Advances in turbulent combustion modelling based on 1D ... - DANSIS

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Feb 22, 2014 (3 years and 5 months ago)

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SINTEF Energy Research

1



Advances in turbulent

combustion modelling

based on

1D turbulence models





Sigurd Sannan

SINTEF Energy Research





In collaboration with:

Alan R. Kerstein, Sandia National Laboratories, USA


Torleif Weydahl, SINTEF Energy Research


DANSIS seminar


Combustion and Reactive Flows

DONG Energy Power, October 5, 2011

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2

2

CO
2

CAPTURE TECHNOLOGIES

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Outline



Motivation


The Linear Eddy Model (LEM)


One
-
dimensional turbulence model (ODT)


LEM3D


a 3D turbulence simulation concept


Mixing of scalars in a turbulent jet


LEM3D coupled to RANS


Summary


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MOTIVATION


resolution of scales



4
















RANS


Coarse mesh,
bulk approximation


No resolution of
turbulence scales

LES


Large energy
-
containing
eddies are resolved


No resolution of small
-
scale
structure

DNS


Resolution down to the
smallest eddies


No models
needed




Numerical experiment

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MOTIVATION


multi
-
regime flows

5










H
2
/N
2

transverse

jet in
cross
-
flow

of

air


Domain

25x20x20 mm


1.6x10
9

grid points


48000
core

DNS at Oak
Ridge NL


4 million CPU
hours


R.Grout

et al. (PCI, 2011)


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MOTIVATION


multi
-
regime flows

6









RANS and LES
models

show
poor

results

in
predicting

this

canonical

configuration


Multi
-
regime,
multi
-
mode
combustion
; let
alone

at
high

pressure
!

Well
-
stirred

p
artially

p
remixed

flame
region (Da<1)

Flame

t
endrils

anchor

in s
hear

l
ayer

vortices

Low

Velocity

Region
<
--
> High Heat
Release

Diffusion

f
lame

r
egion

Flamelet
-
like p
artially

p
remixed

f
lame

r
egion

(Da>1)

O
2
-
depleted jet
core region

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MOTIVATION


challenges in turbulent combustion

7










Small
-
scale structures
are important



DNS is very costly



Turbulent stirring is an
advective transport
phenomenon



State of the art in
modelling:


Most models do not
make an explicit
distinction between
turbulent stirring and
diffusion at small scales








Courtesy of J.H Chen,

CRF, Sandia Nat. Labs.

1D line
of sight

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The LINEAR EDDY MODEL (LEM)


Concept for modelling turbulent reactive flow on a 1D domain

(Alan Kerstein, 1988


1992)


Explicit distinction between molecular diffusion, turbulent
advection (stirring), and chemical reaction:




All spatial and temporal scales are resolved down to the
smallest turbulence scales


Turbulent stirring is represented by stochastic
rearrangements of scalar fluid elements (triplet maps)


Regime
-
independent approach


The 1D formulation makes small
-
scale resolution
computationally affordable
























events

Stirring
x
D
x
t
M
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The triplet maps











x
s
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
a
f
t
e
r
m
a
p
p
i
n
g
e
v
e
n
t
b
e
f
o
r
e
m
a
p
p
i
n
g
e
v
e
n
t


No property discontinuities



Gradients are tripled



Captures the compressive strain and
rotational folding effects of turbulence




Turbulent stirring is modeled as a sequence of triplet maps



Implemented numerically as a permutation of fluid cells

c(y)

y

c(y)

y


A triplet map emulates the effect
of a 3D turbulent eddy on
property profiles along a 1D line
of sight

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Triplet map characteristics


A fluid cell subject to a random sequence of triplet maps goes
through a 1D random walk


The random walk is governed by the turbulent diffusivity:




where is the individual fluid cell displacements


Kolmogorov cascade picture gives inertial range scaling:





The normalized probability function of eddy sizes (


) is




The eddy event frequency parameter (units: length x time)
-
1

is









t
D
j
T
2
2



j

3
4
,


p
l
D
p
T
max
min
4
4
ˆ
,
ˆ
)
ˆ
(
max
min
k
k
k
k
k
k
f
k
k
k
p
p







1
2
3
)
(
)
1
(
2
max
min













k
f
k
k
d
D
k
k
k
T

k
l
3

δ
1
δ
2
δ
3
δ
4
δ
5
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ONE
-
DIMENSIONAL TURBULENCE MODEL (ODT)








ODT subsumes the capabilities of LEM



All scalars
and

velocity carried on the 1D domain



Application:

Piloted methane
-
air flame (Kerstein; Sandia flame D)

One realization


Horizontal segments
denote eddy events

Average of 100
realizations

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LEM3D


A 3D TURBULENCE SIMULATION CONCEPT



3 orthogonal arrays of 1D LEM
domains


Each LEM domain spatially
refines RANS control volumes in
one coordinate direction


Small
-
scale resolution is achieved
in all 3 spatial directions

Flow solution #1

Flow solution #2

Flow solution #3

Property profiles on the

3 LEM domains that
intersect a control volume

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LEM3D


A 3D TURBULENCE SIMULATION CONCEPT


Cubic control volumes (CVs):


Defined by the intersections of
orthogonal LEM domains


Contain information from all 3
intersecting domains


May correspond to CVs in LES or
RANS


Resolution, e.g.:


LEM3D: 20x3 = 60


DNS: 20
3
= 8000






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Coupling of LEM domains


2D illustration of domain
-
coupling procedure


Domains coupled by cell transfers
prescribed by RANS mean velocities


3D continuity is satisfied


In this example, there is net vertical inflow
and net horizontal outflow through CV faces


Horizontal LEM domain: cut at
red

line and
displace uniformly,
leaving a gap


Vertical domain:
green

region is removed
and inserted into the gap on the horizontal
domain (between the
red

lines), then
displace uniformly above and below the
green

region, causing the solid
blue

lines to
merge

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MIXING OF SCALARS IN A TURBULENT JET




Two ring sources (various diameter combinations) at x/Dj=9 release
scalars A and B, respectively


A
-
B cross correlation,

ρ
,
is measured at various downstream locations
(Tong & Warhaft, 1995)


This configuration has not previously been modelled

A

D
j
= 3 cm

U
j

=

9 m/s

Re
j

=

18,000


LEM3D simulation:


121x121x200 ~ 2.93x10
6

3DCV grid cells


Resolution of 30 cells in
each 3DCV


87.8x10
6

LEM cells


A corresponding DNS:
2.93x10
9

grid cells


Arrow:

Large motion
sweeps both plumes


can cause
negative

r

B

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LEM3D captures the mixing within the jet


Centerline mean temperature for rings at x/D
j
= 9

Radial profiles of
ρ

for 10,15 mm ring pair

Centerline profiles of
ρ

for ring pairs at x/D
j
= 9

Radial profiles of
ρ

for 35,40 mm ring pair

10
12
14
16
18
x
D
j
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
35
,
40
mm
rings
10
,
15
mm
rings
10
,
30
mm
rings
20
,
40
mm
rings
10
12
14
16
18
20
22
x
D
j
5
10
15
20
C
r
T
c
x
D
j
40
mm
ring
30
mm
ring
20
mm
ring
10
mm
ring
0.02
0.04
0.06
0.08
0.1
r
x
0
0.2
0.4
0.6
0.8
1
x
15
D
j
x
13
D
j
x
11
D
j
x
10
D
j
0.02
0.04
0.06
0.08
0.1
r
x
0
0.2
0.4
0.6
0.8
1
x
15
D
j
x
13
D
j
x
11
D
j
x
10
D
j
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Demo of dispersion in a turbulent jet

LEM3D simulation


10 mm heated ring in a
turbulent jet


Re
j

= 18000


15 million LEM cells


Mean velocity field and scalar
field are decoupled

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LEM3D COUPLED TO RANS


A variable
-
density formulation is under development


Two
-
way RANS
-
LEM3D coupling


RANS provides LEM3D with velocity and turbulence fields


LEM3D provides RANS with an updated statistical density field






LEM3D sub
-
regions

will be
imbedded in flow simulations to
resolve mixing locally


Chemical kinetics will be
incorporated


Convergence by an iterative
process between RANS and LEM3D


Validation against a purpose
-
built
tri
-
coaxial jet experiment


LEM3D

conventional
closure

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Tri
-
coaxial jets experiment




Mixing and combustion
behaviour

of H
2

in tri
-
coaxial turbulent jets


Inner jet: 50% H
2
, 50% N
2


Middle jet: 100% N
2


Outer jet: 50% N
2
, 50% CO
2


Multi
-
stream mixing experiment
tailored to validate LEM3D


Differential diffusion effects


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SUMMARY




1D turbulence models (LEM and ODT) can be applied to simple flow
configurations


For complex flows, the 1D models is coupled to global solvers:


Subgrid

closures (LEMLES, LESODT)


In LEM3D, the 1D LEM is embedded in a 3D framework:


Molecular diffusion, turbulent stirring and chemical reaction are treated as
distinct processes


Small
-
scale resolution at lower cost than DNS


Regime
-
independent approach


LEM3D has been validated against a non
-
reactive mixing experiment


The mixing of scalars within the turbulent jet is captured


LEM3D
-
RANS coupling


LEM adds small
-
scale resolution and unsteadiness to RANS


Prospect of higher fidelity than any commercially affordable turbulent
thermal
-
fluid simulation