# Ramadan Youssef Sakr Moustafa_Lecture9-Turbulent Combsution

Mécanique

22 févr. 2014 (il y a 7 années et 10 mois)

388 vue(s)

Turbulent Combustion

Outline

Types of Flames

Basic Concept of Turbulence

Turbulent Flame

Flame Stability

Types of Flames

Two basic categories

Pre
-
mixed

Non
-
premixed
(Diffusion)

Both characterized as
Laminar or Turbulent

Premixed

Results from gaseous
reactants that are mixed
prior to combustion

Flame propagates at
velocities slightly less
than a few m/s

Reacts quite rapidly

Example: Spark Ignition Engine

Non
-
premixed (Diffusion)

Gaseous reactants
are introduced
separately and mix
during combustion

Energy release rate
limited by mixing
process

Reaction zone
between oxidizer and
fuel zone

Example: Diesel Engine

Laminar

Premixed

Ex. Bunsen Burner

Flame moves at fairly low
velocity

Mechanically create laminar
conditions

Diffusion

Ex. Candle Flame

Fuel: Wax, Oxidizer: Air

Reaction zone between wax
vapors and air

Turbulent

Premixed

Heat release occurs much faster

Increased flame propagation

No definite theories to predict
behavior

Diffusion

Can obtain high rates of
combustion energy release per
unit volume

Ex. Diesel Engine

Modeling is very complex, no
well established approach

Turbulence : Basic Concepts

Turbulent

flow

results

when

instabilities

in

a

flow

are

not

sufficiently

damped

by

viscous

action

and

the

fluid

velocity

at

each

point

in

the

flow

exhibits

random

fluctuations
.

The

random

associated

with

various

flow

properties

is

the

hallmark

of

a

turbulent

flow

and

is

illustrated

for

the

axial

velocity

component

in

the

next

figure
.

One

particularly

useful

way

to

characterize

a

turbulent

flow

field

is

to

define

mean

and

fluctuating

quantities
.

Mean

properties

are

defined

by

taking

a

time
-
average

of

the

flow

property

over

a

sufficiently

large

time

interval

∆t

=

t
2

t
1
.

The fluctuation, p'(t), is the difference between the
instantaneous value of the property, p(t), and the mean
value, p
avg

, or

p(t)= p
avg
+ p'(t)

Or, in general, we can write:

Y(t)= Y
avg

+ Y
i
'(t)

This manner of expressing variables as a mean and a
fluctuating component is referred to as the
Reynolds
decomposition
.

At this point, the key question arises :

“What is the physical nature of a
turbulent flow”?

The following figure gives a
question. In this figure, we
see fluid blobs and filaments
of fluid intertwining. A
common notion in fluid
mechanics is the idea of a
fluid eddy

An
eddy

is considered to be
a macroscopic fluid element
in which the microscopic
elements composing the
eddy behave in some ways
as a unit.

For example, a
vortex

imbedded in a flow would be
considered an eddy.

A turbulent flow comprises many eddies with a multitude
of sizes and vorticities, a measure of angular velocities.

A number of smaller eddies may be imbedded in a larger
eddy. A characteristic of a fully turbulent flow is the
existence of a wide range of length scales, i.e., eddy
sizes.

For a turbulent flow, the Reynolds number is a measure
of the range of scales present; the greater the Reynolds
number, the greater the range of sizes from the smallest
eddy to the largest. It is this large range of length scales
that makes calculating turbulent flows from first
principles intractable. We wilt discuss length scales in
more detail in the next section.

The rapid intertwining of fluid elements is a
characteristic that distinguishes turbulent flow
from laminar flow.

The turbulent motion of fluid elements allows
momentum, species, and energy to be
transported in the cross
-
stream direction much
more rapidly than is possible by the molecular
diffusion processes controlling transport in
laminar flows.

Because of this, most practical combustion
devices employ turbulent flows to enable rapid
mixing and heat release in relatively small
volumes.

LENGTH SCALES IN TURBULENT FLOWS

In the turbulence literature, many length scales have
been defined; however, the following four scales are of
general relevance to our discussion and, in general,
are frequently cited. In decreasing order of size, these
scales are as follows:

1
. (L) Characteristic width of flow or macroscale

This is the largest length scale in the system and is the
upper bound for the largest possible eddies. In a
reciprocating internal combustion engine, L might be
taken as the time varying clearance between the
piston top and the head, or perhaps the cylinder bore.

2
.
(l

o
) Integral scale or turbulence macroscale

The integral scale physically represents the
mean size of the large eddies in a turbulent
flow; those eddies with low frequency and large
wavelength. The integral scale is always
smaller than L, but is of the same order of
magnitude.

3
. (l

)

Taylor microscale

The Taylor microscale is an intermediate length
scale between the integral scale (
l
o) and
Kolmogorov Scale (
l
k), but is weighted more
towards the smaller scales. This scale is
related to the mean rate of strain.

4
. (lk)

Kolmogorov microscale

The Kolmogorov microscale is the smallest length scale
associated with a turbulent flow and, as such, is
representative of the dimension at which the dissipation
of turbulent kinetic energy to fluid internal energy occurs.
Thus, the Kolmogorov scale is the scale at which
molecular effects (kinematic viscosity) are significant.

The final point we wish to make concerning
lk

is possible
physical interpretations. In
Tennekes

model of a
turbulent flow,
lk

represents the thickness of the smallest
vortex tubes or filaments that permeate a turbulent flow,
while others suggest that
lk

represents the thickness of
vortex sheets imbedded in the flow.

DEFINITION OF TURBULENT FLAME
SPEED

Unlike a laminar flame, which has a propagation velocity
that depends uniquely on the thermal and chemical
properties of the mixture, a turbulent flame has a
propagation velocity that depends on the character of the
flow, as well as on the mixture properties.

For an observer traveling with the flame, we can define a
turbulent flame speed
, S
t

as the velocity at which
unburned mixture enters the flame zone in a direction
normal to the flame.

In this definition, we assume that the flame surface is
represented as some time
-
mean quantity, recognizing
that the instantaneous position of the high
-
temperature
reaction zone may be fluctuating wildly.

Since the direct measurement of unburned gas velocities
at a point near a turbulent flame is exceedingly difficult,
at best, flame velocities usually are determined from
measurements of reactant flow rates. Thus, the turbulent
flame speed can be expressed as :

St= m / (Aavg

u
)

The reason for using this time
-
smoothed flame area is
shown below :

Experimental
determinations of
turbulent flame speeds
are complicated by
determining a suitable
flame area. A, for thick,
and frequently curved,
flames. The ambiguity
associated with
determining this flame
area can result in
considerable uncertainty
in the measurement of
turbulent burning velocity.

STRUCTURE OF TURBULENT PREMIXED
FLAMES

Again, referring to the previous figure we can say that
The instantaneous flame front is highly convoluted, with
the largest, folds near the top of the flame (Fig. a). The
positions of the reaction zones move rapidly in space,
producing a time
-
averaged view that gives the
appearance of a thick reaction zone (Fig. b).

This apparently thick reaction zone is frequently referred
to as a
turbulent flame brush
.

The instantaneous view, however, clearly shows the
actual reaction front to be relatively thin, as in a laminar
premixed flame. These reaction fronts are sometimes
referred to as laminar
flamelets
.

As mentioned above, spark
-
ignition engines operate with
turbulent premixed flames. Recent developments in
laser
-
based instrumentation have allowed researchers to
explore, in much more detail than previously possible,
the hostile environment of the internal combustion
engine combustion chamber. This is shown in the next
slide.

In these flame visualizations, we see that the division
between the unburned and burned gases occurs over a
very short distance and the flame front is distorted by
both relatively large
-

and small
-
scale
wrinkles
.

This figure shows a time
sequence of two
-
dimensional flame
visualizations in a spark
-
ignition engine from a
study.

The flame begins to
propagate outward from
the spark plug, as shown
in the first frame, and
moves across the
chamber until nearly all
the gas is burned.

Three Flame Regimes

The visualizations of
turbulent, flames
presented before suggest
that the effect of
turbulence is to wrinkle
and distort an essentially
laminar flame front.

Turbulent flames of this
type are referred to as
being in the
wrinkled
laminar
-
flame regime
.

This is one pole in our
classification of turbulent
premixed flames. At the
other pole is the
distributed
-
reaction
regime
.

Falling between these
two regimes is a region
sometimes referred to as
the
flamelets
-
in
-
eddies
regime
.

Regime Criteria

Recall that the smallest scale, the Kolmogorov
microscale,
lk
, represents the smallest eddies in the flow.
These eddies rotate rapidly and have high vorticity,
resulting in the dissipation of the fluid kinetic energy into
internal energy, i.e., fluid friction results in a temperature
rise of the fluid.

At the other extreme of the length
-
scale spectrum is the
integral scale,
lo

which characterizes the largest eddy
sizes. The basic structure of a turbulent flame is
governed by the relationships of
lk

and
lo

to the laminar
flame thickness,

l.

The laminar flame thickness characterizes
the thickness of a reaction zone controlled
by molecular, not turbulent, transport of
heat and mass. More explicitly, the three
regimes are defined by :

Wrinkled laminar flames:

l

<
l
k

Flamelets in eddies:
l
o

>

l

>
l
k

Distributed reactions:

l

>
l
o

When the flame thickness, is much thinner than the
smallest scale of turbulence, the turbulent motion can
only wrinkle or distort the thin laminar flame zone. The
criterion for the existence of a wrinkled laminar flame is
sometimes referred to as the
Williams
-
Klimov
criterion
.

At the other extreme, if all scales of turbulent motion are
smaller than the reaction zone thickness, then transport
within the reaction zone is no longer governed solely by
molecular processes, but is controlled, or at least
influenced, by the turbulence. This criterion for the
existence of a distributed
-
reaction zone is sometimes
referred to as the Damkohler criterion.

Hence, in addition to the Reynolds Number (Re), we
have another number that that characterizes the
turbulent flame velocity called Damk
Öhler number (Da).

The fundamental meaning of the Damk
Ö
hler number,
Da, used here is that it represents the ratio of a
characteristic flow or mixing time to a characteristic
chemical time
.

It represents the ratio between the characteristic flow
time to the characteristic chemical time.

When chemical reaction
rates are fast in
comparison with fluid
mixing rates, then Da >
1
,
and a
fast
-
chemistry
regime

is defined.
Conversely, when
reaction rates are slow in
comparison with mixing
rates, then Da <
1
.

This is shown in the
figure to the right.

Definition of the three flame regions

1
) WRINKLED LAMINAR
-
FLAME REGIME

In this regime, chemical reactions occur in thin
sheets.

Referring again to the previous figure, we see
that reaction sheets occur only for Damkohler
numbers greater than unity, depending on the
turbulence Reynolds numbers, clearly indicating
that the reaction
-
sheet regime is characterized
by fast chemistry (in comparison with fluid
mechanical mixing).

2
) DISTRIBUTED
-
REACTION REGIME

One way to enter this regime is to require
small integral length scales, (lo / lk) <
1
, and
small Damkohler numbers (Da <
1
). This is
difficult to achieve in a practical device,
since these requirements imply that,
simultaneously, lo, must be small and vrms
must be large, i.e., small flow passages and
very high velocities.

Pressure losses in such devices surely
would be huge and, hence, render them
impractical. Also, it is not clear that a flame
can be sustained under such conditions.

3
) FLAMELETS
-
IN
-
EDDIES REGIME

This regime lies in the wedge
-
shaped
region between the wrinkled laminar flame
and distributed
-
reaction regimes as shown
in the previous figure. This region is
typified by moderate Damkohler numbers
and high turbulence intensities. This
region is of particular interest in that it is
likely that some practical combustion
devices operate in this regime.

Flame stabilization

Low velocity bypass ports

Refractory burner tiles

Bluff body Flame
-
holder (Recirculation)

Swirl or jet
-
induced recirculating flows

Rapid increase in flow area creating
recirculating separated flow