ht2009 88113

Absortivity correlation for CO2 at

elevated pressures by employing tree

regression analysis and logistic dose

functions

Realized by:

Yesenia León

Freddy Malpica

Andrés Tremante

1. Introduction

2. Problem Scope

3. Previous work

4. Methodology

5. Results

6. Conclusions

7. References

Index

Introduction

Thermal Efficiencyincrease

Inlet TemperatureIncrease

Materials And Cooling

OpticalProperties

Turbines

Current applications are

above 1700K, as a

result radiative transfer

phenomena is

important

Temperaturesdistributions

productionenergyndissipatioViscous

sourceEnergyq

tcoefficienpansionexThermal

donde

qqTkDx

DpT

Dt

DTCp

d

dr

'''

'''

:

Transparents

Combustion Products CO2, H2O, CO, N2 y O2

Radiative

term focus

Introduction

Problem Scope

•This study develops an absortivity correlation for CO2 at low

resolution spectra, available from literature (D. K. Edwards

1960), for high pressure by employing a tree regression

analysis and logistic dose function approach.

•For a rank of temperature from 294K to 1390K, for pressure 1

atm to 10 atm, and for infrared spectra between 2.35 μm and

12.7 μm .

Fundaments

Gases shows great

variation in the

optical properties

with wave length

and with

Pressure, Temperat

ure and molar

composition.

These variations

are linked to

spectroscopic

transitionsLine intensity by 15 μm band for CO2 at 1390K and 1 atm (HITRAN)

Optical Properties

Fundaments

Optical Properties

This study is focused on carbon dioxide (CO2), a

triatomic, lineal and symmetric molecule, which have 4

degrees of freedom.

Normal vibracional frequencies for carbon dioxide (CO2) are

as follows:

Vibracional Mode [cm-1] [μm]

ν1 1351 7.4

ν2 667 14.9

ν3 2396 4.2

Absorption strong bands

667

2396

Methodology

1. Multivariable analysis

Banda

100

350

600

850

1100

1350

02468

10

0

100

200

300

400

500

0.02.55.07.510.012.515.0

10035060085011001350

Temp

w

0 500010000150002000025000

0 2 4 6 8 10

P

x

0.0 0.2 0.4 0.6 0.8 1.0

0.02.55.07.510.012.515.0

0 100200300400500

0

5000

10000

15000

20000

25000

0.0

0.2

0.4

0.6

0.8

1.0

A

Methodology

2. Regression tree Variable

Evaluation

Methodology

3. Branch CorrelationVariable

Evaluation

Hierarchy

Tree

F X Y Z( )

Methodology

Tree structured Branch correlation vs.

Hottel emissivitiesVariable

Evaluation

Hierarchy

Tree

4

,

T

AIl

llb

1

2

1

2,

2

0

25

0

1

5

0

10,

TC

TCb

e

C

e

CTI

k

CC

CC

02

2

01

Methodology

4. Single correlation generation by logistic

functionsVariable

Evaluation

Hierarchy

Tree

Branch

Correlation

A1 A2

F1

A3

F2 F7

F8

nm

c

D

x

x

fff

f

fffxfy

1

)( 121

121

Results

1. Branch Correlation

Branch Correlation

• Total absorption by branch

• Emissivity by branch

3

1 2 4 5

6 7 8 9

10 11 12 13Single

Correlation

• Total absorption

• Total emissivity

• 15μm band adjustment

Results and Discussion

Total absorption branch 4 @ 1atm

Branch Correlation



Single Correlation




200 350 500 650 800 950 1.1 103

1.25 103

1.4 103

10

100

1 103

Single correlation Branch 4 Band=2.7 P=1atm

Edwards Data Band=2.7 P=1atm

Single correlation Branch 4 Band=4.3 P=1atm


Edwards correlation Band=2.7 P=1atm

Edwards correlation Band=4.3 P=1atm

HITRAN Band=2.7 P=1atm

HITRAN Band=4.3 P=1atm

T [K]

A [

cm-1

]


Branch Correlation



Single Correlation




0 300 600 900 1.2 103

1.5 103

1.8 103

2.1 103

2.4 103

2.7 103

3 103

1.4131 105

0.0478

0.0955

0.1433

0.191

0.2388

0.2865

0.3343

0.382

0.4298

0.4775

Hottel Emiss ivity PL=1atm.ft




Edwards Emissivity PL=4.23atm.ft

Branch 4 Correlation Emissivity PL=4.23atm.ft(bands 2.7 y 4.3)

Edwards Emissivity Band 2.7 PL=4.23atm.ft

Edwards Emissivity Band 4.3 PL=4.23atm.ft

Edwards Emissivity Band 15 PL=4.23atm.ft

Branch 12 Correlation Emissivity PL=4.23atm.ft(band 15)

T [K]

Em

issi

vit

y


Branch Correlation



Single Correlation




2. Single Correlation – Total absorption

@1atm

200 350 500 650 800 950 1.1 103

1.25 103

1.4 103

10

100

1 103

Single correlation Band=15 P=1atm

Edwards Data Band=15 P=1atm

Single correlation Band=4.3 P=1atm


Single correlation Band=2.7 P=1atm


HITRAN Band=15

HITRAN Band=4.3

HITRAN Band=2.7

T [K]

A [

cm-1

]


Branch Correlation



Single Correlation




2. Single Correlation – Total absorption @5atm

vs Band

0 2 4 6 8 10 12 14 161

10

100

1 103

Single Correlation T=294K

Edwards's data T=294K





B [micron]

A [

cm

-1]


Branch Correlation



Single Correlation




0 300 600 900 1.2 103

1.5 103

1.8 103

2.1 103

2.4 103

2.7 103

3 103

1.4131 105

0.0381

0.0761

0.1142

0.1522

0.1903

0.2283

0.2664

0.3045

0.3425

0.3806

Hottel Emissivity PL=1atm.ft





Single Correlation Emissivity PL=4.23atm.ft

2.7 Band Edwards Emissivity PL=4.23atm.ft


15 Band Edwards Emissivity PL=4.23atm.ft

HITRAN Emissivity

T [K]

Em

issi

vit

y


Branch Correlation



Single Correlation




3. Single Correlation – 15 μm band adjustment

wBAcf

FFFF

D

,155

1181112

002.052.05.0152.12,15 BwBwBAc

F8 F11

F12


Branch Correlation



Single Correlation




0 300 600 900 1.2 103

1.5 103

1.8 103

2.1 103

2.4 103

2.7 103

3 103

1.4131 105

0.023

0.0459

0.0689

0.0919

0.1148

0.1378

0.1607

0.1837

0.2067

0.2296






Single Correlation Emissivity Adjusted by Band=15 PL=4.23atm.ft



15 Band Edwards Emissivity PL=4.23atm.ft

HITRAN Emissivity

T [K]

Em

issi

vit

y

Conclusions

A single correlation for total absorption of the band for CO2

has been generated from low resolution spectral data by

means of tree structures regression analysis and logistic

dose functions.

The single correlation has shown a standard deviation with

correlation generated by Edwards and his experimental data

of error of 4.43*10-1 for pressures from 5 atm to 9.9 atm.

An additional term was added to the single correlation in

order to adjust 15 μm band overestimation of the emissivity ,

reducing the deviation to 3%.

Recommendations

The adjusted single correlation is recommended for thermal

radiation estimation in gas turbines and thermal applications

until 10 atm for CO2.

This methodology can be extended to obtain total

absorption of the band for other gases of engineering

interest.

Generation of high resolution spectral data for high

pressures and temperatures in order to improve adjustment

of the correlation.

Thanks!!!

ht2009 88113

Documents

lnea y

lorentz es

finalmente es

lnea es incierta

lnea es una funcin

carbon dioxide co2

absorcin y

punto relevante es que