AIAA-98-0352
FLAME SPEED CONTROL USING A COUNTERCURRENT
SWIRL COMBUSTOR
S. Lonnes, D. Hofeldt, P. Strykowski*
University of Minnesota
Mechanical Engineering
Minneapolis, MN 55455
Abstract
The Countercurrent Swirl Combustor (CSC) is a modified cyclone design that utilizes fluid dynamic mechanisms
as a means of control. Previous investigations have demonstrated the CSC’s ability to operate as a low NOx
combustion source1. Although low pollutant concentrations are demanded by present and future legislation, a
practical combustor must also exhibit variable energy release, or turn down. Inherent in the CSC design is the
potential to effectively control flame speeds and thus turn down. The CSC geometry consists of two axial
counterflowing but tangentially co-swirling annular reactant ring jets, at different radii, contained within a
cylindrical vessel. An exhaust port is located on the axis of the cylinder at one end. The countercurrent shear layer
between the two annular jets pumps fluid from the outer ring jet radially inward along the entire axis of the cylinder.
A self-stabilized, constant diameter cylindrical flame sheet resides inside of the shear layer, with the low density
products confined along the axis by the swirl field. The turbulence levels in the near field of the flame are
controlled by manipulating the vorticity in the shear layer through axial shear, tangential shear, and radial ring jet
separation. Flame speed suppression is achieved by increasing the global swirl velocity. The present fundamental
study has experimentally observed flame speeds ranging from laminar to 3.5 times laminar values using natural gas
as a fuel. A dimensionless parameter is proposed that incorporates turbulence generation mechanisms, swirl
suppression, and turbulent scale adjustments. Data collapse is observed over a wide range operating conditions and
geometries using this parameter.
Introduction
Legislative restrictions on pollutant emissions have
motivated the combustion community to seek new low
emission combustion techniques that are practical
industrial energy sources. The ultra low NOx emission
characteristics of the Countercurrent Swirl Combustor
(CSC) have previously been documented1. In addition
to low NOx emissions a practical combustion source
needs to demonstrate, for most applications, a range of
variable heat release or turn down. The ability to
consume fuel is limited primarily by flame area and
turbulent flame speed. With the motivation to
maximize volumetric heat release, the turbulent flame
speed is the remaining turn down control parameter.
The present study focuses on CSC flame speed control.
The Countercurrent Swirl Combustor is a modified
cyclone combustor design. Cyclone combustors have
been studied in various forms since the 1960’s using
fuels ranging from coal to natural gas. The reactants
enter tangentially at one end, flow axially toward the
opposite end of the chamber, reverse directions axially,
and exhaust out of a centerline port on the same end as
* Corresponding Author
Copyright © 1998 by the American Institute of
Aeronautics and Astronautics, Inc. All rights reserved.
the inlet. Most NOx investigations of cyclone
combustors focused on generating sub-thermal NOx
operating temperatures2 by stabilizing a flame at low
equivalence ratios or by heat removal from the flame
zone4. The methods proved to be effective at the
expense of energy diverted to cooling water or
additional pumping work for excess combustion air.
Four different flame configurations, or modes, have
been experimentally observed and documented3 in
cyclone combustors using natural gas as a fuel. The
transition between modes was proposed3 to be primarily
a function of equivalence ratio. The first two modes are
characterized by a flame burning up to the reactant inlet
ports without penetrating the axial length of the
chamber. These modes reside within the thermal NOx
temperature range. The integrated residence times of
post flame fluid elements as they decelerate to zero
axial velocity and then accelerate out combustor
generate undesirable NOx levels. The preferred low
NOx mode is distinguished by a flame residing close to
the chamber walls and extending axially over the
combustor length. This mode does not reside in the
thermal NOx temperature range, thus the elevated
residence times do not produce excessive NOx levels.
A plot 3 of mass flow of fuel consumed versus
equivalence ratio reveals a bounded operating space for
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AIAA-98-0352
this mode. The operating range is limited between
equivalence ratios of 0.5 to 0.7 and fuel flow rates of 1
kg/hr and 5 kg/hr (a turn down limit of about 5). The
final mode is identified by a substantially smaller
diameter flame than the previous mode and also extends
the axial length of the combustion chamber. This flame
configuration was only observed during very lean
operation, equivalence ratio less than 0.55. A plot of
mass flow of fuel consumed versus equivalence ratio
does not exhibit an upper limit on the fuel consumption
rate (higher turn down ratio potential). This mode of
operation was considered of no practical significance.
The explanation cited for disregarding this mode was
“inefficient” combustion. Characteristic of this mode
is a thin annular gap between the exhaust nozzle and
flame, figures 2 and 4. Reactants exit the CSC via this
gap. Many possible techniques exist for consuming or
eliminating the reactant flux. The hydrocarbons are
presently consumed by circulation over a hot surface.
Presuming complete combustion, this mode of
operation offers several benefits. Turbulent structures
generated in the reactant stream shear layer are
convected into the flame. Manipulation of the shear
layer vorticity in the near field of the flame allows
turbulent flame speed control. The swirl induced radial
pressure gradient in conjunction with the
reactant/product density interface permits variable
turbulence suppression. The vigorous mixing of the
exhaust jet with entrained air rapidly freezes NOx
kinetics while maintaining sufficient temperatures for
hydrocarbon consumption. The small constant diameter
flame significantly reduces residence times at flame
temperatures, thus reducing thermal NOx. Additionally,
a stability ceiling is not observed with increased total
mass flow.3 The motivation for the following study is
to assess the potential for the low NOx CSC to act as a
high volumetric heat release combustion source with a
wide turn down ratio.
the CSC axis of symmetry. Reactants are ejected from
the “Front” drive swirl assembly into the glass
combustion chamber via a discretely variable annular
jet. The “Front” axial momentum is generated by
varying the annulus gap (≈ 3 mm gap). Thus, for a
given mass flow, the boundary conditions on the axial
and tangential velocity components can be
independently controlled for the front drive.
"Rear"
Glass Cylinder
"Front"
Fuel+Air
b.)
"Front"
"Rear"
Swirl Ring
Flame Sheet
Countercurrent Swirl Combustor
The CSC incorperates geometric modifications to
the cyclone design to facilitate shear layer control. The
CSC geometry consists of two axial counterflowing but
tangentially co-swirling annular reactant ring jets, at
different radii, ejecting into a cylindrical vessel, figure
1. The present study used lean premixed natural gas
and air as reactants. The premixed reactants enter the
“Front” and “Rear” swirl chambers tangentially through
the inlets at each end. The swirl chambers homogenize
the inlet jet signatures and generate the CSC
momentum boundary conditions. The “Front” angular
momentum is generated by passing the reactants
through a swirl ring located in the “Front” swirl
chamber, figures 1b and 1c. A swirl ring consists of 30
6.4 mm holes drilled at a preselected angle relative to
Flame Sheet
Fuel+Air
RR
UR,z UR,θ mR
c.)
mTotal = m F + mR
δ= R F− R R
R
ρ1
ρ2
RF
UF,z UF,θ mF
Glass Cylinder
Fig. 1 a) Countercurrent Swirl Combustor experimental
facility b) isometric view c) cross-sectional view.
The "Rear" portion of the CSC permits discrete
variability of the annular radius RR, figure 1c, with a
fixed gap (3 mm gap). A glass cylinder approximately
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AIAA-98-0352
30.5 cm in length and 10.2 cm in diameter contains the
reactant ring jet flows. A 5.1 cm diameter exhaust port
is located along the axis through the front drive. This
configuration is useful for experimental study but is not
necessarily the desired configuration for a practical
system. The mass flow of reactants provided to the CSC
is determined by a venturi, with dynamically adjusting
calibration coefficients, for air and a rotameter for fuel.
A flame is initiated in the mixture by inserting a spark
ignitor into the rear portion of the CSC near the
centerline, figure 1a. The ignitor is withdrawn to
prevent flame and/or flow field interactions. The flame
seats on a water cooled stainless steel plug that
comprises the center of the rear annular ring jet.
Heat release rates of 30kW up to (but not limited to)
150kW have been observed. Various CSC geometries
and operating conditions have been investigated.
Parameters were varied over the following ranges;
chamber lengths of 30.5 cm and 15.3 cm, radial ring jet
separation of δ=3.4 mm to 35.1 mm (figure 1c), total
mass flows of 0.015 kg/s to 0.060 kg/s, front inlet swirl
angles of 31°, 41°, and 68°, rear inlet swirl angles of 0°
and 80°, rear mass flows of 0% to 60% of the total mass
flow, and equivalence ratios between 0.68 and 0.85.
products causes the element to be restored to its initial
position. Extending Rayleigh’s circulation criteria to
include a density discontinuity elucidates the principle.
The diameter of the flame sheet is observed to
remain constant along the axis of the chamber, figure 3.
Although the diameter remains axially invariant, the
turbulence intensity of the flame varies with axial
location, figure 5. The associated local increase in
radial flame propagation velocity requires elevated
radial manifolding into the flame to maintain a constant
diameter flame.
Proposed Operational Physics
The reactant shear layer formed between the two
counterflowing ring jets resides at a radius greater than
the flame, figure 2. This is supported by experimental
observation of the inclination angle of helical striations
on the flame interface. A 2-D perspective of the 3-D
striations are visible in right images of figures 5b and
5c. The contained swirling flow field establishes a
radial pressure field which balances the centrifugal
acceleration exerted on each fluid element.
"Rear"
"Front"
Flame Sheet
Reactant Shear Layer
Glass Cylinder
Fig. 2 Cross-sectional view of the Countercurrent Swirl
Combustor (swirl ring not shown).
This swirling flow is the primary means for flame
stabilization. If a structure, convected from the shear
layer, radially perturbs an element of the flame sheet,
the density difference between the reactants and
Fig. 3 Typical CSC twenty frame composite image of
the flame (exhaust port is located on the right).
A possible explanation for the constant diameter flame
sheet is a coupling between the radial manifolding of
reactants into the flame sheet and the local turbulent
flame speed along the cylinder axis. It is believed that
reactants are drawn radially into the flame at a rate
functionally related to the axial velocity ratio across the
layer and local reactant axial velocity.
To simplify the following discussion, little or no rear
drive flow is assumed, rear drive flow is considered
later. Conservation of mass and momentum require
that the axial velocity of the outer ring jet decrease with
increasing distance from the front drive assembly. As
the reactants cross the flame sheet, mass is added at
fixed area to the product flow, which causes the axial
velocity of the products to accelerate toward the
exhaust nozzle, figures 2 and 4. The radial gradient of
the axial velocity decreases with increased distance
from the front drive, figure 4. This results in a nonuniform turbulence intensity distribution along the axis
of the CSC, assuming that to the lowest order the
turbulence intensity scales with ∂Uz/∂r. Figures 5a and
5b demonstrate axial variance of flame turbulence
intensity for low values of rear flow. The mean
convective speed of structures in the shear layer also
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AIAA-98-0352
decreases with increased distance from the front drive.
The turbulence intensity distribution in conjunction
with the effective transport of mass through the nonuniform mean structure velocity creates a radial
manifolding of reactants into the flame that decreases
with increased distance from the front drive.
"Rear" Glass Cylinder
Flame Sheet
generating non-convecting temporally unstable modes
is well documented.6 The associated increase in spatial
amplification rates allow sufficient turbulence
generation in a compact geometry.
"Front"
Axial
Velocity Profile
Radial
Velocity Profiles
Fig. 4 Representation of anticipated velocity profiles
within the combustor.
To accommodate the non-uniform manifolding of
reactants into the flame, the local flame speed must be a
function of axial position. Since the reactants are
premixed, the laminar flame speed is constant
throughout the chamber. The mechanism that is
believed to provide the non-uniform flame speed is the
level of turbulence along the axis. At any axial location,
a reactant fluid element passing through the shear layer
will transmit the level of turbulence experienced in the
shear layer directly to the flame front. This creates a
turbulent flame speed that is directly coupled to the
radial velocity. The radial velocity is in turn coupled
to the total mass flow through the CSC by the injection
velocities into the chamber. The best evidence of this
theory has been qualitatively observed. With minimal
rear drive flow, the flame appears almost laminar at the
rear drive assembly and becomes increasingly more
turbulent toward the exhaust nozzle, while maintaining
a constant flame diameter, figures 5a and 5b.
Additional supporting evidence is a constant diameter
flame observed with increased total mass flow through
the CSC.
When flow is introduced through the rear drive
assembly, the local shearing increases both the radial
manifolding of reactants as well as the turbulence
transmitted to the flame. The local increase in
turbulence transmitted to the flame is observed in the
image sequence from 5a to 5d, while the increase in
radial manifolding is supported by the observed
constant diameter. Continuous control of the vorticity,
turbulence intensity, radial manifolding, and the
turbulent flame speed is facilitated with rear drive flow.
The utility of a countercurrent shear layer for
Fig. 5 Images of the CSC flame at the “Rear” (left) and
“Front” (right) with rear mass fractions of a) 10%, b)
20%, c) 30%, and d) 40% of the total mass flow. Each
image extends 7.5 cm axially.
The flame sheet resides at a position where the
flame speed determined by the reactant equivalence
ratio and the local turbulence intensity match the radial
inward velocity. Since the radial velocity must be zero
at the axis and at the wall, a maximum must exist,
figure 4. As long as this maximum is greater than the
local flame speed, the flame remains confined, if the
flame speed exceeds the maximum radial velocity, the
flame changes modes and propagates to the cylinder
wall.
Turbulence suppression is achieved by
exploiting the density discontinuity between the
reactants and products. A perturbation (increase in
flame area, flame speed) to an element of the flame
results in a restoring force that is related to the radial
pressure gradient established in the chamber. The
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AIAA-98-0352
radial pressure gradient is proportional to the square of
an integrated tangential velocity or global swirl
velocity. By controlling the global swirl field,
turbulence effects encountered by the flame sheet can
be variably suppressed, figure 6.
Percent Increase in Flame Speed (%IFS)
200
150
100
50
0
0
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035
2
1 Uθ
Fig. 6 Percent increase in flame speed versus the
inverse of a squared average chamber (global) swirl
velocity.
The trend observed in figure 6 reinforces the radial
pressure gradient (centrifugal acceleration) effect
proposed. Decreased global swirl results in an increase
in turbulent flame speed. Figure 6 corresponds to data
points using front swirl angles of 31°, 41°, and 68° with
all other parameters fixed. The definition of the global
swirl velocity can be found on page 8, equation (9) and
the percent increase in flame speed is referenced to the
laminar flame speed at the given equivalence ratio,
reactant temperature, and pressure. The anticipated
near linear behavior with centrifugal acceleration is
observed. The image sequence of figure 5a to 5d
corresponds to increased levels of rear mass flow as
well as global swirl. The transition observed from
turbulent to laminar, figures 5a (right) to 5d (right),
indicate the suppressive effects of global swirl. The
structures generated near the front drive no longer
possess enough energy to distort the flame at higher
global swirl velocities.
Flame Speed Measurement Technique
An average flame speed within the CSC is used to
document flame speed controllability. The flame speed
is defined as the mass flow of reactants consumed
within the CSC divided by the flame area and reactant
density. Local turbulence intensity and radial velocity
measurements are planned for the future. Calculation
of the flame speed requires measurement of the reactant
mass flow consumed within the burner, the reactant
density, and average flame area.
The average flame area is determined by flame
imaging and image analysis. Figures 3 and 8b show
typical images of the CSC cylindrical flame. Black
matting is used to isolate the flame intensity from the
surroundings. A 20 frame composite image is used to
create an average flame location using a 480 x 640
pixel 8 bit b/w CCD camera. Regions of high
turbulence create a flame interface that appears
brushed. The gray scale values gradually decrease from
the bright flame interior to the dark background with
increased radial distance. Whereas, a laminar interface
appears as a sharp intensity jump from the black
background to the intense flame. The objective is to
define a consistent location within the gray scale
gradient, for all images.
The image matrix of gray scale values is
interrogated using Matlab. A thresholding approach is
used to distinguish the flame and define a representative
flame area. The surface plot shown in figure 7
represents the image intensity, or gray scale value,
mapped to the vertical axis. Thresholding consists of
selecting a scalar intensity, setting the image
information below the threshold value to 0 (black), and
replacing the remaining values with 1 (white).
Fig. 7 Representation of a flame image with the gray
scale value plotted on the vertical axis.
The area sliced by the threshold plane in figure 7
indicates the values that would be replaced with white.
Integrating the white area in figure 7 and multiplying
by pi yields the cylindrical flame sheet area
corresponding to the selected gray scale value. A plot
of flame area versus threshold number can be generated
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by thresholding the image over the range intensities,
from black to white, and integrating each corresponding
area. A typical flame area versus threshold number plot
is shown in figure 8a.
100
Flame Area (in2)
80
60
40
20
0
0
0.2
0.4
0.6
Threshold Number
0.8
1
a.)
Fig. 8 a) Cylindrical flame sheet area as function gray
scale threshold value b) corresponding flame image and
c) image contours at threshold values of 0.34, 0.54, and
0.69.
Threshold numbers between 0 and 0.2 correspond to
the black background. The values between 0.2 and 0.8
correspond flame areas from the outer fringe of the
turbulent brush to the intense inner core. The slope of
the region from 0.2 to 0.8 is related to the globally
averaged turbulence intensity. The line between 0.2
and 0.8 on figure 8a would appear more horizontal for a
sharp laminar interface. A line is fit to linear region of
figure 8a and the center point is defined as a
representative flame area. The point corresponds to the
center of the gray scale gradient formed by the flame
brush. A contour plot of the image using gray scale
values of 0.34, 0.54, and 0.69 identifies local regions
turbulence by observing the relative radial separation of
the contour lines along the axis of the flame interface,
figure 8c.
In addition to the flame area, the mass flow of
reactants consumed by the flame is required for a flame
speed determination. The mass flow of reactants
consumed by the flame is determined by subtracting the
reactant mass flow exiting the CSC from the mass flow
entering the CSC. The reactant mass flux exiting the
CSC, through the gap between the flame and exhaust
nozzle, is quantified by direct measurement using a
specially designed vectoring velocity temperature
probe.
The measurement challenge arises in attempting to
integrate the axial component of a swirling variable
density reactant stream over a radial distance of about 5
mm (the gap thickness). A novel low profile vectoring
velocity-temperature probe was designed. The probe
was designed to allow, nominally, a point vectorvelocity-temperature measurement in a 2-D flow field.
The probe consists of a 1 mm Ø type ‘K’ thermocouple
centered between two 1 mm Ø pressure taps and
confined in a plane, refer to figure 9. Each of the
pressure tubes were bent 90° and sheared at the bend.
One tube is directed into the oncoming flow while the
other is directed parallel to the flow. The approach
flow observes a 1 mm thick planar obstruction.
The probe was calibrated using a well-conditioned
free jet, between the facility limits of 10 to 75 m/s. An
unusual asset of the probe design is the invariant nature
of the calibration coefficient with respect to velocity
(above 18 m/s). Additionally, the location of the
maximum pressure with respect to rotation appears to
be independent of velocity. The probe also provides
good pressure signal amplification (139% of a standard
pitot reading). A measurement with the probe is
straight forward; rotate the probe until the maximum
pressure is observed, multiply the maximum pressure
by 0.721, record the temperature and angle, and then
use Bernoulli's equation to find the velocity.
The probe is mounted flush with the CSC exhaust
face and is attached to a unidirectional traverse with a
rotary chuck. A typical measurement entails moving
the probe radially with the traverse (typically 0.5 mm
increments), rotating the probe to read the maximum
pressure, recording pressure and temperature and then
proceeding incrementally until the flame is reached.
Assuming that the thermocouple is exposed to a
turbulent combination of reactants and products, the
flame edge is defined to exist where the probe reads
600°F. The density and axial velocity are resolved at
each radial location with the information provided by
the probe. Integration of the mass flow across the gap
yields the outflow of reactants from the CSC. With the
inflow of reactants, outflow of reactants, density, and
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AIAA-98-0352
flame area known, the average flame speed can be
calculated.
elevate a fluid element one integral length scale in the
presence of gravity and a density gradient.
Ri =
(g ρ)(∂ρ ∂y)
(∂u ∂y)2
(1)
The Richardson number defined in this way is a local
quantity associated with local gradients. Beér et al.8
extended the definition to rotating flows by replacing
gravity with a local centrifugal acceleration and
converting to radial gradients, as shown in equation (2).
Ri
*
(1 ρ)( ∂ρ ∂r )( u θ2
=
(∂u z ∂r )2
r
)
(2)
Toqan et al.9 use this modified Richardson number to
quantify the turbulent interaction effects in a low NOx
radially stratified swirl combustor. Challenges arise in
using Equation (2) if there are density discontinuities.
A parameter formulation is proposed that follows
the energy method of Prandtl7 but uses a density
discontinuity to represent the flame interface. The
turbulent kinetic energy per unit volume associated
with a structure can be approximated using Prandtl’s
mixing length theory, equations (3) and (4).
1.0 mm Ø
u′ = λ
Type 'K'
Thermocouple
Flow Perspective
End View
(Looking Down Support)
Fig. 9 Magnified views of the Low Profile Vectoring
Velocity-Temperature Probe.
∂u
∂y
(3)
∂u
1
E s = ρ1λ2
∂y
2
2
(4)
Where λ is the integral length scale, u´ is the velocity
fluctuation, and ρ1 is the reactant density. The work per
unit volume required to raise a fluid element of the
flame (low density) one integral length scale through
the constant density reactants (high density) can be
expressed as,
y1 + λ
Parameter Formulation
A parameter is sought that incorporates the primary
physics that govern the behavior of the flame interface.
The balance between turbulence generation in the shear
layer and turbulence suppression at the flame are the
fundamental mechanisms driving flame speed control.
Prandtl7 used energy methods to quantify the effects of
a radially stratified density field under the influence of
gravity on turbulence. This quantity, known as the
Richardson number, characterizes the energy associated
with a turbulent structure and the work required to
W=
∫ g(ρ
1
− ρ2 )dy
(5)
y1
W = g∆ρλ
(6)
where ρ 2 is the product density, and g is gravity. A
Richardson number formed from the ratio of equations
(5) and (6) is expressed in equation (7).
Ri + =
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2g∆ρ
ρ1λ(∂u ∂y)
2
(7)
AIAA-98-0352
The primary difference between equations (1) and (7) is
the appearance of the integral length scale in Ri+. Large
structures appear to more effectively disturb the flame
interface.
Using the approach of Beér et al.8, equation (7) can
be extended to a rotating environment.
ρ1λ(∂u ∂r )
(
2 ∆ρ u θ2 r
)
(m˙ F R F U F,θ ) + (m˙ R R R U R,θ )
˙ Total R
m
(8)
(9)
Where the numerator represents the total angular
momentum supplied to the CSC, see figure 1c for
parameter definitions. The turbulence generation term
in (8) "∂u/∂r" can be replaced a global term that is
functionally related. Referring to equation (3), the
turbulent kinetic energy generated by the shear layer
can be approximated by,
∆U z 
u ′z = λ 
 δ 
Es =
u θ′ = λ
 ∆U θ 
 δ 
2
2
1  2  ∆U z 
 ∆U θ  
ρ1 λ
+ λ2
 δ  
2   δ 

(10)
(11)
Where ∆Uz=UF,z - UR,z and ∆Uθ = UF , θ - UR,θ are the
velocity differences from the front and rear ring jets.
The quantity δ is the radial separation of the front and
rear ring jets. Note that ∆U/δ is a measure of the
vorticity across the shear layer initiated by the front/rear
ring jet interactions. Incorporating the results of
equations (9) and (11) into (8) yields,
Ri′ =
(
ρ1λ ∆U 2z + ∆U θ2
(
2 ∆ρ
U θ2
)
Rδ
2
)
(
ρ1 ∆U 2z + ∆U θ2
(12)
Typically for free shear layers the integral length scale
is assumed to be some constant fraction of the shear
layer thickness. If the assumption is made that shear
(
2 ∆ρ
2
For the purposes of clarity during data presentation the
reciprocal of the standard Ri definition is used for Ri++.
Equation is (8) relies on knowledge of local quantities
at the flame interface. A practical form of equation (8)
is desired that relates the global operating conditions to
the local variables. The centrifugal acceleration in
equation (8) can be replaced with a global swirl
velocity and radius. A global swirl velocity can be
derived from angular momentum conservation.
Uθ =
Ri′′ =
U θ2
)
(13)
)
Rδ
The plot in figure 10 demonstrates reasonable data
collapse using equation (13) considering the extension
from local variables to global variables.
250
Percent Increase in Flame Speed (%IFS)
Ri ++ =
layer thickness is defined by the radial ring jet
separation, then λ scales with δ . Equation (12)
becomes,
200
150
100
50
Ri′′ =
(
ρ1 ∆U 2z + ∆U θ2
(
2 ∆ρ
U θ2
)
)
Rδ
0
0
200
400
600
800 1000 1200 1400 1600
Ri''
Fig. 10 Percent increase in flame speed (%IFS) versus
the constant density Richardson # (Ri", eq. 13).
The measurand is a normalized turbulent flame speed.
The experimentally determined flame speed is
normalized by the laminar flame speed15 corrected for
the inlet reactant temperature16 and pressure.17 Data
was collected for many CSC geometries and operating
conditions. Data points correspond to 30.5 cm and 15.3
cm chamber lengths, δ=3.4 mm and 16.1 mm radial
ring jet separations, total mass flows of 0.030 kg/s and
0.040 kg/s, front inlet swirl angles of 31°, 41°, and 68°,
rear inlet swirl angles of 0° and 80°, rear mass flows of
10% to 50% of the total mass flow, and equivalence
ratios between 0.68 and 0.85.
Countercurrent shear layers are known to provide
broadband excitation over a cascade of turbulent scales
ranging from integral to Kolmogorov. Recent work10-14
has indicated that large structures are more effective at
distorting a flame interface. This is in agreement with
equation (7). The equations of motion governing large
structures are dominated by inviscid mechanisms, while
small structures are dominated by viscous mechanisms.
It has been proposed that the substantial increase in
kinematic viscosity at the flame zone damps small
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structures. A structure cut-off size greater than an order
of magnitude larger than the Kolmogorov scale, was
experimentally observed by Roberts et al.10
A turbulent scale correction term to Ri'' is proposed.
The term should account for the fraction of structures
that are of insufficient size to modify the flame
interface. Dimensional analysis provides a relationship
between the range of anticipated scales and the
turbulent Reynolds number.
Re t =
λu ′
ν
(14)
Where νis the kinematic viscosity and η is the
Kolmogorov length scale. Equation (14) indicates that
increased turbulent Reynolds number broadens the
range of length scales. Since the integral length scale is
essentially fixed by geometry (or shear layer thickness)
the Kolmogorov scale becomes smaller to
accommodate the increased turbulent Reynolds number.
When the turbulence intensity in the shear layer is
increased, more energy is transferred to turbulent scales
that are ineffective at flame distortion. This would
indicate that the structure energy in equation (12) is
weighted too heavily. There is not a direct transfer of
structure energy to flame distortion work. An
increasing fraction of the energy is lost to small scales
with increased turbulence intensity. Ri'' is corrected by
multiplying by (1/Ret)n where n is an unknown
weighting. A practical form of Ret requires the
substitution of globally significant parameters.
Prandtl's mixing length theory would imply that u´ is
proportional to the effective shear.
(
u ′ = u ′z2 + u θ′ 2
1/ 2
)
(
∝ ∆U 2z + ∆U θ2
1/ 2
)
(15)
Although, it would appear that the radial ring jet
displacement would be the appropriate scaling for λ,
the chamber radius provides better data collapse. The
global turbulence Reynolds number is shown in
equation (16).
Re t =
(
R ∆U 2z + ∆U θ2
ν
1/ 2
)
(16)
Multiplying (13) by the reciprocal of global turbulence
Reynolds number (16) yields the scale adjusted
constant density Richardson number, equation (17). The
turbulence Reynolds number weighting factor was set
equal to unity to minimize data scatter.
(
ρ1 ν
)
(17)
The improved data collapse observed in figure 11
appears to support the turbulent scale correction to
equation (13). No compensation has been attempted for
the thermo-diffusive effect associated with sub-unity
Lewis number reactants.
250
Percent Increase in Flame Speed (%IFS)
λ
3/ 4
= ( Re t )
η
Ri ** =
1/ 2
+ ∆U θ2
2 ∆ρU θ2 δ
∆U 2z
200
150
100
50
Ri
**
=
(
ρ1 ν ∆U 2z + ∆U θ2
1/ 2
)
2 ∆ρU θ2 δ
0
0
5 10-5
0.0001
Ri* *
0.00015
0.0002
Fig. 11 Percent increase in flame speed (%IFS) versus
the scale adjusted constant density Richardson # (Ri**,
eq. 16).
Conclusions
The Countercurrent Swirl Combustor (CSC)
offers unique potential for providing ultra low NOx
combustion and flame speed control. The primary
physics that govern the operation of the CSC are a
balance between shear layer turbulence generation and
swirl suppression. A modified Richardson number,
Ri**, was derived assuming a sharp density interface at
the flame, and reasonable data collapse was observed.
This modified Richardson number was corrected for
turbulent scale effects. The correction factor decreased
the weight of the turbulent energy term in Ri** due to
the inability of small structures to distort the flame
interface.
Considerably better data collapse was
observed using the corrected modified Richardson
number. Flame speeds were observed between laminar
and about 3.5 times laminar. The focus of the present
study was to gain an understanding about the governing
physics involved in the CSC combustion process, not
necessarily flame speed maximization. Further
increases in turbulent flame speed are anticipated in
future studies.
9
American Institute of Aeronautics and Astronautics
AIAA-98-0352
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Lonnes S., Hofeldt D., Strykowski P., Proceedings
of the 1996 Technical Meeting of the Central
States Section of the Combustion Institute, St.
Louis, Missouri, pp 170-175, 1996.
Syred N., Styles A.C., and Sahatimehr A., J. Inst.
Energy, 54:128, pp 125, 1980.
Najim S.E., Styles A.C., and Syred N., Eighteenth
Symposium (International) on Combustion, pp
1949-1957,1981.
Mirzaie H. and Syred N., Third International
Symposium of Gas-Solid Flows-1989, Presented at
the Third Joint ASCE/ASME Mechanics
Conference, San Diego, Ca, 1989.
Abbas N.S.T., Hassan M.A., Hussien A.M.M.,
and Lockwood F.C., Journal of the Institute of
Energy, 65, pp 77-85, 1992.
Strykowski P.J. and Wilcoxon R.K., AIAA
Journal, 31:3, 1993.
Prandtl, L., Collected Works, Vol. II, pp 778,
Springer: Berlin 1961.
Beér, J. M., Chigier N. A., Davies T. W., and
Bassindale K., Combustion & Flame, 16, pp 3945, 1971.
Toqan, M. A., Beér, J. M., Jansohn, P., Sun, N.,
Testa A., Shihadeh, A., and Teare, J. D., TwentyFourth Symposium (International) on Combustion,
pp 1391-1397, 1992.
Roberts, W. L. and Driscoll, J. F., Combustion
and Flame, 87, pp 245-256, 1991.
Roberts, W. L., Driscoll, J. F., Drake, M. C., and
Goss, L. P., Combustion and Flame, 94, pp 58-69
1993.
Roberts, W. L., Driscoll, J. F., Drake, M. C., and
Ratcliffe, J. W.,Twenty-Fourth Symposium
(International) on Combustion, pp 169-176,
1992.
Driscoll, J. F., Sutkus, D.J., Roberts, W. L.,
Post, M. E., and Goss, L. P., Combustion Science
and Technology, 96, pp 213-229, 1994.
Poinsot, T., Veynante, D., and Candel, S.,
Twenty-Third Symposium (International) on
Combustion, pp 613-619, 1990.
Vagelopoulos, C. M., Egolfopoulos, F. N., Law,
C. K., Twenty-Fifth Symposium (International) on
Combustion, pp 1341-1347, 1994.
Andrews, G. E. and Bradley, D., Combustion and
Flame, 19, pp 275-288, 1972.
Egolfopoulos, F. N., Cho, P., and Law, C. K.,
Combustion and Flame, 76, pp 375-391, 1989.
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American Institute of Aeronautics and Astronautics