Modelling of Combustion & Heat Transfer Effects in A Rankine Cycle

Modelling of Interactions between Source of Power & Steam Power ……

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Fuel Model

Analysis of Fuel

• Proximate Analysis & Ultimate Analysis.• Proximate analysis - to determine the moisture, ash,

volatiles matter and fixed carbon• Ultimate or elementary analysis - to determine the

elemental composition of the coal• The Energy content -- CFRI Formulae --• Low Moisture Coal(M < 2% ) -- CV (Kcal/kg) = 71.7 FC + 75.6

(VM-0.1 A) - 60 M• High Moisture Coal(M > 2%) -- CV(kcal.kg) = 85.6 {100 -

(1.1A+M)} - 60 M

• Where, M, A, FC and VM denote moister, ash , fixed carbon and Volatile mater (all in percent), respectively.

Fuel Model

• Ultimate Analysis of fuel: Gravimetric : • Percentage of carbon : x --- Number of k moles, X = x/12• Percentage of combustible hydrogen : y --- Number of

atomic kmoles

Percentage of sulfur: z – Number of atomic kmoles, Z = z/32Equivalent chemical formula : CXHYSZOK

Equivalent Molecular weight : 100 kgs.Also called as Representative Chemical Formula (RCF).A mathematical model for useful part of 100kg of fuel.

19M

yY

Percentage of available oxygen for combustion : k --- Number of atomic kmoles, K = k/16

169

8Mk

K

Fuel Model

• Ultimate Analysis of fuel: Gravimetric : • Percentage of carbon : x --- Number of k moles, X = x/12• Percentage of combustible hydrogen : y --- Number of

atomic kmoles

Percentage of sulfur: z – Number of atomic kmoles, Z = z/32Equivalent chemical formula : CXHYSZOK

Equivalent Molecular weight : 100 kgs.Also called as Representative Chemical Formula (RCF).A mathematical model for useful part of 100kg of fuel.

19M

yY

Percentage of available oxygen for combustion : k --- Number of atomic kmoles, K = k/16

169

8Mk

K

Model Testing for Determination of important species

Air Flow Rate

Fuel Flow Rate

Water Flow Rate

Flue gas Analysis

Selection of Excess air

Optimization of Furnace Parameters.

Average value of CO at different O2 %

y = 226.73x4 - 1900.5x3 + 5809.9x2 - 7698.6x + 3757.9

R2 = 0.9665

0

100

200

300

400

500

0 1 2 3 4

O2 % in Flue gas

CO

( in

pp

m)

U/C % at Different O2 % (in Flue Gas)

y = 3.0149x5 - 28.108x4 + 97.822x3 - 153.3x2 + 98.668x - 13.094

R2 = 0.9953

0123456789

10

0 1 2 3 4

% O2 in FG

U/C

(in

%)

Results of Model Testing.

• For a given fuel and required steam conditions.• Optimum air flow rate.• Optimum fuel flow rate.• Optimum steam flow rate.• Optimum combustion configuration!!!

Realization of MATt Theory

• Mixing: Fuel preparation systems.

• Air: Draught systems.

• T : Preheating of fuel.

• t : Dimensions of combustion chamber. : Turbulence generation systems.

Stoichiometry of Actual Combustion

• CXHYSZOK + 4.773 (X+Y/4+Z-K/2) AIR → P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO

• Conservation species:

• Conservation of Carbon: X = P+V• Conservation of Hydrogen: Y = 2 Q• Conservation of Oxygen : K + 2 (X+Y/2+Z-K/2) =

2P +Q +2R +2U+V• Conservation of Nitrogen: 2 3.76 (X+Y/2+Z-K/2) = T• Conservation of Sulfur: Z = R

Stoichiometric Analysis of Furnace at Site

• CXHYSZOK + 4.76 (X+Y/2+Z-K/2) AIR + Moisture in Air + Ash Moisture in fuel→ P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash

• Mass of air: *4.76* (X+Y/2+Z-K/2) *28.89 kg.• Mass of Coal: 100 kg.• Excess Air: -1)4.76* (X+Y/2+Z-K/2) *28.89 kg.

Fuel of Mass

Air of Mass RatioFuelAir

Composition of Gas in A Furnace

• For every 100 kg of Coal (A Representative Molecular Weight).

• CXHYSZOK + 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash Moisture in fuel → P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash

• Dry Exhaust gases: P CO2 +R SO2 + T N2 + U O2 + V CO kmols.

• Volume of gases is directly proportional to number of moles.

• Volume fraction = mole fraction.

• Volume fraction of CO2 : x1 = P * 100 /(P +R + T + U + V)

• Volume fraction of CO : x2= VCO * 100 /(P +R + T + U + V)

• Volume fraction of SO2 : x3= R * 100 /(P +R + T + U + V)

• Volume fraction of O2 : x4= U * 100 /(P +R + T + U + V)

• Volume fraction of N2 : x5= T * 100 /(P +R + T + U + V)

• These are dry gas volume fractions.

• Emission measurement devices indicate only Dry gas volume fractions.

• Measurements:• Volume flow rate of air.• Volume flow rate of exhaust.• Dry exhaust gas analysis.

• x1 +x2 +x3 + x4 + x5 = 100 or 1

• Ultimate analysis of coal.• Combustible solid refuse.

nCXHYSZOK +n 4.76 (X+Y/4+Z-K/2) AIR +

Moisture in Air + Ash & Moisture in fuel

→

x1 CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2 CO + x7 C + Ash

nCXHYSZOK +n 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → x1 CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2

CO + x7 C + Ash

•x1, x2,x3, x4 &x5 : These are dry volume fractions or percentages.

•Conservation species:

•Conservation of Carbon: nX = x1+x2+x7

•Conservation of Hydrogen: nY = 2 x6

•Conservation of Oxygen : nK + 2 n (X+Y/4+Z-K/2) = 2x1 +x2 +2x3 +2x4+x6

•Conservation of Nitrogen: n 3.76 (X+Y/4+Z-K/2) = x5

•Conservation of Sulfur: nZ = x3

nCXHYSZOK +n 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → x1 CO2 +x6 H2O +x3

SO2 + x5 N2 + x4 O2 + x2 CO + x7 C + Ash

• Re arranging the terms (Divide throughout by n):

CXHYSZOK + 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → (x1 /n)CO2 +(x6/n) H2O +

(x3/n) SO2 + (x5/n) N2 + (x4/n) O2 + (x2/n) CO + (x7/n) C + Ash

CXHYSZOK + 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash Moisture in fuel

→ P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash

Specific Flue Gas Analysis

• For each kilogram of fuel:• Air : 4.76 (X+Y/2+Z-K/2) * 29.9 /100kg.

• CO2 : P * 44/100 kg.

• CO : V * 28/100 kg.• Oxygen in exhaust : 32 * U/100 kg.• Unburned carbon: 12*12/100 kg.

Excess

air

%

Moles of NiAFT (K) VCPi

(KJ/Kg K)CO2 H20 O2 N2

0 3.279 1.165 0 13.79 2220 1.4137

103.279 1.165

0.366 15.174 2085 1.3919

203.279 1.165

0.7323 16.55 1966 1.3723

303.279 1.165

1.098 17.93 1864 1.3553

403.279 1.165

1.465 19.3 1776 1.3398

503.279 1.165

1.83 20.68 1696 1.3242

First Law Analysis of Furnace at Site

• CXHYSZOK + 4.76 (X+Y/2+Z-K/2) AIR + Moisture in Air + Ash Moisture in fuel→ P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash

Qlosses + n air hair + n fuel hfuel = n fluegas hfluegas + W

• Unburned carbon losses.• Incomplete combustion losses.• Loss due to ash.

• Radiation and Convection Losses from Furnace Surface

Capacity of Flue Gas

Total Thermal Power available with flue gas:

chimneyflamegaspgas TTcm ,

Rate of steam production:

steam

chimneyflamegaspgassteam h

TTcmm

,

s

1

2

3

4

5

6

2f

2s

4523 hhmhhm mreheatsteafmainsteam

Paths of Steam and Gas

Water walls

Drum

Economizer

Sequence of Energy Exchange from Flue Gas to Steam

FLUE GAS

PLATEN SH

PENDENT SH

COVECTIVE SH

ECONOMIZER

RHEVAPORATOR

Fuel Power

Furnace absorption

Platen SH

Final SHLTSH

Reheater

Economizer APH

Combustion Losses C & R losses Hot Exhaust Gaslosses

Sequence of Energy Exchange from Flue Gas to Steam

FLUE GAS

PLATEN SH

PENDENT SH

COVECTIVE SH

ECONOMIZER

RHEVAPORATOR

FEGT

1225

1200

1175

1150

1125

1100

0C

FEGT of An Healthy Furnace

It is very essential to know the mass flow rates of Fuel, Air and various flue gases for further Design and Analysis!

Heat available for Radiation

• Incomplete combustion loss

• Unburned Carbon loss

• Loss due to slag

• Energy brought in by preheated air & fuel.

44wafleffflaislagCCOcfu TTAQQQQLHVmQ

COQ

slagQ

CQ

aiQ

Simplified Approach

• Emitted Radiation heat flux of flames:24 / mkwTJ flflfl

flabs Jq

kWTAQ flflabs 4

444flflwafleffradabs TAkWTTAQQ

• Emitted Radiation = Available Heat

Heat flux absorbed by walls :

Thermal efficiency factor, .

The rate of heat absorption

flame

fufl A

QJ