# Presentation: 527990

## Simulations of Laboratory-Scale Flames without Turbulence Models

- John Bell   Marcus Day   Joseph Grcar
- JBBell@lbl.gov       MSDay@lbl.gov           JFGrcar@lbl.gov

-  Center for Computational Science and Engineering
-  Lawrence Berkeley National Laboratory
-  Berkeley, CA 94720 USA

## International Workshops on Premixed Turbulent Flames

- International Workshops on Premixed Turbulent Flames

**8****th**** – Tokyo**

**7****th**** – Cambridge**

**9****th**** – Evanston**

- http://eetd.lbl.gov/aet/combustion/workshop/workshop.html

## Taxonomy of Premixed Flames

- Stationary Flames with Isotropic Turbulence
- Oblique Flame
- Envelope Flame
- Unattached Flame
- Stationary Flames with Shear Turbulence
- Jet Flames
- Large Bluff-Body Flames
- High Swirl Flames
- Non-stationary Flames

- Cheng and Shepherd, *Combustion and Flame*, 85 (1991)
- http://eetd.lbl.gov/aet/combustion/workshop/Database/flame-config.html

## Taxonomy of Premixed Flames

- Stationary Flames with Isotropic Turbulence
- Oblique Flame
- Envelope Flame
- Unattached Flame
- Stationary Flames with Shear Turbulence
- Jet Flames
- Large Bluff-Body Flames
- High Swirl Flames
- Non-stationary Flames

- Cheng and Shepherd, *Combustion and Flame*, 85 (1991)
- http://eetd.lbl.gov/aet/combustion/workshop/Database/flame-config.html

**31****st**** Symposium**

## Numerical Simulation of a Laboratory-Scale Turbulent Slot Flame

- John Bell1   Marcus Day1   Joseph Grcar1
- Michael Lijewski1   James Driscoll2   Sergei Filatyev3

- 1 Center for Computational Science and Engineering
-   Lawrence Berkeley National Laboratory
-   Berkeley, CA 94720 USA

- 2 Department of Aerospace Engineering
-   University of Michigan
-   Ann Arbor, MI 48109 USA

- 3 School of Mechanical Engineering
-   Purdue University
-   West Lafayette, IN 47907 USA

## Slot Flame is an Envelope Flame

- Slot dimensions:
- 3 @ 2.5  5.0 cm
- Center slot: turbulent
- Mean inflow 3.0 m/s
- 	(2.7 m/s on centerline)
- Integral scale 0.52 cm
- Kolmogorov scale 200 m
- Side slots: laminar
- Burner stabilized flames
- Isolate center from ambient
- Chemistry
- Methane / air
- Stoichiometry  = 1.0

- Filatyev, Driscoll, Carter, and Donbar,
*Combustion and Flame*, 141 (2002)

## Slot dimensions:
3 @ 2.5  5.0 cm
Center slot: turbulent 
Mean inflow 3.0 m/s
	(2.7 m/s on centerline)
Integral scale 0.52 cm
Kolmogorov scale 200 m
Side slots: laminar
Burner stabilized flames
Isolate center from ambient
Chemistry
Methane / air
Stoichiometry  = 1.0 

- Slot dimensions:
- 3 @ 2.5  5.0 cm
- Center slot: turbulent
- Mean inflow 3.0 m/s
- 	(2.7 m/s on centerline)
- Integral scale 0.52 cm
- Kolmogorov scale 200 m
- Side slots: laminar
- Burner stabilized flames
- Isolate center from ambient
- Chemistry
- Methane / air
- Stoichiometry  = 1.0

## 3D Simulation of the Experiment

- Want to observe what is not easily measured in the laboratory
- 3D shape of flame
- All chemical species
- Vortex structure
- Requires the simulation make no compromises
- Geometry:
- Chemistry:
***No turbulence model***

- Day and Bell, *Combustion Theory and Modelling*, 4 (2000)

- DRM-19 mechanism (20 species / 84 reactions)

- 0.375 L domain (7.5  5.0  10.0 cm3)

## 3D Simulation of the Experiment

- Want to observe what is not easily measured in the laboratory
- 3D shape of flame
- All chemical species
- Vortex structure
- Requires the simulation make no compromises
- Geometry:
- Chemistry:
***No turbulence model***

- Day and Bell, *Combustion Theory and Modelling*, 4 (2000)

- DRM-19

- 0.375 L

## 3D Simulation of the Experiment

- Want to observe what is not easily measured in the laboratory
- 3D shape of flame
- All chemical species
- Vortex structure
- Requires the simulation make no compromises
- Geometry:
- Chemistry:
***No turbulence model***

- Day and Bell, *Combustion Theory and Modelling*, 4 (2000)

- DRM-19

- 0.375 L

## 3D Simulation of the Experiment

- Want to observe what is not easily measured in the laboratory
- 3D shape of flame

- Day and Bell, *Combustion Theory and Modelling*, 4 (2000)

**Ridge**

**Valley**

## Outline

- Slot Flame
- Shape of flame
- Vortex structure
- Chemical response
- Flame brush
- Flame surface density
- Curvature
- Shape factor

- Numerics
- Structured grid approach with adaptive mesh refinement (AMR)
- Low Mach number equations
- Modest cost of simulation

## 2. Magnitude of Vorticity

- Finding vortex structures in turbulent flows is a research topic for both
- fluid mechanics
- computer graphics
- Magnitude of vorticity suggests:

|  | unbrnd | burned |
| --- | --- | --- |
| features | fine | coarse |
| vorticity | low | high |

## Flame Sheet Colored by Vorticity

- Absolutely highest vorticity occurs at base where flame ignites
*Along the flame sheet*, highest vorticity is only found just below the ridge crests

|  | blue | red |
| --- | --- | --- |
| vorticity | low | high |

## Flame Sheet Colored by Vorticity

## 3. Chemistry

**CH****4**** ******** CH****3**** ******** CH****2****O ******** HCO ******** CO ******** CO****2**** **

- Note extreme variability of flame height and shape.

## 3. Chemistry

- Markstein number for  = 1.0 methane flame predicts greater fuel consumption where flame is convex to products — at ridges
- Hydrogen species seem to concentrate  at ridge tips

**Hydrogen species **

- Note extreme variability of flame height and shape.

## Agree on:
Height of  0.5 contour
Brush thickness at sides

- Height of  0.5 contour
- Brush thickness at sides

- Contours of “progress variable”
- Exp. Mie scattering oil drops
- Sim. CH4 or temperature

- 4. Flame Brush

## 4. Flame Brush

- Overall shape is sensitive to boundary conditions
- _Wider_ experiment is consistent with centerline inflow
- 2.7 m/s observed
- 3.0 m/s nominal

## Overall shape is sensitive to boundary conditions

- _Narrower_ simulation is consistent with faster coflow

- 7 m/s

- 21 m/s

## 5. Flame Surface Density

- Value from 2D observations underestimates 3D density.

- Experimental value based on Mie scattering images.

## 5. Flame Surface Density

- Value from 2D observations underestimates 3D density.

- Experimental value based on CH PLIF images.

**Overall shape is sensitive to boundary conditions **
_**Narrower**_** experiment is consistent with faster coflow**

## 6. Mean Curvature

- Surface has 2 curvatures, and their mean
- mean= (1 + 2)/2
- Negative curvature:   surface is convex as viewed from products
- Positive curvature:  surface is convex as viewed from reactants
- The blue / red dichotomy is principally between ridge crests / valleys

## 6. Mean Curvature

## 6. Mean Curvature PDF

- Ashurst and Shepherd, *Combustion Science and Technology*, 124 (1997)

- –

**Valleys**

- Agreement for curvatures calculated from 2D slices
- 2D experiment
- 2D simulation
- But refutes     2D > 3D mean

## 7. Shape Factor

- Significant deviations from 0.0 mean flame is not cylindrical (i.e. 2D) in general

- Rutland and Trouve, *Combustion Science and Technology*, 94 (1993).
- Pope, Yeng, and Girimaji, *Physics of Fluids A*, 1 (1989).

## Conclusion

- Science
- is like a

- E. Fermi, J. Pasta, S. Ulam, *Studies of Non- Linear Problems*, report LA1940 (1955).

- Theory
- Experiment
- Computation

## Conclusion

- Possible to simulate laboratory-scale turbulent flames without “models”
- Computation provides data that is difficult to obtain from laser diagnostics
- 3D view
- All species
- Fluid / chemistry correlations
- Conditions must be well characterized to obtain agreement with experiment
- Coflow, turbulence, etc.

## Outline

- Slot Flame
- Shape of flame
- Vortex structure
- Chemical response
- Flame brush
- Flame surface density
- Curvature
- Shape factor

- Numerics
- Structured grid approach with adaptive mesh refinement (AMR)
- Low Mach number equations
- Modest cost of simulation

## Meshing

- Finite element mesh
- Errors may increase with badly shaped triangles
- During movement, very complicated connections must be re-established

- Structured grid
- Errors well understood
- Mesh boxes simply created and destroyed
- Facilitates *adaptive mesh refinement*, AMR

- Antony Gormley sculpture

- AMR
- Level 3
- Level 2
- Level 1

## Meshing

- Finite element mesh
- Errors may increase with badly shaped triangles
- During movement, very complicated connections must be re-established

- Structured grid
- Errors well understood
- Mesh boxes simply created and destroyed
- Facilitates *adaptive mesh refinement*, AMR

- Antony Gormley sculpture

- AMR
- Level 3
- Level 2
- Level 1

## Level 1

- 634 micron resolution

- Y(CH2O)

- Base Mesh

## Level 2

- Y(CH2O)

- 317 micron resolution

- Mesh Refinement

## Level 3

- Y(CH2O)

- 158 micron resolution

- Mesh Refinement

## Level 4

- Y(CH2O)

- 79 micron resolution

- Mesh Refinement

## Adaptive Mesh Refinement

| Level | Resolution | Cells | % of 0.375 L |
| --- | --- | --- | --- |
| 1 | 634 micron | 1,536,000 | 100% |
| 2 | 317 micron | 5,112,832 | 41% |
| 3 | 158 micron | 24,336,384 | 24% |
| 4 | 79 micron | 36,650,496 | 5% |

- Traditional DNS

| Level | Resolution | Cells | % of 0.375 L |
| --- | --- | --- | --- |
| 1 | 79 micron | 786,432,000 | 100% |

- Total  67,635,712

## CFL Stability Time Step Limit

| method | coarse x | speed | t |
| --- | --- | --- | --- |
| low Mach | 637 micron | 13 m/s | 49 micro-sec |
| DNS | 79 micron | 920 m/s | 85 nano-sec |

- The low Mach-number formulation removes acoustic waves, leaving advection the fastest motion

- *

- ‡

## Savings permit smaller computers

*100 to 1000-fold savings*
- Adaptive mesh refinement
- low Mach number model
- Double-rack cluster
- 64 nodes @ 2 processors
- processor @ 2.4 GHz
- 0.6 Tflops speed
- 0.5 TB memory
- 12 TB storage
- $375,000

## Conclusion

- Capital cost of “first principles” calculations is less than laboratory experiments.

- $375,000

- $500,000

## Simulations of Laboratory-Scale Flames without Turbulence Models

- John Bell   Marcus Day   Joseph Grcar
- JBBell@lbl.gov       MSDay@lbl.gov           JFGrcar@lbl.gov

-  Center for Computational Science and Engineering
-  Lawrence Berkeley National Laboratory
-  Berkeley, CA 94720 USA