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On the development of methods and equipment for 2D-tomography in combustion
Evseev, Vadim; Fateev, Alexander; Sizikov, Valery; Clausen, Sønnik; Nielsen, Karsten Lindorff
Publication date:2011
Document VersionPublisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):Evseev, V. (Author), Fateev, A. (Author), Sizikov, V. (Author), Clausen, S. (Author), & Nielsen, K. L. (Author).(2011). On the development of methods and equipment for 2D-tomography in combustion. Sound/Visualproduction (digital)
Danish Physical SocietyAnnual Meeting21-22 June 2011
Hotel Nyborg StrandNyborg
On the developmentOn the development of methods and equipment for 2D tomographyfor 2D-tomography in combustion
Vadim Evseev Alexander Fateev Valery Sizikov*Vadim Evseev, Alexander Fateev, Valery Sizikov*,Sønnik Clausen, Karsten L. Nielsen
*National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia
Motivation
Studying combustion phenomena
It is important to know essential combustion parameters such as
gas temperaturespecies concentration
– resolved temporarily and spatially and simultaneously for every point
Objective of this workTomographic reconstruction of
– gas temperatures– species concentrations
• in flames and hot gas flows
2
Outline
Tomographic reconstruction methods for gas temperaturesdevelopmentresults
Equipment suitable for tomographic measurements of gas temperatures
developmentapplication
Species concentration calculationstheorymodeling
3
Problem Statement
Given is an axisymmetric stable flame produced by a small lab-scale burner*
The temperature profiles at a number of heights above the burner plate are known*
The task is to reconstruct the temperature profile at a chosen height above the burner
from several optical line-of-sight spectral emission/transmission measurements
SpectrometerSpectrometerBlackbody
*Hartung et al. Meas. Sci. Technol. 17 (2006) 2485–2493 4
Problem Statement: Details
Motivation to use optical techniquesThey are advantageous
over thermocouples due to– non-intrusiveness– high temporal resolutiong p
over laser-based techniques due to– low cost– wide spectral rangep g
Motivation to work in the IR spectral rangeThe major combustion species CO2 and H2O have strong fundamentalThe major combustion species CO2 and H2O have strong fundamental rotational-vibrational bands in the near IR range
Equipment used in the experimentq p pFourier Transform Infra-Red (FTIR) spectrometeroptical fiberopticspblackbody radiation source
5
Parallel Scanning
Gas temperatureTg(x,y) = ?
4.8
cm
Bl kb d I (T )
yg( ,y)
9 positions;step 0.6 cm
Blackbody IS(T0)FTIRSpectrometer
x
IR(x)
x
The spectral irradiance I(x,y) by a beam of monochromatic radiation varies according to*
Lambert’s Law Kirchhoff’s Law
dyTITkdyyxITkyxdI gPlanckgg )()(),()(),( +−=
The monochromatic radiative transfer
i
Lambert s Law Kirchhoff s Law
Tg = Tg(x,y) – gas temperaturek(Tg) = k(Tg(x,y)) – the absorption coefficient
equationwithout scattering
* Tourin et al. Applied Optics 4 (2) (1965) 237–242
IPlanck(Tg) – the Planck function at Tg
6
Parallel Scanning
The radiative transfer equation is a differential equationwith respect to I(x,y)The solution of it is a complex integral equation with respect to Tg(x,y)
+⎟⎠⎞⎜
⎝⎛−= ∫
)(
)(0
2
1
)( ),(exp)()( xy
xy gs
R dyyxTkTIxI
⎟⎠⎞⎜
⎝⎛−×
×⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎠⎞⎜
⎝⎛ ′′+
∫
∫ ∫)(
)(
)(
)( )(0
2
2
1 1
)(
)()()(
),(exp
),(exp)(
),(),(
xy
g
xy
xy
y
xy gs
gPlanckg
dyyxTk
dyydyxTkTI
yxTIyxTk
In this work it was solved by means of iterative approximations:
⎟⎠
⎜⎝ ∫ )(1
)( ),(pxy g yy
in the i th approximation an Abel’s integral equation is solved with respect to ki(Tgi(x,y))Tgi(x,y) is found by means of modeling using the spectroscopic databasesg
These values of ki and Tgi are used in the next approximation
7
Parallel Scanning
The reference profile is obtained from the Coherent Anti-Stokes Raman Scattering (CARS) measurements*
these are point measurementsThis work
line-of-sight measurements
*Hartung et al. Meas. Sci. Technol. 17 (2006) 2485–2493 8
Sweeping Scanning
Spectrometer
AdvantageM ti bl ith t t th l diti f i d t i l lMore practicable with respect to the real conditions of an industrial scale
– The idea is to use several synchronized spectrometers with the sweeping scanningTh ll f b il b d f– The walls of a boiler can be used as a reference source
EquationsTh i th ll l b t j t t d t l di tThe same as in the parallel case but just converted to polar coordinates
9
Equipment for Tomography
ObjectiveIt is essential for tomography to have simultaneous spectral measurements from several lines of sight
ApproachSeveral optical fibers + Grating spectrometer + IR Camera
IR Grating
Multichannel Spectrometer
IR Camera
Grating Spectrometer
IR FrameFrame Rate:up to 500 fps Slit
0.04 to 0.1 mm
IR Frameup to 500 fps
∅0 76 mm
1.2 mm1.2 mm
Fast simultaneous spectral measurements
∅0.76 mmThree fibres is not a limit!
10
Multichannel Spectrometer
The exhaust duct of a cylinder
Multichannel SpectrometerTTop = ?
TMiddle = ?
TBottom = ?
Cross-sectionA two-stroke test marine
Diesel engineThe system was successfully tested under real conditions
Diesel engine
The objective was to measure gas temperature simultaneously in the three optical ports
measurements were synchronized with the encoder of the main shaftMAN Diesel & Turbo
Copenhagen R&D Department 11
Multichannel SpectrometerTop
Middle
Gas temperature is not homogeneousIt is increasing from bottom to top
Bottom
Stroke period = 0.5376 s(1.9 Hz)
Temperature points per stroke = 64
(119 Hz)
(synchronized with the encoder
on the main shaft)t [°C]
Time [s] 12
Gaseous Species Concentrations
Calculations are based on Line-By-Line modeling of spectra*which uses spectroscopic databases HITRAN, HITEMP, CDSD
•Gas temperature [K] Tg
•Total pressure [atm] p
Measured Database parameters for the i th transition*•Spectral line transition frequency [cm-1] v0
•Air-broadened pressure shift [cm-1/atm] δp [ ] p
•Absorption path length [cm] L
•Mole fraction of the species [%] c
•Instrument Line Shape Function ILS(v,vc)
p [ / ] δ
•Air-broadened HWHM [cm-1/atm] γair
•Self-broadened HWHM [cm-1/atm] γself
•Coefficient of temperature dependence of γair and γself nInstrument Line Shape Function ILS(v,vc)
•Measured transmittance τm(v)
Coefficient of temperature dependence of γair and γself n
•Spectral line intensity [cm-1/(molecule cm-2)] S0
•Lower state energy of the transition [cm-1] E0Calculated*•Pressure-shift correction of line position [cm-1] v0* (p)•Temperature and pressure correction of line HWHM [cm-1] γ (p,Tg)•Lorentz profile [1/cm-1] f (v T p)
The idea is to compare measured and calculated transmittancesLorentz profile [1/cm ] f (v, Tg, p)
•Temperature correction of line intensity [cm-1/(molecule cm-2)] S (Tg)•Monochromatic absorption coefficient [1/(molecule cm-2)] ki (v, Tg, p)
The mole fraction can then be obtained from the best match between the transmittances
•Calculated transmittance τclc (v)between the transmittances
* Rothman et al. J. Quant. Spectrosc. Radiat. Transfer 60 (5) (1998) 665–710 13
Line-By-Line Modeling
CO2 TransmittanceMeasured in a special hot gas cell developed at Risø DTUVsCalculated using the HITEMP 2010 database
• Gas temperature 1000 K
• Total pressure 1 atmTotal pressure 1 atm
• Absorption path length 53.3 cm
• Mole fraction of CO2 10 %
I t t Li Sh F ti sinc• Instrument Line Shape Function sinc
14
Summary
Tomography methods• Gas temperatures
Axisymmetric case• Parallel scanning
– Successfully applied on a lab burnery pp• Sweeping scanning
– Considered theoretically
Tomography equipment• Multichannel spectrometer
Optical fibres + Grating spectrometer + IR CameraOptical fibres Grating spectrometer IR CameraSuccessfully applied on a test marine engine
– Simultaneous temperature measurements in the three optical ports of the exhaust ductp p
Concentration calculationsMeasurements in the special gas cell are compared p g pwith the line-by-line modeling results
– Excellent agreement in a wide spectral range15
Thank you for your attention!
Tomography in Engines
An existing technique
A group at the University of Manchester headed by Hugh McCann
have established the technique of high-speed Chemical Species q g p pTomography, using near-IR absorption spectroscopy
The concentration distribution of a target molecule can be imaged at rates up to 4,000 frames per second
www.manchester.ac.uk/research/H.mccann/research17
The Aim of the Work
Multichannel
The exhaust duct of a cylinder
(cross-section)
SpectrometerT1 = ?
T2 = ?
T3 = ?
To develop a system for simultaneous gas temperature measurements from several lines of sight
MAN Diesel & TurboCopenhagen
R&D Department
To apply the system on an exhaust duct of a large marine Diesel engine 18
The System with One Channel
Optical Fibre( Chalcogenide
IR CameraIR CameraGrating
SpectrometerGrating
Spectrometer
( Chalcogenide IR-Glass Fiber )
Source
IR SpectrumIR FrameFrame Rate:
up to 100,000 fps
512
pixe
ls5
Working spectral region:
640 pixels3.8–5 μm
(2000–2600 cm-1)Resolving power:
6 nm(4 cm-1) 19
The System with Three Channels
Optical Fibre
IR
Grating Spectro-
meterCamera
SlitSource
Slit0.04 to 0.1 mmIR FrameFrame Rate:
up to 500 fps
1.2 mm1.2 mm
Simultaneous spectral measurements
∅0.76 mm
Th i tp
Three is not a limit!
20
Design Details
A special mechanical adaptor for coupling the three fibers together
The fibers are glued to theinside of the small holes
21
IR Emission Spectrum]]
Working spectral range
A typical IR emission spectrum
A typical IR emission spectrum
(m2·s
r·m
)(m
2·s
r·m
)
COCOBlackbodyBlackbody
of a flue gasof a flue gas
nce
[
W/(
nce
[
W/( CO2CO2
CO2CO2ral R
ad
ian
ral R
ad
ian
H OH OH2OH2O
22
Sp
ect
rS
pect
r H2OH2O
COCO
CxHyCxHyH2OH2O
2.0 3.0 4.0 5.0
CxHyCxHy
Greybody (particles)Greybody (particles)
Wavelength [μm]Wavelength [μm]
22
Temperature Measurement Method
Gas sampleat T [K]λIλ0 λIλ(T)
Spectral absorptivity:is the portion of incident energy absorbedat wavelength λ
0
0 )()(
λ
λλλ
−=αI
TIIT 0
0 )()(
λ
λλλ
−=αI
TIIT
The sample also emits radiation:Gas sampleGas sample N (T)
Nλ(T) – spectral radiance [W/(m2·sr·m)]
pat T [K]
pat T [K] Nλ(T)
Kirchhoff’s law:This relation is a universal function of λ and Tand is independent of a particular sample)(
)()(
TNTTN b
λ=λ )(
)()(
TNTTN b
λ=λ TT
p p pThe Planck function on the right-hand side is given by:
)( 51
λ= λTC
b CTN )( 5
1
λ= λTC
b CTN TT
)()(T λαλ
)()(T λαλ T
R.H.Tourin, ”Spectroscopic Gas Temperature Measurement”, Elsevier Publishing Company (1966)
)1()(
25 −πλ λλ TCe )1()(
25 −πλ λλ TCe T
23
Validation
[°C][°C]The Reference Temperature Profile*
The Measured Value of the Average Temperature is 1705ºCg p
The Reference Value of the Average Temperature is 1647ºC
A flat flame burner with known axisymmetric temperature profile has been used for the validationused for the validation
The deviation is within 4 %
*Hartung et al. Meas. Sci. Technol. 17 (2006) 2485–249324
The Marine Diesel Engine
MAN Diesel & TurboCopenhagen
R&D Department25
The Measurement Diagram
Multichannel Spectrometer Top
Middle
Bottom
The exhaust duct of the cylinder(cross-section)
Bottom
λNλ(T)Gas
sampleat T [K]
Simultaneous emission measurements
( ) at T [K]
They give spectral radiances NλTop , NλMiddle , NλBottom
as functions of time for the top, middle and bottom ports
26
The Measurement Diagram
Multichannel Spectrometer Blackbody (Iλ0)Top
Middle
Bottom
The exhaust duct of the cylinder(cross-section)
Bottom
Nλ(T)
Gas sampleat T [K]
λIλ0λIλ(T)
Transmission measurements were performed for one port at a time
( ) λλ( ) at T [K]
They are necessary for the calculation of spectral absorptivities αλTop, αλMiddle and αλBottom
Th l i h h th t f ll th th tThe ananlysis has shown that αλ for all the three ports can be assumed to be 0.9
The temperatures for each port as functions of time can now be obtainedThe temperatures for each port as functions of time can now be obtained from the spectral radiances NλTop , NλMiddle , NλBottom and αλ=0.9 using Kirchhoff’s law and the Planck function.
27
Gas Temperature vs TimeTop
Middle
Temporal resolution 119 Hz (64 points per stroke) Bottom
A Stroke
t [°C]
Time [s] 28
Towards the tomography of hot gases
Temperature andTemperature and species concentration
distribution in a cross-section
nel
ter
tich
an
nct
rom
et
Mu
ltS
pec
29
Conclusions
The three-channel system has beenThe three channel system has beendevelopedvalidated applied on a large scaleapplied on a large scale
The results of the application on the marine Diesel engine:Temperatures as functions of time have been obtained for the three portsTemperatures as functions of time have been obtained for the three ports on the exhaust duct
The three fibers is not a limit
The system is flexible
The system can find many other applicationsThe system can find many other applications
30
Towards the tomography of hot gases
The 1st step is to validate the methods using the above mentioned lab burner with the known axisymmetric temperature profileThe two measurement diagrams are currently under investigation
[ ]l k
The radiative transfer equation:[ ]dyyxTIyxIyxkyxdI g
Planck )),((),(),(),( νννν −−=
The author of the diagrams on this slide: V. Sizikov, National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia31
Parallel Scanning
Scheme 1. Previous equation is written in the form of Abel's singular integral equation:
R
∫ ≤≤=−
R
xRxxqdrrk
xr
r ,0),()(222
)()()( ln −
⎩⎨⎧
−= RTIxI
xq
)(exp)())((
)(
)(
22022
0
⎪⎫⎟⎞
⎜⎛⎤
⎟⎞
⎜⎛ ′
+⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛′′
−′
′
−−
⎩⎨
∫∫
∫ ∫Rr
R
x
r
xs
gs
s
rr
rdrkxr
rTI
rTIrk
xr
rTI
which is solved by iterations with respect to k(r). In each iteration after finding k(r) one can find
,)(exp)(exp2222 ⎪⎭
⎪⎬⎫⎟⎟⎠
⎞⎜⎜⎝
⎛
−−⋅
⎥⎥⎦
⎤⎟⎟⎠
⎞⎜⎜⎝
⎛′′
−′−+ ∫∫
R
x
r
xdrrk
xr
rdrrdrk
xr
r
In each iteration, after finding k(r), one can find Tg(r) using the spectroscopic databases.Scheme 2 − of type Scheme 1, but for Tg >> T0and flame emission is stronger than absorption.
Scheme 3. Suppose that k(r) has been taken from a database. Then J(r) = Is(Tg(r))/Is(T0) can be found by solving a singular integral equation of Abel's type, and temperature profile will be equal
.1)(
1)exp()()( 0BB ln ⎟
⎠
⎞⎜⎝
⎛ +−= ννrJ
TkhckhcrTg
32
Parallel Scanning
The radiative transfer equation is a differential equationwith respect to I(x,y) for given k(Tg) = k(Tg(x,y)).
The more important is the following integral equationwith respect to k(Tg(x,y)) from measured IR(x)/Is(T0):
),(exp)( )(2)( +⎟⎞⎜
⎛−= ∫xy
gR dyyxTk
xI
),(exp)(
),(),(
),(exp)(
)(
)( )(0
)(02
1 1
1
)()(
)(
)(
⎞⎛
×⎭⎬⎫
⎩⎨⎧
⎟⎠
⎞⎜⎝
⎛ ′′+
+⎟⎠
⎜⎝
∫ ∫∫xy
xy
y
xyg
s
gPlanckg
xyg
s
dyydyxTkTI
yxTIyxTk
dyyxTkTI
.),(exp)(
)(
2
1
)( ⎟⎠
⎞⎜⎝
⎛−× ∫xy
xyg dyyxTk
There are two unknown functions k and Tg. So we consider axial symmetry: Tg = Tg(r), k = k(Tg(r)) and obtain Abel's singular integral equation.
d hMoreover, we consider three cases:
33
Parallel Scanning
Case 1. Previous equation is written in the form of Abel's singular integral equation:
R
∫ ≤≤=−
R
xRxxqdrrk
xr
r ,0),()(222
)()()( ln −
⎩⎨⎧
−= RTIxI
xq
)(exp)())((
)(
)(
22022
0
⎪⎫⎟⎞
⎜⎛⎤
⎟⎞
⎜⎛ ′
+⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛′′
−′
′
−−
⎩⎨
∫∫
∫ ∫Rr
R
x
r
xs
gs
s
rr
rdrkxr
rTI
rTIrk
xr
rTI
which is solved by iterations with respect to k(r). In each iteration after finding k(r) one can find
,)(exp)(exp2222 ⎪⎭
⎪⎬⎫⎟⎟⎠
⎞⎜⎜⎝
⎛
−−⋅
⎥⎥⎦
⎤⎟⎟⎠
⎞⎜⎜⎝
⎛′′
−′−+ ∫∫
R
x
r
xdrrk
xr
rdrrdrk
xr
r
In each iteration, after finding k(r), one can find Tg(r) using the spectroscopic databases.Case 2 the same as case 1, but for Tg >> T0which means that flame emission is stronger than absorption.Case 3. Suppose that k(r) has been taken from a database. Then J(r) = Is(Tg(r))/Is(T0) can be found by solving a singular integral equation of Abel's type and the temperature profile will then be equal toAbel s type, and the temperature profile will then be equal to
.1)(
1)exp()()( 0BB ln ⎟
⎠
⎞⎜⎝
⎛ +−= ννrJ
TkhckhcrTg
34