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CFD - based feasibility study of active control on a combustion instability

Authors:
  • IfTA Ingenieurbuero fuer Thermoakustik GmbH
Conference Paper

CFD - based feasibility study of active control on a combustion instability

Abstract

Active control is a promising measure against thermo-acoustic oscillations, e.g. in power generation gas turbines. Many successful lab-scale demonstrations have been reported in the literature, but commercial application remains challenging due to the unpredictability of control authority. This paper investigates active control of a quarter-lambda thermo-acoustic oscillation of a turbulent premix flame enclosed in a combustor of rectangular cross-section. Several experimental trials to actively damp the combustor's oscillation by modulation of the fuel mass flow, i.e. by reducing the Rayleigh index, were unsuccessful. The controller, which works in the frequency domain, was successfully applied to similar situations in the past. The operating principle can be described in simple terms as a band pass filter combined with proportional amplification and a phase shift. The current study investigates this case in ANSYS CFX. Turbulent combustion is modelled in the SAS-SST context with the burning velocity model (BVM). The controller is included in the simulation as a Fortran script (user function). As in experiment, active control of the combustor is unsuccessful. The convective time delays present in the combustor are evaluated and identified as the cause of the lack of control authority.
CFD-BASED FEASIBILITY STUDY OF ACTIVE CON-
TROL ON A COMBUSTION INSTABILITY
Roel A. J. Müller, Constanze Temmler, Robert Widhopf-Fenk and
Jakob Hermann
IfTA Ingenieurbüro für Thermoakustik GmbH, 82194 Gröbenzell, Germany, www.ifta.com,
e-mail: Roel.Mueller@ifta.com
Wolfgang Polifke
Lehrstuhl für Thermodynamik, Technische Universität München, 85747 Garching, Germany
Phil Stopford
ANSYS UK Ltd., 97, Milton Park, Abingdon, Oxfordshire, OX14 4RY, UK
Active control is a promising measure against thermo-acoustic oscillations, e.g. in power
generation gas turbines. Many successful lab-scale demonstrations have been reported in the
literature, but commercial application remains challenging due to the unpredictability of control
authority. This paper investigates active control of a quarter-lambda thermo-acoustic oscillation
of a turbulent premix flame enclosed in a combustor of rectangular cross-section. Several
experimental trials to actively damp the combustor’s oscillation by modulation of the fuel mass
flow, i.e. by reducing the Rayleigh index, were unsuccessful. The controller, which works in
the frequency domain, was successfully applied to similar situations in the past. The operating
principle can be described in simple terms as a band pass filter combined with proportional
amplification and a phase shift. The current study investigates this case in ANSYS CFX.
Turbulent combustion is modelled in the SAS-SST context with the burning velocity model
(BVM). The controller is included in the simulation as a Fortran script (user function). As in
experiment, active control of the combustor is unsuccessful. The convective time delays present
in the combustor are evaluated and identified as the cause of the lack of control authority.
1. Introduction
This paper describes the simulation of combustion instabilities occurring in a model combustor.
Combustion instabilities are a major nuisance in industrial gas turbines. Strong pressure oscillations
can cause severe hardware damage, while even weaker oscillations can cause an increase in pollutants.
For a thorough introduction to the issues associated with combustion instabilities, as well as possible
solutions, the reader is referred to Culick
1
.
A possible remedy against combustion instabilities is the application of Active Instability Control
(AIC). Compared to passive damping features, such as Helmholtz resonators, AIC has the advantage
of being more flexible in application: one AIC system can attenuate multiple modes of oscillation.
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
Especially for lower frequencies (say
< 500Hz
), the sensors and actuators needed for AIC are much
smaller than passive dampers effective in the same frequency range. As a result, AIC usually needs
smaller structural modifications than passive measures when retrofitting a turbine with instability
issues.
Various authors describe examples of successful attenuation of combustion instabilities, using
AIC with various forms of actuation. For example: Lang et al.
2
use a loudspeaker in the plenum
between fuel injection and flame in a premixed propane burner, Bloxsidge et al.
3
use a valve in the
plenum between fuel injection and flame in a premixed propylene burner, Heckl
4
uses a loud speaker
placed at the downstream end of a Rijke tube, and Hermann et al.
5
uses a piezo actuator in the fuel
supply line of a liquid fuel burner. While most examples of AIC are found on a laboratory scale,
Hermann and Orthmann
6
form a notable exception, using a Direct Drive Valve by Moog Inc. in the
fuel supply line to apply AIC on a heavy duty industrial gas turbine.
Despite these examples, the implementation of AIC on a given gas turbine remains far from
trivial, and it is hard to determine a priori whether a certain actuator mounted on a certain position will
provide satisfactory control authority over the instabilities at hand. The current research is conducted
in the context of the EU-funded Marie Curie research project LIMOUSINE (
Lim
it cycles of thermo-
ac
ous
tic oscillations in gas turb
ine
combustors), which aims to strengthen the fundamental scientific
work in the field of thermo-acoustic instabilities in combustion systems. To this end, several model
combustors were manufactured. A slightly different burner geometry, discussed by Kosztin et al.
7
, had
its instability readily damped (in experiment) using the approach of Hermann and Orthmann
6
. This
approach did however not work on the geometry described in the present paper, which was introduced
by Tufano et al.
8
This paper discusses the investigation of active control on this second burner, in a
simulation in ANSYS CFX.
2. Set-up
2.1 Physical geometry
Fig. 1 gives an overview of the dimensions of the physical LIMOUSINE combustor, as well
as the simplified geometry for the flow simulations. The burner is situated in a duct of rectangular
cross-section with closed/open acoustic boundary conditions, approximating a quarter-wave acoustic
resonator. The rectangular cross section with relatively large aspect ratio leads to an approximately
2-D flow in the x,y plane.



 

 
 


 
Figure 1.
Cross section of the combustor, with (inner) dimensions in mm. The location of the AIC input sensor
is indicated at
x = 200 mm
. The origin of
x
is the top of the flame holder.
Above
: The real combustor; inner
span in z direction is 150 mm. Below: The computational domain; span (thickness) is 2 mm.
Air enters the bottom of the combustor through choked orifices. This guarantees an acoustically
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
hard boundary condition. From there, perforated tubes distribute the air along the span (
z
direction) of
the combustor. The prismatic flame holder, triangular in cross section, rests at about one quarter of
the height of the combustor. The fuel gas (methane) is also passed through orifice plates and injected
through 62 holes along the flame holder. A partially premixed flame forms, stabilised at the top of
the flame holder. There are holes along the length of the combustor wall for sensor access, which are
usually closed. The hole furthest upstream
(x = 200 mm)
is of particular interest, since the sensor
supplying the input signal for AIC is situated there.
2.2 Representation of the geometry in CFD
The simulation takes advantage of the prismatic geometry, by considering only a thin
(2mm)
slice of the combustor with symmetry boundary conditions set on both sides in
z
direction. The
computational grid, consisting of 82 k hexahedral elements (112 k nodes), is a structured grid with five
layers in the z direction around the flame holder and in the upstream side of the combustion chamber,
to capture the most essential features of the three-dimensional flow caused by the fuel injection (see
Fig. 2). Half a fuel injector hole is modelled at either side of the flame holder, and a short stub of the
fuel supply line is modelled as well, to take the compressibility of the gas in the fuel supply system into
account. To save computational cost, the grid is two-dimensional in the plenum and the downstream
end of the combustion chamber, where gradients in z direction are negligible.
Fuel injectors
Fuel inlet
Figure 2. Detail of the computational grid around the fuel injection and the mixing region.
The air inlet is modelled as a fixed mass-flow boundary condition. The plenum is slightly longer
than in experiment, to maintain its real volume in a simpler shape. The open outlet is modelled as
an opening (allowing in-flow) at constant pressure. This end is elongated as well, to represent the
complex boundary condition in the form of an end correction. The controller output determines the
mass flow set on the fuel inlet boundary condition.
2.3 Computational model
The transient simulation in ANSYS CFX v14.5 used 8 cores, with
10
5
s
time steps. The thermal
power
P
th
= 40 kW
, and the equivalence ratio
¯
F = 0.71 (l = 1.4)
. Turbulence is modelled with
the Scale Adaptive Simulation model (SAS-SST) model
9
. Combustion is simulated by the Burning
Velocity Model (BVM)
10,11,12
using a new model option for improving accuracy for non-premixed
flames
13
. Several other models, such as the eddy dissipation model, as well as the Extended Coherent
Flame Model (ECFM) were tried out, but gave an oscillating behaviour which was much less in line
with experiment. The liner walls are modelled as thermally conductive with a heat transfer coefficient
of
50W/(m
2
K)
, based on an estimate of the heat loss by free convection and radiation, towards an
environment at 300 K.
The convective time from the fuel inlet
(t)
is computed as an additional variable
14
. To this
end, first two auxiliary variables, each representing passively convected scalars, are defined:
C
t
(~x,t)
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
and
C
1
(~x,t)
. At the air inlet, both are defined to be zero. At the fuel inlet,
C
t
= t
(the simulation
time at which the fuel entered the domain), while
C
1
= 1
. The expression
C
t
/C
1
will remain constant
when the fuel expands, dilutes, or gets consumed. Its value represents the time at which the fuel (or
corresponding combustion products) entered the domain.
t
tot
(~x,t)=t C
t
/C
1
is now the convective
time from the fuel inlet, viz. the boundary of the domain.
2.4 Implementation of active control in CFX
The controller, which works in the frequency domain, is identical to the one used by Hermann
and Orthmann
6
. In simple terms, it comprises of a band-pass filter and an amplification plus phase shift,
which can be set according to preferences. The controller is run as a command line application which
reads a log file with under-sampled (in time) pressure data from the sensor position and writes the
output value to another file. In CFX, a user function (written in Fortran) updates the pressure log file
and reads the output value from the controller. This value is used to set the fuel inlet mass flow. The
goal is to create a modulation of the equivalence ratio, which causes a fluctuating heat release out of
phase with the pressure fluctuation at the flame, i.e. damping by reduction of Rayleigh’s coefficient.
3. Results
3.1 Mode shapes without control
The simulation was run without control for a total time of
0.23s
. The limit cycle develops
quickly and mode shapes are evaluated over the simulated time minus the first
0.06s
. After applying a
Blackman window to the time domain data, the frequencies of the mode shapes were estimated from
a Fourier-spectrum. The mode shapes, viz. amplitude and phase as a function of
x
, were acquired
through evaluation of the Fourier coefficients corresponding to the estimated frequencies.
The mode shapes found in this way, are presented in Figs. 3 and 4 in comparison to the
mode shapes found in experiment
15
. Phase is defined to be zero at the peak in the heat release, or
experimentally at the peak in the OH* chemiluminescence signal.
f [Hz]
x [m]
|
ˆp
|
[Pa]
x [m]
|
ˆp
I
|
[Pa]arp
I
[]
Figure 3. Left
: Overview of the amplitude of the pressure fluctuation in the simulation, as a function of
frequency and position. Vertical solid lines indicate the individual modes (
1
/4
,
3
/4
and
5
/4
wave). The second
harmonic of the first mode is dashed. The third harmonic coincides with the third mode, viz. the
5
/4
wave.
Right: Comparison of the first mode shape (quarter wave) in experiment and simulation.
Considering the relative simplicity of the simulation, and the great sensitivity of the results to
minor model changes, the comparison is by all means satisfactory. The shapes generally show good
agreement, though the amplitude of the second mode is too high in the simulation. The reason for
this is unknown. The third mode is stronger than in experiment, since it coincidences with the third
harmonic of the first mode. In experiment, this coupling was seen at slightly other operating conditions.
In line with experiment, there is only a small phase difference between heat release and pressure at the
location of this flame, meaning a positive modal Rayleigh coefficient for all these modes.
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
x [m]
|
ˆp
II
|
[Pa]
(CFD)
(Experiment)
arp
II
[]
x [m]
|
ˆp
III
|
[Pa]
(CFD)
(Experiment)
arp
III
[]
Figure 4.
Comparison between mode shape in experiment and simulation. Mind the double scaling.
Left
: second
mode shape (three-quarter wave). Right: Third mode shape (five-quarter wave).
3.2 Estimation of desired controller settings
The pass band of the controller is set to
[50,500] Hz
. This allows the dominant oscillation around
240Hz to be damped, without the risk of causing instabilities at other frequencies.
3.2.1 Phase lags in the control loop
The controller phase shift required for a heat release in anti-phase with the pressure fluctuation
is found as:
arg
p
0
S
p
0
˙
Q
+(t
ac
+
¯
t
cv
)w
I
+ Dj
AIC
=(2n + 1) p , (1)
where
w
I
is the angular frequency of the dominant oscillation.
arg
p
0
S
/p
0
˙
Q
represents the phase
difference between the pressure fluctuation
p
0
at the sensor (S) and at the flame (
˙
Q
). Together with the
phase shift caused by acoustic (ac) and convective (cv) delay, and the phase shift set for the controller,
this should add up to
n
-and-a-half a cycle. Regarding the fuel system as a Helmholtz resonator, its
resonance frequency is much higher than that of the oscillation at hand. Therefore the fuel system can
be regarded as acoustically compact, and the acoustic time delay between fuel inlet and fuel injector
can be neglected
(t
ac
0)
. The compliance of the fuel system remains significant, so the fuel system
should still be included in the computational domain.
The momentary average
¯
t
cv
and dispersion
s
cv
of the convective time between injector and flame
are found as
¯
t
cv
(t)=
¯
t
˙
Q
t
inj
, with
¯
t
˙
Q
(t)=
w
CH
4
(~x,t) t (~x,t) dV
w
CH
4
(~x,t) dV
,
and
s
cv
(t)=
v
u
u
u
t
w
CH
4
(~x,t)
t (~x,t)
¯
t
˙
Q
(t)
2
dV
w
CH
4
(~x,t) dV
,
where
w
CH
4
is the rate of consumption of
CH
4
.
t
inj
is evaluated at the end of the fuel injector. To get
a homogeneous value here, the diffusion of
t
is set to
10
4
m
2
/s
in the fuel system. In the rest of the
domain, this is zero.
¯
t
cv
and
s
cv
are shown as a function of time in Fig. 5, which also gives a graphical
interpretation of Eq. 1. Fig. 6 shows the variable
t
cv
as a function of position, in combination with the
rate of consumption of
CH
4
. It can be seen that the flame consumes regions with different values of
t
cv
simultaneously.
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
p
0
˙
Q
0.3p
p
0
S
Dj
AIC
) 0.6 p
F
0
AIC
w
I
t
cv
4.1 p
˙
Q
0
D
˙
Q
0
AIC
t [s]
¯
t
cv
± s
cv
[s]
(
¯
t
cv
± s
cv
) w
I
[rad]
Figure 5. Left
: Phasor plot corresponding to Eq. 1 (amplitudes not to scale). A resulting phasor
˙
Q
to the right
implies a positive Rayleigh coefficient.
Right
: Convective time delay as evaluated by CFX. Averaged over the
indicated interval:
¯
t
cv
± s
cv
= 8.80 ± 2.15 ms or equivalently (
¯
t
cv
± s
cv
)w
I
=(4.12 ± 1.00) p rad.









0.2249 s
maximal
compression
0.2255 s 0.2261 s
e
xhalation
0.2267 s 0.2273 s
maximal
e
xpansion
0.2279 s
0.2285 s
inhalation
0.2291 s
Figure 6.
Variation of the variable
t
cv
and the rate of combustion (flame) over one pressure cycle. The red
region below is due to the fact that t
cv
is not well defined (C
t
/C
1
= 0/0) in the air-only region downstream.
The variation in time of the convective delay as shown on the right in Fig. 5, is a serious problem
from the perspective of active control. A phase shift which should be optimal for at certain moment,
might be unfavourable a little while later. Since the convective time is large compared to the period of
oscillation, a relatively small change, for instance caused by a small shift in flame position when using
another combustion model, can mean a significant change in the resulting Rayleigh coefficient and the
resulting oscillation.
3.2.2 Controller gain and attenuation of control authority by dispersion
The high dispersion
s
cv
means the equivalence ratio fluctuation realised at the injector will have
lost quite some definition when it arrives at the flame. This can be modelled as a low pass filter, as
done by Polifke et al.
16
In that paper, a comparison is made between the stability of combustors where
the fluctuation of the heat release follows the fluctuation of the equivalence ratio at the injector with
various impulse responses. In the case of a simple time lag, i.e. the impulse response is a Dirac delta
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
function, the transfer function becomes
˙
Q
0
F
( f )
¯
˙
Q
=
F
0
inj
( f )
¯
F
e
2p ift
,
with
˙
Q
0
F
the fluctuation in heat release due to equivalence ratio fluctuations at the injector
F
0
inj
. When
the time lag is assumed to have a Gaussian distribution instead, the transfer function gets a low-pass
characteristic, as
˙
Q
0
F
( f )
¯
˙
Q
=
F
0
inj
( f )
¯
F
e
2p
(
ps
2
f
2
+ift
)
.
In the case of a combustor without active control, this is generally a good thing, since an increase of
stability is found. Currently however, the dispersion causes an attenuation of the control signal and a
reduction of control authority. After substitution of the values found before
˙
Q
0
F
( f )
¯
˙
Q
=
F
0
inj
( f )
¯
F
0.007 exp(0.37 i) ,
which means the heat release fluctuation realisable by the active control is less then a percent. This is
very small compared to the heat release fluctuation caused by the dominant instability:
˙
Q
0
I
/
¯
˙
Q = 0.29
.
Considering the challenges identified in Subsec. 3.2.1, the controller gain is set as high as possible
whilst keeping the output signal between zero and unity, not to influence the mean operating conditions.
Currently, the controller gain is set to 1.5 · 10
5
.
3.3 Simulation with Active Instability Control (AIC)
To get a direct comparison between the simulation running with and without AIC, the simulation
was restarted from intermediate results without AIC after
0.12s
. The comparison is shown in the time
domain in Fig. 7. The active control clearly has some influence on the pressure fluctuation (the blue
and red lines do not overlap), but due to the varying nature and dispersion of
¯
t
cv
, this does not result in
a satisfactory over-all attenuation of the oscillation.
t [s]
p
0
S
[Pa]
AIC signal
Figure 7.
Comparison of pressure history with AIC on or off. Although AIC does influence the oscillation, over
a longer time range, the amplitude does not decrease (or increase) significantly. The cycle shown in Fig. 6 is
indicated on the right.
4. Discussion and conclusion
The simulation in CFX gives a satisfactory agreement with the experimental data, especially
considering the great simplifications applied to reduce computational time. The active control feedback
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20th International Congress on Sound and Vibration (ICSV20), Bangkok, Thailand, 7-11 July 2013
loop with modulation of the fuel mass flow rate is implemented in a manner analogous to experiment.
Controller settings are based on the results of a simulation without active control. Active control was
unsuccessful in experiment, for reasons not properly understood. The computational results suggest
that the dispersion and temporal variation of the convective time delay are decisive for success or failure
of active control by fluctuation of the fuel mass flow. Since the convective time is relatively large, a
small change in the combustion model can also cause great differences in the predicted combustion
instability.
Generally, this form of actuation for active control is considered problematic when
s
cv
or
¯
t
cv
is too large, i.e. when the flame is too long, or stabilised too far downstream of the fuel injector, or
when mixing causes too much dispersion in the convective time between the injector and the flame.
For comparison it would be interesting to repeat this analysis with a similar combustor where active
control was applied successfully in experiment, e.g. the one discussed by Kosztin et al.
7
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Self-excited combustion instabilities of a bluff-body-stabilized premixed flame are investigated. The burner is situated in a duct of rectangular cross-section with closed/open acoustic boundary conditions, representing a quarter-wave acoustic resonator. Fuel gas (methane) is injected through small holes a short distance upstream of the flame, such that it burns in partially premixed mode. Operating points (i.e. thermal power and equivalence ratio) where instability occurs are identified. Variation of amplitude and frequency while operating conditions are changed are discussed for the dominant mode of oscillation, as well as its second and third harmonic. For certain operating points, the harmonics of the first mode seem to couple with higher independent modes. Pressure oscillations during limit cycle operation for one constant operating point are measured along the combustor length. The shape and amplitude of several independent thermo-acoustic modes, as well as the most significant higher harmonics, are reconstructed, identified and interpreted in relation to the combustor geometry. The phase shift between pressure variation at the flame and heat release (Rayleigh index) is discussed for the independent modes, as well as the higher harmonics.
Conference Paper
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The impact of premix nozzle shape on combustion stability in a geometry representative of an annular low-emission combustor is investigated by a combination of numerical and analytical means. For three elliptical premix nozzle geometries with varying eccentricity, the flame shape is computed with computational fluid dynamics using a standard stationary Reynolds-averaged formulation with Reynolds-Stress and turbulent flame speed closure models. From the CFD solution, the time lags for convective transport from the fuel injector to the flame front are determined through Lagrangian particle tracking. Interpreting the histograms of particle arrival times as the unit impulse response of fuel consumption to a perturbation of fuel injection, the corresponding fuel transport frequency response F(LJ) is computed and used to achieve closure for a linear acoustic model of the behavior of a compact premix flame. Using this model for the flame dynamics in a network model of linear acoustics in annular geometries, the impact of nozzle shape and fuel transport time lag distribution on the thermo-acoustic stability of a premixed combustor is explored. For the configurations investigated, the elliptical premix nozzles produce wider time lag distributions with smaller mean values than the circular base configuration and are less prone to combustion instabilities. © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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Theoretical background, details of implementation and validation results of a computational model for turbulent premixed gaseous combustion at high turbulent Reynolds numbers are presented. The model describes the combustion process in terms of a single transport equation for a progress variable; closure of the progress variable’s source term is based on a model for the turbulent flame speed. The latter is identified as a parameter of prime significance in premixed turbulent combustion and is determined from theoretical considerations and scaling arguments, taking into account physico-chemical properties of the combustible mixture and local turbulent parameters. Specifically, phenomena like thickening, wrinkling and straining of the flame front by the turbulent velocity field are considered, yielding a closed form expression for the turbulent flame speed that involves, e.g., speed, thickness and critical gradient of a laminar flame, local turbulent length scale and fluctuation intensity. This closure approach is very efficient and elegant, as it requires only one transport equation more than the non-reacting flow case, and there is no need for costly evaluation of chemical source terms or integration over probability density functions. The model was implemented in a finite-volume based computational fluid dynamics code and validated against detailed experimental data taken from a large scale atmospheric gas turbine burner test stand. The predictions of the model compare well with the available experimental results. It has been observed that the model is significantly more robust and computationally efficient than other combustion models. This attribute makes the model particularly interesting for applications to large 3D problems in complicated geometries.
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