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

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

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113

Aerodynamics

4.1 Introduction

Aerodynamic processes play a vital role in the design and performance of

gas turbine combustion systems. When good aerodynamic design is allied

to a matching fuel-injection system, a trouble-free combustor requiring only

nominal development is virtually assured.

Many types of combustors, differing widely in size, concept, and method

of fuel injection, have been designed. However, close inspection reveals that

many aerodynamic features are common to all systems. In the diffuser and

annulus, the main objectives are to reduce the ow velocity and distribute

the air in prescribed amounts to all combustor zones, while maintaining

uniform ow conditions with no parasitic losses or ow recirculation of any

kind. Within the combustion liner itself, attention is focused on the attain-

ment of large-scale ow recirculation for ame stabilization, effective dilu-

tion of the combustion products, and efcient use of cooling air along the

liner walls.

Mixing processes are of paramount importance in the combustion and

dilution zones. In the primary zone, good mixing is essential for high burn-

ing rates and to minimize soot and nitric oxide formation, whereas the

attainment of a satisfactory temperature distribution (pattern factor) in the

exhaust gases is very dependent on the degree of mixing between air and

combustion products in the dilution zone. A primary objective of combustor

design is to achieve satisfactory mixing within the liner and a stable ow

pattern throughout the entire combustor, with no parasitic losses and with

minimal length and pressure loss.

Successful aerodynamic design demands knowledge of ow recircula-

tion, jet penetration and mixing, and discharge coefcients for all types of

air admission holes, including air swirlers. The purpose of this chapter is

to review existing knowledge in these areas and to develop relationships

among combustor size, pressure loss, and pattern factor, thus providing a

rational basis for good aerodynamic design.

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

4.2 Reference Quantities

A number of ow parameters have been dened to facilitate the analysis of

combustor ow characteristics and to allow comparison of the aerodynamic

performance of different combustor designs. These parameters include the

reference velocity, U

ref

, which is the mean velocity across the plane of maxi-

mum cross-sectional area of the casing in the absence of a liner; i.e.,

ref

Also,

ref

and

ref

(

)

05.

4.3 Pressure-Loss Parameters

Two dimensionless pressure-loss parameters are important in combustor

design. One is the ratio of the total pressure drop across the combustor to the

inlet total pressure (ΔP

3−4

), and the other is the ratio of the total pressure

drop across the combustor to the reference dynamic pressure (ΔP

3−4

ref

). The

two parameters are related by the equation

∆∆P

RmT

34 33

−−













refref



(4.1)

The left-hand side of Equation 4.1 is normally referred to as the overall

pressure loss and is usually quoted as a percentage. Values range from 4 to

8%. Normally, it does not include the hot loss, i.e., the fundamental loss in

pressure due to combustion.

The term ΔP

3−4

ref

is the so-called pressure-loss factor. It is of prime impor-

tance to the combustion engineer, since it denotes the ow resistance

introduced into the airstream between the compressor outlet and the tur-

bine inlet. Aerodynamically, it may be regarded as equivalent to a “drag

coefcient.” Unlike the overall pressure loss, which depends on operating

conditions, the pressure-loss factor is a xed property of the combustion

Aerodynamics 115

chamber. It represents the sum of two separate sources of pressure loss:

(1) pressure drop in the diffuser and (2) pressure drop across the liner. Thus,

∆∆∆P

34−

ref

diff

ref

(4.2)

It is important to keep ΔP

diff

to a minimum, since any pressure loss

incurred in the diffuser makes no contribution to combustion. In practice,

there is little the combustion engineer can do to minimize diffuser pres-

sure loss other than observe the recognized principles of diffuser design. It

is equally important to minimize the liner pressure-loss factor, although in

this case there is an important difference in that a high liner pressure drop

is benecial to the combustion and dilution processes. It gives high injection

air velocities, steep penetration angles, and a high level of turbulence, which

promotes good mixing and can result in a shorter liner.

The liner pressure-loss factor is determined essentially by the total effec-

tive hole area in the liner A

h.eff

. Thus,

∆P

= ,

(4.3)

∆P

RmT

heff3















(4.4)

Substituting the right side of Equation 4.4 into Equation 4.1 gives

∆P

ref

heff













(4.5)

Thus, the total effective area of the holes in the liner is governed by the cas-

ing reference area and the available pressure drop across it. Rearranging

Equation 4.5 gives

Pq Pq

heff

ref

refdiffref

−

(

)

−

∆∆

(4.6)

The effective ow area of the liner may be calculated from the expression

ACA

heff D.ih.i.

∑

(4.7)

where C

D.i

h.i

is the effective ow area of ith hole and n is the total number

of holes.

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

The quantity (R/2)



mT AP

ref

(

)

in Equation 4.1 is effectively a

measure of combustor reference velocity, since it can be rewritten as

URT

ref

. As



mT P

is xed by the compressor design, the only control

over



mT AP

ref

afforded to the combustion engineer is in the selection of

the maximum casing area, A

ref

. Thus, Equation 4.1 confronts the designer

with a serious dilemma. For low fuel consumption, the overall pressure loss

of the chamber (the left side of Equation 4.1) must be low. Typically, a one

percentage point increase in pressure loss can produce either a half percent

reduction in thrust or around a quarter of a percent increase in specic fuel

consumption. However, if the chamber is to be small and have adequate

mixing, both terms on the right side of the equation must be large. These

conicting requirements can be optimized only in the context of specic

engine applications; e.g., for a lift engine, a high overall pressure loss, and

hence a high fuel consumption, may be tolerated in return for a small engine

(low value of A

ref

). On a long-range cruise engine, low fuel consumption is of

paramount importance, and a large-diameter, low-pressure-loss combustor

would be advantageous.

Some typical values of “cold” pressure loss in practical chambers are given

in Table 4.1. The third column on the table shows that the annular chamber

has the lowest pressure-loss factor. This may seem to conict with the fact

that a high pressure-loss factor is necessary for good mixing. However, in

annular chambers, most of the losses arise across the liner air-inlet holes,

where they contribute to mixing, and there are fewer losses in the diffuser

and inlet ducting. The resultant advantage of the annular chamber shows

up clearly in the rightmost column. Although the overall pressure loss is the

same as that for a tubular chamber (second column), the term



mT AP

ref

is much larger, implying a lower value of A

ref

and hence a smaller chamber

for any given aerodynamic loading.

As indicated in Table 4.1, the value of the pressure-loss factor to be used in

determining the reference area can vary from around 20 for a straight-through

annular combustor to almost 40 for a tubular combustor. In practice, the

actual value of ΔP

3−4

ref

is governed by the various performance require-

ments that dictate the pressure drop across the liner, such as pattern factor

and pollutant emissions, and by the compressor outlet velocity and the type

of diffuser employed, e.g., dump, faired, or hybrid.

TABLe 4.1

Pressure Losses in Combustion Chambers

Type of Chamber

∆P

−

∆P

34−

ref

Tubular 0.07 37 0.0036

Tuboannular 0.06 28 0.0039

Annular 0.06 20 0.0046

Aerodynamics 117

The values of overall pressure loss listed in Table 4.1 represent the cold loss

only, i.e., the losses arising from turbulence and friction that can be measured

with reasonable accuracy from cold-ow tests. Under burning conditions,

these losses are augmented by the fundamental loss due to combustion. For

uniform mixtures owing at low Mach number through a constant-area

duct, this may be derived from momentum considerations as

∆P

hot

ref

=−

(4.8)

where ρ

and ρ

are the air densities at inlet and outlet air temperatures of

and T

, respectively. Hence,

∆P

hot

ref

≅−

(4.9)

Analyses of the factors governing ΔP

hot

ref

in practical chambers have

indicated relationships of the form

∆P

hot

ref

=−













(4.10)

Actual values of K

and K

, as determined experimentally, are contained in

Reference [1]. For chambers of moderate temperature rise, ΔP

hot

usually lies

between 0.5 and 1.0% of P

4.4 Relationship between Size and Pressure Loss

For straight-through combustors, the optimal cross-sectional area of the cas-

ing A

ref

is determined from considerations of overall pressure loss and com-

bustion loading, as discussed in Chapter 5. However, for most industrial

combustors and some aircraft combustors, the casing area needed to meet

combustion requirements is so low as to give an unacceptably high pressure

loss. Under these conditions, the overall pressure loss dictates the casing

size, and A

ref

is obtained from Equation 4.1 as

RmT

ref



















−−

34 34



∆∆



















−1

05.

(4.11)

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

At rst sight, it might appear advantageous to make the liner cross-sectional

area as large as possible, since this results in lower velocities and longer

residence times within the liner, both of which are highly benecial to igni-

tion, stability, and combustion efciency. Unfortunately, for any given casing

area, an increase in liner diameter can be obtained only at the expense of a

reduction in annulus area. This raises the annulus velocity and lowers the

annulus static pressure, thereby reducing the static pressure drop across the

liner holes. This is undesirable, since a high static pressure drop is needed

to ensure that the air jets entering the liner have adequate penetration and

sufcient turbulence intensity to promote rapid mixing with the combus-

tion products. These considerations suggest that a satisfactory criterion for

mixing performance would be the ratio of the static pressure drop across the

liner Δp

to the dynamic pressure of the ow in the combustion zone q

. If

the ratio of liner cross-sectional area to casing cross-sectional area is denoted

by k, then the optimal value of k, which gives the highest value of Δp

, can

be derived as [2]

Pq r

opt

ref

=−

−−

−













−

()



λ∆

(4.12)

Hence

AkA

Lopt ref

= .

(4.13)

Equations 4.11 through 4.13 are valid for all “straight-through” tubular,

tuboannular, and annular chambers.

4.5 Flow in the Annulus

Flow conditions in the annulus have a substantial effect on the airow pat-

tern within the liner and inuence the level and distribution of liner wall

temperatures. The mean velocity in the annulus is governed by the combus-

tor reference velocity and the ratio of liner area to casing area. In practice,

appreciable variations in annulus velocity occur because of changes in inlet

velocity prole and as air is drawn into the liner through rows of holes and

cooling slots.

Although a high annulus velocity augments the convective cooling of the

liner walls, low velocities are generally preferred because they provide the

following benets:

Minimum variation in annulus velocity and static pressure, ensur-•

ing that all the liner holes in the same row pass the same airow

Aerodynamics 119

Higher hole discharge coefcients•

Steeper angles of jet penetration•

Lower skin-friction loss•

Lower “sudden-expansion” losses downstream of liner holes and •

cooling slots

In most combustors, the critical areas are at the upstream end of the liner

and in the vicinity of the dilution holes. At the upstream end, the air issuing

from the diffuser sometimes has a thick boundary layer that prohibits the

use of static-pressure-fed cooling slots. Even with total-head cooling slots,

problems are caused by the ow separation that often occurs as a result of

the bend formed at the junction of the diffuser and annulus. As the ow

proceeds along the annulus, its velocity prole gradually improves as air is

drawn off through the various apertures in the liner; however, if the air is

allowed to ow without restriction into the space downstream of the dilu-

tion holes, ow disturbances can arise that cause air to recirculate upstream

within the annulus in an intermittent and random manner. Tuboannular

combustors are especially prone to this phenomenon, which, in severe cases,

causes some of the liner holes to receive air from different directions. This

produces an internal ow pattern that is not only distorted, but also varies in

an irregular manner with time.

One method of alleviating this problem is by tting a “backstop” just

downstream of the dilution holes. This is simply an annular plate that is

designed to t between the inner and outer combustor casings. It is pierced

with large, round holes to accommodate the liners, and provision is made

for some air to ow through the plate to cool the hot sections downstream.

Plates of this type can be very effective in combating large, random recircu-

lations in the annulus ow.

On annular liners, the backstop is often in the form of a continuous dam,

located immediately downstream of the dilution holes. Typically, the dam

blocks off about two-thirds of the annulus area. Another method of control-

ling the ow in the dilution-hole region is by tapering the liner walls outward

to prevent excessive diffusion in the annulus passage adjacent to these holes.

If the pitch of the dilution holes is greater than the annulus height, a vortex

can form in the ow entering the hole; this changes the penetration and mixing

characteristics of the dilution air jet. The strength of the vortex depends on the

ratio of the annulus area, as measured in the plane of the holes, to the hole area.

A high value for this ratio inhibits vortex formation, thus providing another

argument in support of designing liners with adequate pressure drop.

Vortex formation, which can occur on both tubular and annular liners,

may be eliminated or subdued by tting a longitudinal splitter plate across

each dilution hole. The plate, which may be attached to either the liner or the

outer casing, is especially effective when used in conjunction with a spec-

tacle plate, or dam, as illustrated in Figure 4.1.