Thermodynamics & Gas dynamics of Real Combustion in Turbo Combustor

P M V Subbarao

Professor

Mechanical Engineering Department

Tools for precise estimation of fuel-air ratio….

Thermochemistry of Combustion

Modeling of Ideal Combustion

Modeling of Actual Combustion

LHVm

hmhmm

Δh

Δhη

fuel

in0,airex0,fuelair

ideal0,

actual0,combustor

LHVmηhmhmm fuelcombustorin0,airex0,fuelair

LHVmηhmhm fuelcombustorin0,airex0,gas

LHVmηhmhm fuelcombustorin0,airiex,0,igas,

LHVmηTcmTcm fuelcombustorin0,airp,airiex,0,ip,igas,

Modeling of Combustion

• CXHYSZ + 4.76 (X+Y/4+Z) AIR + Moisture in Air + Moisture in fuel → P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO

• Exhaust gases: P CO2 +QH2O+R SO2 + T N2 + U O2 + V CO kmols.

• Excess air coefficient : .• Emission measurement devices indicate only Dry gas volume

fractions.• Volume fraction = mole fraction or ppm• 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 Standards

• 15% oxygen is recommended in exhaust.

• NOx upto 150 ppm.

• SO2 upto 150 ppm.

• CO upto 500 ppm.• HC upto 75 ppm.• Volume fractions of above are neglected for the

calculation of specific heat flue gas.

2222

2222222

ONOHCO

ONp,NOHp,OHCOp,COp,fluegas UMTMQMPM

cUMcTMcQMcPMc

kJ/kgK1000

T0.39

1000

T1.27

1000

T1.670.45c

32

COp, 2

kJ/kgK1000

T0.20

1000

T0.586

1000

T0.1071.79c

32

steamp,

kJ/kgK1000

T0.42

1000

T0.96

1000

T0.481.11c

32

Np, 2

kJ/kgK1000

T0.33

1000

T0.54

1000

T0.00010.88c

32

Op, 2

Specific Heat of flue gas :

LHVmηTcmTcm fuelcombustorin0,airp,airex0,p,fluegasgas-flue

•For a given mass flow rate of fuel and air, the temperature of the exhaust can be calculated using above formula.•If mass flow rates of fuel and air are known.

•Guess approximate value of specific heat of flue gas.•Calculate T0,ex.•Calculate cp,flue gase.•Re calculate T0,ex.

•Repeat till the value of T0,ex is converged.

Total Pressure Loss in Turbo Combustor

• The loss of pressure in combustor (p0,ex <p0,in) is a major problem.

• The total pressure loss is usually in the range of 2 – 8% of p0,in.

• The pressure loss leads to decrease in efficiency and power output.

• This in turn affects the size and weight of the engine. • There are several methods of quantifying the total pressure

loss in a combustor,Relative to the total inlet pressure :

in0,

ex0,in0,combustor0, p

ppΔp

Relative to the inlet Dynamic pressure :indyn,

ex0,in0,combustor0, p

ppΔp

Relative to a reference dynamic pressure:ref

ex0,in0,combustor0, p

ppΔp

Gas Dynamic Studies on Combustors

• Effect of heat generation on one dimensional ideal compressible flow.

• Effect of varying mass flow rate .• Effect of combined heat generation and friction.

Frictional Flow with Heat Transfer

Governing Equations

no body forces, viscous work negligible

Conservation of mass for steady flow: m

md

A

dA

V

dV

ρ

dρ

Conservation of momentum for frictional steady flow :

Conservation of energy for steady flow :

0

0

p

'''2

T

dT

TC

q

V

dVM1

T

dT

δγ

0V

dVM

p

dp

D

fdxM

22

h

2 γγ

0V

dVM1

T

dT

TC

q 2

p

'''

γδ

0R

dR

T

dT

ρ

dρ

p

dpIdeal Gas law :

Mach number equation : 0V

dV

M

dM

2T

dT

m

md

A

dA

V

dV

ρ

dρ

0R

dR

T

dT

ρ

dρ

p

dp

0V

dV

M

dM

2T

dT

m

md

A

dA

V

dV

R

dR

T

dT

p

dp

m

md

A

dA

M

dM

R

dR

2T

dT

p

dp

Simplification of Continuity Equation

0V

dVM

p

dp

D

fdxM

22

h

2 γγ

0V

dV

M

dM

2T

dT

0M

dM

2T

dTM

p

dp

D

fdxM

22

h

2

γ

γ

Simplification of Momentum Equation

T

dT

TC

q

M

dM

2T

dTM1

T

dT 0

p

'''2

δγ

0M

dM

2T

dTM

A

dA

M

dM

2T

dT

R

dR

m

md

D

fdxM

22

h

2

γ

γ

0M

dM

2T

dTM

p

dp

D

fdxM

22

h

2

γ

γ

m

md

A

dA

M

dM

R

dR

2T

dT

p

dp

Combined Momentum and Continuity Equation

Constant flow rate, Constant Area, Non-reacting, Steady Compressible Flow with Friction Factor and Heat Generation

0M1TCm

Lq

D

fM

M1

M2

11

Mdx

dM 2

0p

p''

h

22

2

22

γγ

γ

Constant flow rate, Constant Area, Non-reacting, Steady Compressible frictionless Flow with Heat Generation

0M1TCm

Lq

M1

M2

11

Mdx

dM 2

0p

p''

2

2

22

γ

γ

Supersonic RAM Jets

'''0p dqdTC

Variation of Stagnation Temperature