Lefebvre A.H., Ballal D.R. Gas Turbine Combustion: Alternative Fuels and Emissions

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70 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

turbulence properties, and thickness. For more detailed information on

ashback, reference should be made to Plee and Mellor [57].

The CIVB ashback has been studied by Sattelmayer and coworkers [58,59].

This phenomenon is characterized by an upstream propagation of the ame

on the burner axis, with propagation speeds far beyond the turbulent ame

speed, against high axial velocity ow. Especially, burner systems without

central bluff body and purely swirl-stabilized ame stabilization are prone

to CIVB. This type of ashback was successfully correlated with a chemical

time scale describing local quenching of the ame.

2.14 Stoichiometry

Complete combustion of a hydrocarbon fuel requires sufcient air to convert

the fuel completely to carbon dioxide and water vapor. Since 23% by mass

(21% by volume) of oxygen in the air participates in combustion, the stoichio-

metric AFR can be calculated from the reaction equation. For example, one

mole of C

requires 11 moles of oxygen for complete combustion:

CH OCOHO.

7162 2

+= +11 78

Hence, by substituting the appropriate atomic weights (C = 12, H = 1, O = 16),

we obtain

100 352 308 144gggg.+=+

Thus, 1 g of fuel requires 3.52 g of oxygen or 3.52 × 100/23 = 15.3 g of air. This

shows that for C

, the stoichiometric AFR is 15.3. Sometimes, this quan-

tity is expressed in a reciprocal form, i.e., as the stoichiometric fuel/air ratio.

For C

, the stoichiometric fuel/air ratio is 1/15.3 = 0.06535. For kerosine

), the stoichiometric fuel/air ratio is 0.0676.

Stoichiometric mixtures, by denition, contain sufcient oxygen for com-

plete combustion; thus, operation at the stoichiometric AFR will release all

the latent heat of combustion of the fuel. If the fuel is burned at a numerically

larger AFR, the mixture is referred to as lean or weak. Combustion at an AFR

lower than the stoichiometric value implies a deciency of oxygen; hence,

combustion is incomplete, and partially burned fuel, principally in the form

of carbon monoxide and unburned hydrocarbons, will escape from the com-

bustion zone.

In comparing the combustion characteristics of different fuels, it is some-

times convenient to express the mixture strength in terms of an equivalence

ratio ϕ. The equivalence ratio is the actual fuel/air ratio divided by the stoi-

chiometric fuel/air ratio. Thus, for all fuels, ϕ = 1 denotes a stoichiometric

Combustion Fundamentals 71

mixture. Also, for all fuels, a value of ϕ < 1 indicates a lean mixture, whereas

a value of ϕ > 1 indicates a rich mixture.

2.15 Adiabatic Flame Temperature

Flame temperature is perhaps the most important property in combustion

because it has a controlling effect on the rate of chemical reaction. The term

“ame temperature” may imply a measured value or a calculated one. If the

latter, it is usually the adiabatic ame temperature. This is the temperature

that the ame would attain if the net energy liberated by the chemical reac-

tion that converts the fresh mixture into combustion products were fully

utilized in heating those products. In practice, heat is lost from the ame

by radiation and convection, so the adiabatic ame temperature is rarely

achieved. Nevertheless, it plays an important role in the determination of

combustion efciency and in heat-transfer calculations. In high-temperature

ames, say above 1800 K, dissociation of combustion products occurs to a

signicant extent and absorbs much heat. At low temperatures, combustion

of a stoichiometric or lean fuel–air mixture would be expected to give only

and H

O; however, at higher temperatures, these products are them-

selves unstable and partly revert to simpler molecular and atomic species

and radicals, principally CO, H

, O, H, and OH. The energy absorbed in dis-

sociation is considerable, and its effect is to substantially reduce the maxi-

mum ame temperature.

2.15.1 Factors influencing the Adiabatic Flame Temperature

The factors of prime importance to adiabatic ame temperature are fuel/air

ratio, initial temperature and pressure, and vitiation of the inlet air by prod-

ucts of combustion.

2.15.1.1 Fuel/Air Ratio

The variation of adiabatic temperature rise with change in fuel/air ratio is

illustrated in Figure 2.19. The departure from linearity as the ame tempera-

ture rises is due partly to the increase in specic heat of the combustion

products with an increase in temperature and, at the highest temperatures

(>1800 K), to the effects of dissociation.

2.15.1.2 Initial Air Temperature

An increase in initial air temperature will always increase the ame tem-

perature. However, the extent of this increase diminishes with an increase in

72 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

ame temperature. For near-stoichiometric mixtures, only about one half of

an increase in initial air temperature is translated into an increase in ame

temperature.

2.15.1.3 Pressure

For a constant inlet air temperature, an increase in pressure yields a higher

ame temperature. This effect can be explained by examining the form of

the CO

and H

O dissociation equations:

CO CO O

HO HO

These reactions are endothermic, i.e., they absorb heat. They also lead to

an increase in the number of moles (volume) of the combustion products. By

opposing this increase in volume, an increase in pressure results in less dis-

sociation and hence a higher ame temperature.

2.15.1.4 Inlet-Air Vitiation

Tests of combustion systems are sometimes carried out using vitiated air, i.e.,

high inlet-temperature requirements are met through precombustion, which

results in abnormally high CO

and H

O concentrations and lower O

con-

centrations. Their combined effect is to lower the maximum ame tempera-

ture. If the actual ame temperature is to be simulated, then oxygen must be

added to replace that lost in the precombustion process.

0.01

500

1000

1500

P = 100 kPa (1 atm)

P = 2000 kPa (20 atm)

, K

300

500

750

1000

Temperature rise, K

2000

0.02 0.03 0.04

Fuel/air ratio

0.05 0.06 0.07 0.08

Figure 2.19

Adiabatic temperature rise curves for kerosine (JP 5) fuel. Lower specic energy = 43.08 MJ/

kg (18,520 Btu/lb).

Combustion Fundamentals 73

Nomenclature

B mass-transfer number

C concentration

collision factor

specic heat at constant pressure

D drop diameter

Sauter mean diameter

mean diameter

mean surface diameter

mean volume diameter

quenching distance

E activation energy

min

minimum ignition energy

f fraction of total fuel in vapor form

k thermal conductivity

L integral (large) scale of turbulence



mass ow rate

m exponent of fuel concentration in Equation 2.40

n reaction order, or pressure exponent in Equation 2.40

P pressure

R universal gas constant

S burning velocity

laminar burning velocity

turbulent burning velocity

T temperature

ΔT temperature rise

ame temperature

ignition temperature

mixture temperature

t time

evaporation time

ignition delay time

U velocity

u′ RMS value of uctuating velocity

V volume

fuel concentration

oxygen concentration

α thermal diffusivity (k/c

ρ)

δ thickness of reaction zone

laminar ame thickness

74 Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition

λ evaporation constant

η Kolmogoroff scale of turbulence

combustion efciency, or fraction of fuel burned

υ kinematic viscosity

ρ density

ϕ equivalence ratio

Subscripts

A air

ad adiabatic value

F fuel

g gas

o initial value, or fresh mixture value

st stoichiometric value, or steady-state value

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Diffusers

3.1 Introduction

In axial-ow compressors, the stage pressure rise is very dependent on

the axial ow velocity. To achieve the design pressure ratio in the mini-

mum number of stages, a high axial velocity is essential; in many aircraft

engines, compressor outlet velocities may reach 170 m/s or higher. It is,

of course, impractical to attempt to burn fuels in air owing at such high

velocities. Quite apart from the formidable combustion problems involved,

the fundamental pressure loss would be excessive. For example, for an air

velocity of 170 m/s and a combustor temperature ratio of 2.5, the pressure

loss incurred in combustion would be approximately 25% of the pressure

rise achieved in the compressor. Thus, before combustion can proceed,

the air velocity must be greatly reduced, usually to about one-fth of the

compressor outlet velocity. This reduction in velocity is accomplished by

tting a diffuser between the compressor outlet and the upstream end of

the liner.

In its simplest form, a diffuser is merely a diverging passage in which

the ow is decelerated and the reduction in velocity head is converted

to a rise in static pressure. The efciency of this conversion process is of

considerable importance because any losses that occur are manifested as

a fall in total pressure across the diffuser. In long diffusers of low diver-

gence angle, the pressure loss is high due to skin friction along the walls,

as shown in Figure 3.1. Such diffusers are, in any case, impractical because

of their extreme length. On all aircraft engines, and also on many indus-

trial engines, length is crucial, and it is essential, therefore, that diffusion is

accomplished in the shortest possible distance. With an increase in diver-

gence angle, both diffuser length and friction losses are reduced, but stall

losses arising from boundary-layer separation become more signicant.

Clearly, for any given area ratio, there is an optimum angle of divergence

at which the pressure loss is a minimum. Usually this angle lies between

6° and 12°.