Simulation and Modelling
of
Turbulence and Combustion
UNIVERSITY OF
CAMBRIDGE
DEPARTMENT OF
ENGINEERING
Computational Fluid Dynamics Laboratory
Stewart Cant
The CFD Lab combustion group
:
Carol Armitage, Gianluca Caretta, Nilan Chakraborty, Karen Hansen,
Karl Jenkins, Yun Kang, Michela Oliviero, Andrew Parker, Stephen Tullis, Pankaj
Vaishnavi, Saffron Wyse
plus
Daniele Baraldi, Paul Birkby, Kendal Bushe, Evatt Hawkes, Laurent Leboucher,
John Ranasinghe
and
Bill Dawes, Mark Savill; Caleb Dhanasekeran, Will Kellar, Noel Rycroft
Rob Prosser
Jackie Chen, Chris Rutland
People
Financial support for the work has been provided by:
EPSRC
Alstom Gas Turbines Ltd
Shell Global Solutions Ltd
Rolls

Royce plc
with high

performance computing and support from:
EPSRC; through EPCC, CSAR and HPCx
Cambridge

Cranfield High

Performance Computing Facility
Daresbury Laboratory (Dr. David Emerson)
CTR Stanford/NASA Ames, Sandia National Labs
Acknowledgements
•
RANS
Average the governing equations

model all scales
Modelling generally well developed
Inexpensive (relatively!)

remains standard for industrial problems
•
LES
Filter the governing equations

modelling required at the sub

grid scale
Combustion physics and chemistry tends to happen on sub

grid scales
Now becoming applicable to industrial problems
•
DNS
Solve the governing equations directly

no modelling of the physics
Resolution of all scales required

high accuracy numerical methods
Computationally very expensive
Feeds modelling data to LES and RANS
CFD

based Modelling Techniques
"
Structured gridding
:

2D Cartesian and axisymmetric

non

uniform

3
rd
order QUICK scheme in space

flux

limited to 2
nd
order using CCCT limiter

1
st
order Euler/2
nd
order Crank

Nicholson in time

turbulence modelling:
Reynolds stress or k

epsilon

combustion modelling using Bray

Moss

Libby type
laminar flamelets + partially premixed extensions
Code
TARTAN
RANS Approach

1
Reheat buzz combustion instability
CFD (Tartan) vs. experiment
Unstructured adaptive gridding:

tetrahedral cells

semi

automatic grid generation for arbitrary geometries

2nd order Jameson scheme in space

2nd order 4

step semi

implicit Runge

Kutta in time

local grid refinement on any specified quantity

standard turbulence modelling: k

epsilon

combustion modelling using BML

type laminar flamelets
"

parallel decomposition using standard tools
Code
McNEWT
RANS Approach

2
Flow with combustion past obstacles
∙
Dynamic mesh adaption for uRANS and LES
Combustion in a vented channel
∙
Static and dynamic mesh adaption
Oil industry case study

1
∙
CAD import
via 3Dgeo
Oil industry case study

2
∙
Surface mesh
Oil industry case study

3
∙
Volume mesh
Oil industry case study

4
Flames developing from
two separate ignition sources

test case for HPCx
Gas turbine combustion instability
∙
Full 3D mesh
∙
ca. 500 000 cells
∙
Geometrical length scales
from 0.7mm to 0.7m
Gas turbine combustion instability
∙
Sector mesh
∙
ca. 160 000 cells
∙
Rising to ca. 700 000 cells
with solution adaption
Gas turbine combustion instability
∙
Mixture fraction & pressure vs.time
Fuel injectors
time
pressure
The understanding…
∙
CFD shows a self sustaining cycle
mixture entering combustor is richer
more heat release
–
pressure rises
mixture entering combustor is weaker
less heat release
–
pressure falls
less fuel enters
–
and is pushed away from combustor
more fuel enters
–
and is drawn into combustor
LES sub

grid reaction rate
Flame surface density (FSD or SDF) approach
Extension of flamelet formalism to LES sub

grid modelling

transport equation or algebraic closure
Further extension to partial premixing
Results are broadly in line with RANS experience

but terms depend on filter size
•
Applications to gas turbine combustion instability
LES modelling test case
∙
close

up view
Cambridge Buzz Rig: flameholder
DNS in support of modelling
DNS involves
no
modelling
–
must resolve all scales
DNS remains too expensive for application to industrial systems
Run canonical cases and extract statistical data
Develop and calibrate modelling for LES
Flame propagation; FSD and transport terms
Flame kernel configuration
–
spherical
Inflow

outflow configuration
–
planar
Grid sizes 64
3
, 96
3
, 128
3
, 192
3
, 384
3
, (512
3
)
Requires access to world class supercomputing

HPCx
Flame Kernel Surface
grid size = 128
3
c = 0.5
Contours of reaction progress variable
with velocity vectors in x

z plane
superposed
Flame wrinkling and thickening due to turbulence
Reaction progress variable profile across the
flame brush along with the progress
variable profile of the initial laminar flame
Mean behaviour of displacement speed S
d
T
he variation of
ρS
d
/ρ
0
S
L
, S
d
/S
L
and
(
S
r
+S
n
)
/S
L
across the flame brush
Variation of (1/
τ
grad
c

S
L
) div
u
compared
with
ρS
d
/ρ
0
S
L
plotted across the flame brush
Behaviour of the terms affecting displacement speed S
d
Reaction rate term, molecular diffusion
term, normal component of molecular
diffusion term, tangential diffusive term
and reactive

diffusive imbalance across
the flame brush
The variation of surface averaged SDF
across the flame brush is shown by the red
line. The scatter of SDF is shown by the
blue dots.
Budget of strain rate, curvature and propagation terms
in the transport equation for flame surface density
Budget of strain rate, curvature and propagation terms across the flame brush
Effect of tangential strain rate and curvature on
SDF strain rate term
Contours
of
joint
pdf
between
SDF
strain
rate
term
and
tangential
strain
rate
Contours
of
joint
pdf
between
SDF
strain
rate
term
and
mean
curvature
Statistics of flame normals and
flame normal interactions
Pdf of N
1
on different
c
isosurfaces
Pdf of N
2
on different
c
isosurfaces
Pdf of N
3
on different
c
isosurfaces
Mutual interactions between flame normal components
c
= 0.7
c
= 0.7
c
= 0.7
Scatter of N
1
and N
2
on
c
= 0.7 isosurface
Scatter of N
1
and N
3
on
c
= 0.7 isosurface
Scatter of N
2
and N
3
on
c
= 0.7 isosurface
Future Work in Combustion DNS
Implementation of unsteady non

reflecting inlet boundary condition for viscous
reacting flows
Simulation for higher turbulent Reynolds number and grid size
Effect of filter size of FSD transport equation terms
Comparative study of algebraic models for FSD and wrinkling factor
Extension of FSD based modelling in thin reaction zone regime
Modelling of surface averaged S
d
for LES combustion modelling
Test case for non

reflecting inlet and outlet
boundary conditions
•
RANS combustion modelling is highly developed

remains valuable for industrial applications

offers a high level of geometrical flexibility

requires desktop or PC cluster hardware
•
LES is the major CFD tool for the future

techniques are under active development

combustion requires high

level modelling

requires PC clusters to supercomputers
•
DNS is an invaluable tool for the support of modelling

requires top

end supercomputing
HPCx provides an excellent service for CFD
Conclusions
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