Measurement of the Conditioned Turbulence and Temperature Field of a... Stabilized Bunsen Type Premixed Burner Using Planar Laser Rayleigh Scattering...

advertisement
Measurement of the Conditioned Turbulence and Temperature Field of a Ring
Stabilized Bunsen Type Premixed Burner Using Planar Laser Rayleigh Scattering and
Stereo Particle Image Velocimetry
Sebastian Pfadler, Micha Löffler, Friedrich Dinkelacker, Alfred Leipertz
Lehrstuhl für Technische Thermodynamik
Friedrich-Alexander Universität Erlangen-Nürnberg
Am Weichselgarten 8
D-91058 Erlangen, Germany
E-Mail: [email protected]
1 ABSTRACT
The turbulence and temperature field of Bunsen type turbulent lean methane/air flames has been investigated
using Planar Laser Rayleigh Scattering (PLRS) and Stereo Particle Image Velocimetry (Stereo PIV). Temporal
averaged reaction progress variable plots have been computed from PLRS measurements in order to provide a
basis with regard to the verification of CFD models. Turbulence was characterised by Stereo PIV in one plane
for all directions in space. Averaged velocity fields have been calculated as well as Reynolds decomposed
fluctuation vector fields. Conditioned RMS-values of the turbulent fluctuations in terms of unburnt and burnt gas
could be determined making use of the information gained from a threshold setting procedure in the PIV raw
images. Furthermore several length scales were measured indirectly from PIV vector plots. In this context all
integral length scales being accessible with Stereo PIV were computed separately for burnt and unburnt region
and compared to each others. It could be observed that all integral length scales become longer in the burnt zone.
Additionally, the conditioned Taylor and the Kolmogorov length have been extracted from PIV fields using
correlation equations suggested by Bradley and Tennekes.
2 INTRODUCTION
To improve the models which are the base of nowadays used Computational Fluid Dynamcis (CFD) codes being
applied on the field of turbulent combustion research, a close collaboration between numerical investigations and
experimental studies is of importance. This means that experimental work has to provide the necessary data in
order to verify numerical results and thus to establish a basis for an improvement of current numerical models.
Of special interest is the knowledge of the flow and turbulence field, thus averaged velocities, their fluctuations,
the turbulence intensity and relevant length scales need to be known.
Since the flame influences the flow and turbulence field significantly, for instance, flame generated turbulence is
a well known phenomena, a distinction of the turbulence characterisation has to be done between burnt and
unburnt part of the flame. This article describes which turbulence parameters are accessible from PIV data and
highlights conditioned results achieved in a turbulent premixed combustion system.
For a useful comparison with numeric investigations additionally temperature fields were measured with PLRS.
From this temperature fields averaged reaction progress variables have been determined.
3 EXPERIMENTAL SETUP
3.1 Burner
In the following investigation a ring stabilized turbulent Bunsen type burner was applied. The operating range
was changed in terms of fuel-air ratio and total mass flow rate resulting in 8 stable working points representing
the complete stable range. Lean methane/air mixtures have been investigated as they are of most essential
technical interest. (an overview of the operating points is given in Figure 10)
In order to reach nearly homogenous isotropic turbulence conditions a perforated plate with holes of 4 mm
diameter was used. After passing the turbulence plate the flow is forced through a conical part and thus gets
accelerated. Without the flame stabilising ring at the burner outlet very lean flames at high outlet velocities
would lift off and extinguish. The advantage of this way of flame stabilisation is the benefit of having the
stabilizer conform to the burner port. This leads to an almost complete combustion without any leakage of fuel
combined with non-changed emissions compared to the unstabilized construction (Johnson, Kostiuk et al. 1998).
stabilising ring
perforated plate
Figure 1: Ring stabilized
Bunsen type burner
3.2 PIV System
In order to achieve high resolution instantaneous vector fields Particle Image Velocimetry was used. A
stereoscopic viewing of the flow field gave access to three directions in space, also known as Stereo PIV (Raffel,
Willert et al. 1998).
As luminous source of the PIV system two separate frequency doubled Nd:YAG lasers were used with a
maximum pulse energy of 270 mJ each. The temporal separation of the two pulses was adjusted to 30 µs in order
to give an optimal shift of the scattered light in the image plane. The beams were superposed by a polarising
beam splitter cube. After focusing into the area of interest the beams were expanded to a diverging light sheet
with a height of about 60 mm in the measured region. The light sheet was located 5 mm above the burner outlet.
Two double-shutter cameras (PCO Sensicam, 1280*1024 pixel) were positioned at one side of the laser light
sheet under an opening angle of 70°. The Scheimpflug criterion was satisfied via tilting the image plane towards
the laser sheet so that image-, object,- and lens plane intersect in one point.
The premixed methane air mixture was seeded with TiO2 particles with an average diameter of 0.8 µm.
The 3-D flow field was deduced from applying a cross-correlation technique to the successive images of both
cameras and a adjacent geometrical calculation of the out of plane directed velocity component.
3.3 PLRS System
Planar Rayleigh Scattering was used for measurement of the temperature fields of the flames (Namer and
Schefer 1985). For that a laser-light-sheet was placed in the object of interest, being oriented through the
symmetry axis of the burner. The scattered light of a volume element in the light sheet plane attains to the
assigned pixel of the CCD-camera with help of an objective. The detectable scattering power PDet depends
essentially on the number density of the molecules and whose scattering cross section in the volume element.
N
 ∂σ 
PDet = η opt ⋅ ⋅ I 0 ⋅ ∫∆Ω 
 dΩ
(1)
V
 ∂Ω  eff
I0 is the incident laser intensity, (∂σ / ∂Ω )eff the effective, differential scattering cross section. The effective
scattering cross section is the fraction weighted sum of the scattering cross sections of the participating
molecules, N/V the total number density of the molecules. For eliminating the unknown setup constants ηopt and
the scattering collection angle Ω usually for temperature determination the pixelwise quotient is formed with a
reference picture at known temperature Tref and pressure pref (from dry air at room temperature).
( p / T )ref I 0,ref σ ref
PDet ,ref
=
⋅
⋅
Q Ray =
(2)
PDet
p /T
I0
σ
The temperature of each pixel is accessible with an accuracy, which is in particular depending on the change of
the medium scattering cross section. Dealing with methan/air flames this deviation is smaller than 2-4%
(Dinkelacker 1993) (Kampmann, Leipertz et al. 1993).
PDet , ref σ
p ref
T = Tref ⋅
⋅
⋅
(3)
PDet σ ref
p
The first of the two PIV-laserpulses (pulsed Nd:YAG laser) was applied for Rayleigh-thermometry. A doubleintensified CCD-camera (LaVision StreakStar) was employed as detector. To minimize light reflexes in the
background, the burner was built in a housing equipped with a for 30° inclined backplane and two sidewalls with
thin oblong apertures for the optical access. With this setup it was possible to make measurements with a
minimum distance to the burner top edge of less then 10 mm, the whole picture area is about 50 x 50 mm². For
the temperature field measurements were taken series of 50 pictures each.
4 THEORY OF INTEGRAL LENGTH SCALES
Adapting Reynolds decomposition of the instantaneous velocity at a specified location in space yields a time
averaged velocity for the considered location and a instantaneous fluctuation.
v
v
v
ui(x,t) = U i(x ) + ui′(x,t )
(4)
Using PIV, time averages are normally replaced by ensemble averages from several consecutive measurements.
Besides this Reynolds decomposition, spatial correlation lengths are of significant interest to characterise
turbulent flows. Spatial correlations may be described by the correlation tensor between the velocity fluctuations
of two vector components of two adjacent vectors at two different locations (Rotta 1972),
v
v
v v
Rij (r , t ) = u i′ ( x , t ) ⋅ u ′j ( x + r , t )
(5)
v
where r describes the displacement vector between two measurement locations. For the following
considerations only correlations of the same velocity components are compared (thus i is equal to j). Figure 2
gives an overview of the accessible correlation possibilities of the three vector components. Depending on the
direction of r a longitudinal or transverse correlation can be calculated. As even Stereo PIV is just a planar
measurement technique, only in-plane correlations are instantanously available (Figure 2).
In order to gain integral length scales from the aforementioned vector correlations an integration over the
Figure 2: In-plane auto-correlation possibilities with Stereo
PIV
distance r needs to be done for each averaged pair of multiplied vector components. If the correlation is directed
perpendicular to the considered vector component the correlation function is denominated as transverse
v
correlation function q(r). In case that the direction of r points towards the respective vector component a
longitudinal correlation function l(r) is formed (Rotta 1972). The mathematical description (with suitable
normalisation) follows as:
(u′j ) A (u′j ) B
(u′ ) (u′ )
l (r ) = i A i B q(r ) =
(6)
ui′2
u′j 2
In practice of integral length scale calculation from PIV vector plots the averaging follows over the number of
taken vector fields after multiplying all vector pairs with a given distance r of the same spatial component in
each plot (Figure 3).
n=4
n=3
n=2
n=1
average over all images
dr
Figure 3: Averaging procedure for correlation tensor
calculation from PIV data
The integration itself is defined as:
∞
∫
∞
∫
Ll = l (r )dr L q = q(r )dr
0
(7)
0
The upper boundary of the integration is limited to the size of the PIV vector plots and can thus only reach the
maximum height or width of the considered field depending on the direction of correlation.
Figure 4 exemplifies a typical longitudinal and transverse spatial correlation of the main flow direction. At a
1
0.9
0.8
0.7
0.6
0.5
longitudinal correlation l(r)
transversal correlation q(r)
0.4
0.3
0.2
0.1
0
0
5
10
15
20
r [mm]
Figure 4: Typical shape of spatial correlation
25
30
distance of 0 mm the vector component is correlated with itself. With increasing distance the value of the
correlation function decreases until it reaches almost zero. Corresponding to Equation 7 characteristic correlation
or integral length scales can be determined, being visualized also in Figure 5.
It is of interest to determine also smaller length scales from PIV measurements, although here the resolution of
the measurements have to be regarded. Following turbulence theory the Taylor length scale λT of a flow can also
be estimated from the shape of correlation (Figure 5) (Rotta 1972), being described by Equation 8:
−1
−1
 ∂ 2l 
 ∂ 2q 
λT = −  2 
= − 2 2 
 ∂r 
 ∂r 

r =0

r =0
(8)
Figure 5: Taylor length calculation from course of
correlation
Alternatively, the Taylor length scale λT can be determined indirectly from the integral length scale, if the
turbulent Reynolds number Ret = u'Ll,q/ν is known (Tennekes and Lumley 1972). Bradley 1992 proposed to use a
prefactor of 6.35 (Equation 9):
0 , 25
ν 3 
L
λT =   = 6.35 ⋅ x0 ,5
(9)
Re t
 εT 
From theory also the Kolmogorov scale η as the characteristic scale of the smallest appearing eddies in the flow
may be determined with (Tennekes and Lumley 1972)
η ≈ Lx ⋅ Re t−3 / 4
(10)
5 THRESHOLD SETTING PROCEDURE IN PIV RAW IMAGES
For the investigation of flame generated turbulence it is strongly advisable to measure turbulence properties in a
conditioned way. This means that the turbulence parameters should be evaluated and designated separately in
terms of burnt and unburnt gas mixture. The raw images for vector calculation of premixed flames in PIV do not
only carry information about displacement of particles and thus velocities. Apparently they also contain
information where burnt and unburnt gas mixture is located (Figure 6). The gasdynamic expansion of the
reacting gases leads to a distinct decrease in particle density in the region where the burnt mixture is located. An
image processing procedure including averaging over a small number of particles extracts the information
expressed in Figure 7. The actual threshold is located in between the two appearing maxima, one representing
the cold region in the flame, the other the hot zone. This procedure has to be done for each image separately as
particle seeding might feature some changes during measurement.
250
5
original
frequency
hot maximum
smoothed
4
1st derivation
3.5
150
3
2.5
threshold value
100
2
cold maximum
1.5
50
1
0.5
0
0
0
100
200
300
400
500
600
intensity (counts)
Figure 6: PIV raw image of
turbulent flame
Figure 7: Histogram of raw image, threshold setting
700
value of 1st derivation
200
4.5
6 EXPERIMENTAL RESULTS
6.1 PLRS Measurements
2500 K
Rayleigh temperature distribution
counts [a. u.]
40000
35000
A 1,0
B 0,8
C 0,7
D 0,8
E 0,7
F 0,62
G 0,7
H 0,62
30000
25000
20000
15000
10000
5000
0
0
500
1000
1500
temperature [K]
2000
2500
3000
position
Figure 8:
Temperature distribution for the eight operating Figure 9:
points with different ϕ and massflows
250 K
Snapshot of temperature
field at operating point B
The probability distribution of the temperatures is presented in Figure 8, showing how often a specified
temperature occurs in the pixels of all 50 pictures. The temperature distribution is clearly bimodal. The mean
temperature of the hot burnt gas was calculated from the center of the area of the hot peak with:
B
TRay ,coa =
∑ Ti ⋅ counts(Ti )
i= A
(11)
B
∑ counts(Ti )
i= A
and is listed in Table 1 for the flames A to H. Here, the summation boundaries are fixed with the doubled peakwidth at half height for both directions separatly.
Table 1:
Mean temperature of hot burnt gas
operating point
TMean [K]
A
2041
B
1944
C
1769
D
1958
E
1802
F
1611
G
1696
H
1534
For determination of the reaction progress variable, a series of 512 pictures was taken for each flame case. The
reaction progress c can be calculated as the normalised flame temperature.
T − Tcold
c=
(12)
Thot − Tcold
With the shown bimodal behaviour of the temperatures, being typical for premixed turbulent combustion, the
flame can be divided in an unburnt and a burnt zone (thin flame approximation). Then the average reaction
progress variable can be interpreted also as the probability to find burnt gas. For that a suitable threshold value
for the binarization of the pictures is required, being based on the median value of the intensities between cold
and hot gas.
All pictures are added up and are normalized to the total number B
1 B
c = ⋅ ∑ cixy B = number of pictures; x, y = pixel indices
(13)
B i =1
The actual recording process is:
• time resolved (10 ns puls length) snap shots of Rayleigh scattering with flame
• pixelwise subtraction of the mean dark noise of the camera
• binarization with given threshold
• add up of the pictures in an extra buffer
• normalization to the number of pictures
• correction of possible distortion caused by the intensifiers
Positioning grids were generated from the images of a positioning target. With respect to the maximum picture
area of 50 x 50 mm², the pictures of the whole flames are composed of up to three single pictures with
overlapping ranges.
90
A
B
C
D
E
F
G
H
70
50
30
10
9 kg/h
ϕ = 1.0
0–10%
12 kg/h
ϕ = 0.8
ϕ = 0.7
10–30%
ϕ = 0.8
30–50%
ϕ = 0.7
15 kg/h
ϕ = 0.6
50–70%
ϕ = 0.7
70–90%
ϕ = 0.6
90–100%
Figure 10: Residence probability of burnt gas of flames with different stoichiometries and mass flows
From the assignment of the pixels with the position over the burner it is possible to determine the height of the
flames as well as the width of the turbulent flame brush. In Table 2, HMax describes the height of the highest
point with c = 5, while W indicates the maximum extension of the turbulent flame brush in the axial direction
between c = 0.1 and 0.9.
Table 2:
Maximum Flame height for c = 0,5
operating point
HMax ( c = 0.5) [mm]
W ( c =0.1-0.9) [mm]
A
28.9
14.9
B
39.1
16.6
C
54.8
20.6
D
45.2
19.0
E
62.7
24.0
F
71.5
26.5
G
63.6
28.3
H
82.2
36.0
6.2 Evaluation of conditioned PIV mesurements
Resulting from the gasdynamic expansion of the
reacting gases the averaged absolute velocities for all
three components are expected to be higher in the
burnt region than in the unburnt zone. Countergradient turbulent transport behaviour is predicted in
this case (Bray 1985). On the other hand, gradient
diffusion of the turbulent flux term may lead to the
opposite behaviour, as is matter of current discussion
in turbulent flame theory (e.g. Veynante 1997).
In Figures 11 and 12 results of the experiments of
one exemplary operating point show a remarkable
increase in velocity, as can be observed at least in
radial direction. In Figure 11 only every fourth
vector is displayed, in order to clearify the
presentation.
This component is directed almost normal to the
average position of the flame front in the presented
measurements. This implies that most of the mass
transport is directed normal to the flame front and
thus suggest counter-gradient turbulent transport
behaviour for those relative low turbulence
intensities of less than unity. Also for the axial
velocity component (y) an increase in averaged
Figure 11: Instantaneous velocity field,
absolute velocity has been observed. The out of plane
background: absolute value of velocity
component of velocity does not follow that trend
which is due to the fact that in average this component is close to zero for that in-centre position of the lightsheet.
Evaluating the conditioned fluctuation velocity the influence of flame produced turbulence can be investigated
via conditioned PIV. Figure 13 shows that the RMS values for all three vector components increase towards the
burnt region of the combustion field.
Following the model of homogenous isotropic flows the turbulence intensities of all three vector components
should be almost equal independent of the position in the flow. Obviously the axial turbulence intensity stays
almost constant for both unburnt and burnt region (at about 0.9). On the contrary the radial degree of turbulence
decreases despite of the fact that the total fluctuations increase.
2.50
2.50
u-avg unburnt
u-avg burnt
u' unburnt
u' burnt
2.00
2.00
1.50
u' [m/s]
u-avg [m/s]
1.50
1.00
1.00
0.50
0.50
0.00
x
y
z
0.00
total
Figure 12: Conditioned absolute
velocities at 15kg/h and φ=0.6
x
y
z
Figure 13: Conditioned averaged
fluctuation velocities at 15kg/h and φ=0.6
This shows that the assumption of homogenous isotropic turbulence is only partly fulfilled even in the unburnt
part of the flame. The burnt part shows a modified distribution in space of turbulence energy.
longitudinal
5.00
4.00
transverse
4.00
3.00
2.00
2.00
1.00
0.00
0.00
burnt
Figure 14: Axial-Correlation
lengths at 9 kg/h and φ=0,7
transverse
3.00
1.00
unburnt
longitudinal
length [mm]
5.00
length [mm]
length [mm]
In the following the results of integral length scale calculations are discussed. Here, it is interesting to show the
influence of the mass flow rate, while holding the fuel air ratio constant. Figures 14, 15 and 16 show exemplarily
the results for the axial velocity component.
5.00
longitudinal
4.00
transverse
3.00
2.00
1.00
0.00
unburnt
burnt
Figure 15: Axial-Correlation
lengths at 12 kg/h and φ=0,7
unburnt
burnt
Figure 16: Axial-Correlation
lengths at 15 kg/h and φ=0,7
It can be seen that the longitudinal correlation length is larger than the transversal correlation length in all cases,
being consistent to theory (Rotta 1972). With increasing total mass flow rate the integral length scales for all
correlations of the three directions in space become longer.
The influence of the combustion reaction itself on turbulence is mirrored well by the conditioned investigation of
the integral length scales. The experiments have shown that due to the strong increase of temperature within the
flame front the eddy spectrum is notably influenced. As a result of the gasdynamic expansion the integral length
scales downstream the flame brush are larger compared to regions in the flow where unburnt gas is located.
Obviously the eddies represented by the integral length scales are stretched when passing through the flame in
the case of relatively low turbulence intensities of the studied flames.
But not only the largest length scales become stretched. Even the smaller scales which are accessible by the
aforementioned procedures feature a certain dilation (Figure 17, 18 and 19).
Also the eddies representing middle length scales in the spectrum of turbulence, known as Taylor length, seem
to be lengthened with increasing total mass flow rate. The transition from the unburnt to the burnt part of the
3.00
Kolmogorov length
3.00
Kolmogorov length
2.50
Taylor length via eq.7
2.50
Taylor length via eq.7
2.50
Taylor length via eq.7
2.00
Taylor length via eq.8
2.00
Taylor length via eq.8
2.00
Taylor length via eq.8
1.50
1.00
0.50
0.00
1.50
1.00
0.50
unburnt
burnt
Figure 17: Taylor and
Kolmogorov length in ydirection at 9 kg/h and φ=0,7
0.00
length [mm]
Kolmogorov length
length [mm]
length [mm]
3.00
1.50
1.00
0.50
unburnt
burnt
Figure 18: Taylor and
Kolmogorov length in ydirection at 12 kg/h and φ=0,7
0.00
unburnt
burnt
Figure 19: Taylor and
Kolmogorov length in ydirection at 15 kg/h and φ=0,7
flame leads to longer Taylor eddies as well. In addition it seems that Equation 7 and 8 yield almost the same
results for the unburnt zone. Using Equation 8 for the burnt gases yields physically no sensible length scales,
since here Equation 8 gives Taylor length scales to be even longer than the integral ones. Here, the turbulent
Reynolds number reaches too low values, decreasing due to strong temperature influence on viscosity. As a
result Equation 8 should be used only for Taylor length scale estimation for sufficintly high turbulent Reynolds
numbers, which is fulfilled in the unburnt part of the investigated flames.
For the Kolmogorov scale no trend could be observed with increasing mass flow whereas the combustion exerts
an influence on this smallest scale. Obviously the Kolmogorov scale is significantly shifted to larger values
while passing the reaction zone.
7 CONCLUSIONS
It has been observed that the conditioned approach to turbulence characterisation exposes interesting influences
of the interaction of flame and turbulence.
With increasing mean velocity, resulting from the jump in temperature within the flame and thus from the
decrease in density, also the turbulent fluctuations increase in the burnt part of the flame. This holds for all three
components of the velocity. For the presented flames with comparatively low turbulence intensity this points
towards a counter gradient behaviour of turbulent transport.
The investigation of the behaviour of the 6 accessible integral length scales has revealed that these eddies
become larger downstream the reaction zone in the burnt region (Fig. 14-16).
The same holds for the Taylor length scale determined from the curvature of the spatial correlation function
(Eq.5) of the main flow direction (Fig. 17-19). Using the correlation equation (Eq. 9) in the burnt region of the
flame yields no reasonable results. Thus Equation xx should only be used in the unburnt regions of the flame.
8 ACKNOWLEDGEMENT
The authors gratefully acknowledge the support of this work in the framework of the Bavarian Research
Cooperation FORTVER.
9 REFERENCES
Bradley, D. (1992). "How fast can we burn." Proceedings of the Combustion Institute 24: 247-262.
Bray, K. N. C., Libby, P.A., et al. (1985). "Unified modeling approach for premixed turbulent combustion-part I:
General formulation." Combustion and Flame 61: 87-102.
Dinkelacker, F. (1993). Entwicklung und Anwendung multidimensionaler Laserlichtschnitt-Techniken zur
simultanen Geschwindigkeits-, Konzentrations- und Temperaturfeldmessung in hochturbulenten
Vormischflammen. Physikalisch-Chemisches Institut, Universität Heidelberg.
Johnson, M. R., Kostiuk, L.W., et al. (1998). "A ring stabilizer for lean premixed turbulent flames:." Combustion
and Flame 114: 594-596.
Kampmann, S., Leipertz, A., et al. (1993). "Two-dimensional temperature measurements in a technical
combustor with laser Rayleigh scattering." Applied Optics 32(30): 6167-6172.
Namer, J., Schefer, R.W. (1985). "Error estimates for Rayleigh scattering density and temperature measurements
in premixed flames." Experiments in Fluids 3: 1-9.
Raffel, M., Willert, C., et al. (1998). Particle Image Velocimetry. Berlin, Springer.
Rotta, J. C. (1972). Turbulente Strömungen, Eine Einführung in die Theorie und ihre Anwendungen. Stuttgart,
B. G. Teubner.
Tennekes, H., Lumley, L.J. (1972). A first course in turbulence. Cambridge, Mass., MIT Press.
Veynante, D., Trouvé, A., et al. (1997). "Gradient and counter-gradient scalar transport in turbulent premixed
flames." Journal Fluid Mechanics 332: 263-293.
Download