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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