HeaRT Code

• HeaRT Heat Release and Turbulence
• unsteady
• axi-symmetric
• solver
• explicit
• 3rd order accurate in time (Shu-Osher,
  Runge-Kutta scheme)
• 2nd order accurate in space (centered
  differences)
• parallelized ( ENEA )
• WS cluster
• FERONIA Alpha cluster (ENEA)
• 40 nodes
• each node has 2 CPUs with 1GB RAM and 4 MB Cache

17
Checking the Source Term S (1/10)- Test case
Sydney University Burner Masri et al., 2002 -

• Non-premixed coaxial burner at p1atm

Computational domain 3 ZONES
Experiment

• Burner
• length 40cm
• radius 7.5cm
• Axial Pipe
• length 5cm
• radius 0.18cm
• Coaxial Pipe
• length 5cm
• radius 7.5cm
• Number of nodes
• 1,405,312
• Axial Jet CH4/H2
• Uz 118 m/s
• T 300 K
• Re 13500
• Coaxial Jet Aria
• Uz 40 m/s
• T 300 K

0
18
2D Nonreactive Test Case (2/10)

• Choose Axisymmetric 2D domain for
• simplicity
• lower computational cost
• Nonreactive flow Air only
• ? source term contains only viscous terms

Recirculation zone
? S is always negative (kinetic energy is
always dissipated)
Undisturbed Flow
Axial jet
(Instantaneous Flowfield)
19
Compare New S and ?t (3/10)

• E.g. Radial profile at z10-4m
• ? S and ?t have opposite trend but same physical
  meaning for xlt0.025m
• Close to the walls (xgt0.025m)
• ? ReD increases (grid stretching)
• ? ?t increases (?ReD)
• ? viscous dissipation decreases
• ? magnitude of S decreases

• Axial profile at x5?10-4m
• ? opposite trend, same physical meaning
• minima and maxima due to eddies in
• recirculation zone (zlt0.15m)
• ? large dissipation linked to
• axial jet
• high speed
• high velocity gradients

20
3D Reactive Test Case
4/10
21
3D Reactive Case Source Distribution (5/10)

• Source term S
• ? may be positive and negative ? combustion can
  produce kinetic energy (backscatter)
• S field different than in the cold case S
  depends on combustion

Reactive zone
Production of kinetic energy by combustion
Non reactive zone
Viscous Dissipation of kinetic energy
Viscous Dissipation of kinetic energy
(Field snapshot)
22
Comparison Between Temperature and S Fields (6/10)

• S depends mostly on chemical reactions ? depends
  on T
• ? S and T have similar fields!

(Field snapshot 1)
23
Comparison Between Temperature and S Fields (7/10)

• ? Combustion takes place
• within shear layers
• between eddies
• (where molecular
• mixing is faster)
• ? High subgrid kinetic energy
• production in shear layers

(Field snapshot 2)
24
Instantaneous Expansion of Dissipative Scale
(8/10)

• Vr depends on chemical reactions
• depends on T
• ? Vr gt0 for exothermic reactions
• ? Vr lt0 for endothermic reactions

• Radial Profile

? Vr is very small with respect to but
dilatation is high!
25
Analysis of Terms Involved in Kinetic Energy
Source (9/10)
Look at radial profiles of ,
and viscous dissipation terms at z10-4m
Viscous Terms
m2/s3
? always negligible
? S depends mainly on

• where there are chemical reactions

• viscous dissipation linked to
• in the axial jet
• high speed
• high speed gradients
• where there is no combustion
• and turbulence is less intense

26
Compare New S and ?t (10/10)
Look at Profiles of S and along z at
x5?10-4m

• zgt0.16m
• ? no combustion
• ? S viscous terms only
• S order of magnitude lower than in the reactive
  zone and in the axial jet
• z0.12m
• ?
• ?
• model turns itself off
• automatically

• depends on T
• but not directly on chemistry
• ? S and not correlated

27
Conclusions (1/2)

• Kinetic energy source S obtained via
  Crocco-Vazsonyi equation correctly describes
  physics of interaction between turbulence and
  chemical reactions
• In the nonreactive case S modeling obeys
  expected physics, agrees with
• Comparison with shows eddy viscosity
  models do not account directly for effects of
  combustion
• In the reactive case
• S and not correlated they describe
  different phenomena
• S takes into account kinetic energy production
  due to combustion, not considered by

The present no eddy viscosity type SGS model
based on S has been proposed to close LES
equations
28
SGS Model Based on Kinetic Energy Source S (2/2)

• Advantages
• describes effects of combustion on
  fluid-dynamics
• does away with eddy viscosity , an
  unphysical quantity
• more realistic physical modeling of small scales
• Disadvantages
• computational cost
• S must be included in Navier-Stokes equations ex
  novo
• (not a simple change)
• ROM of S ? numerical instabilities?
• ? Keep testing!