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

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

From a designer’s viewpoint, an ideal diffuser is one that achieves the

required velocity reduction in the shortest possible length, with minimum

loss in total pressure, and with uniform and stable ow conditions at its out-

let. Sufcient experimental data are now available to design such a diffuser,

provided that the inlet velocity prole is symmetrical and not too peaked.

Unfortunately, on many engines, the compressor outlet velocity prole is

both peaked and asymmetric and is also subject to appreciable variation

with changes in engine operating conditions. Under these circumstances,

stable ow conditions cannot always be achieved, with the result that some

engines are plagued by various deciencies, such as a lack of consistency in

the temperature distribution at the combustor exit and an increase in exhaust

gas pollutants.

There is no lack of reliable experimental data on the performance of con-

ventional conical diffusers. Available data on two-dimensional and annular

diffusers are less comprehensive, and nearly all these data are summarized

in a few important papers. Unfortunately, the performance charts pre-

sented in these papers are for boundary-layer-type inlet ows, developed in

approach sections, which differ appreciably from the compressor-generated

ows encountered in combustor diffusers. Moreover, in comparison with

conventional diffusers, there are a number of additional geometric param-

eters that strongly affect the performance of combustor diffusers, such as the

size and shape of the liner and its position relative to the diffuser exit. This

complex interaction between the liner and diffuser explains why there are

no general performance charts for combustor diffusers comparable to those

for conventional diffusers.

At the present time, there is no completely general and accurate method

for predicting combustor-diffuser performance. However, much useful

progress has been achieved with numerical modeling techniques, which

can now successfully predict the gross features of ow elds in combustor

diffusers.

Friction loss

Stall loss

To tal loss

Divergence angle

Pressure loss

Figure 3.1

Inuence of divergence angle on pressure loss.

Diffusers 81

3.2 Diffuser Geometry

The geometry of straight-walled diffusers may be dened in terms of three

geometric parameters, as shown in Figure 3.2. Area ratio, AR, is an obvi-

ous choice as a major parameter because it is directly related to the primary

function of the diffuser in achieving a prescribed reduction in velocity. Some

form of nondimensional length is a logical selection for another because, as

pointed out by Sovran and Klomp [1], in combination with the area ratio,

such a length denes the overall pressure gradient; the principal factor in

boundary-layer development. Usually, either the wall length, L, or the axial

length, N, is used as a characteristic length; it is expressed in nondimen-

sional form by dividing by a representative inlet dimension.

A third parameter is the divergence angle, 2θ, which is not an independent

variable, but is related to the other parameters by

=+12

sinθ,

(3.1)

for two-dimensional units, and

=+ +













sinsin ,θθ

(3.2)

for conical units.

Sovran and Klomp [1] recommend the use of L/ΔR

as the characteristic

dimension for annular diffusers, where L is the average wall length, and ΔR

is the annulus height at the diffuser inlet. This gives an expression for area

ratio that is similar to the expression for conical units when the inlet radius

ratio approaches zero, and similar to the expression for two-dimensional

units when it approaches unity. Thus, the performance characteristics of all

three types of diffuser may be plotted on a single set of coordinate axes as,

for example, in Figure 3.3.

(a) (b)

Figure 3.2

Diffuser geometries: (a) two-dimensional; (b) conical.

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

3.3 Flow Regimes

The rst systematic study of ow patterns in diffusers was carried out by

Kline et al. [2]. Tests were conducted on two-dimensional diffusers with

straight walls, and the inlet ow conditions, the wall length, and the throat

width were held constant. They observed that as the divergence angle is

progressively increased from zero, a number of different ow regimes are

found, which can be described as follows:

1. No “appreciable” stall, with the main ow well behaved and appar-

ently unseparated.

2. Transitory stall, whereby eddies are formed that run along the dif-

fuser, some in close proximity to the wall. These eddies assist the

diffusion process by transporting lethargic air away from the bound-

ary layer and replacing it with more energetic air from the main core

of the ow. This is a region of pulsating ow.

3. Fully developed stall, where the major portion of the diffuser is lled

with a large triangular-shaped recirculation region, extending from

the diffuser exit to a position close to the diffuser throat.

4. Jet ow, in which the main ow is separated from both walls. The

separation begins slightly downstream from the throat, and the ow

does not reattach until well downstream from the diffuser. Jet ow

occurs only at high angles of divergence.

Conical

Straight-core annular

2-D

Equiangular annular

0.8

AR – 1

246810

N/R

or N/∆R

or N/W

20 40 60 80

Figure 3.3

Li nes of rs t st al l. (Fr om Howard, J.Η.G., Thornton-Trump, A.B., and Henseler, H.J., “Perform ance

and Flow Regimes for Annular Diffusers,” ASME Paper 67-WA/FE-21, 1967. With permission.)

Diffusers 83

Howard et al. [3] used wool-tuft techniques to examine the nature of stall in

annular diffusers. The lines of occurrence of rst appreciable stall are shown

in Figure 3.3, where they are compared with data obtained on conical diffus-

ers by McDonald and Fox [4] and on two-dimensional diffusers by Reneau

et al. [5]. The superior performance of conical diffusers is explained on the

grounds that ow separation is delayed due to the absence of corners [5]. It is

also clear from Figure 3.3 that stall may exist in annular diffusers under less

severe geometric conditions than in conical diffusers.

3.4 Performance Criteria

The function of a diffuser is to reduce velocity and to convert kinetic energy

or dynamic pressure into a rise in static pressure, as shown schematically

in Figure 3.4. To assess the efciency of conversion, it is necessary to dene

the quantity of available dynamic pressure. This is usually based on a mean

velocity, u, which is obtained directly from the continuity equation as

um=



(3.3)

The dynamic pressure is then obtained as

qu=ρ

(3.4)

The pressure loss in the diffuser is dened as

∆PPP

diff

=−

(3.5)

∆P

diff

Figure 3.4

Energy conversion in a diffuser.

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

where ΔP

diff

includes both the internal energy loss and the effects of redistri-

bution of velocity between inlet and outlet.

For one-dimensional incompressible ow we have

Continuity:



mAuAu==ρρ

11 22

(3.6)

hence

AA uu AR

21 12

==.

(3.7)

Bernoulli:

pqpq P

11 22

+=++∆

diff

(3.8)

From Equations 3.7 and 3.8, the rise in static pressure is given by

ppqARP

211

11−= −

[]

−∆

diff

(3.9)

Several useful parameters for expressing diffuser performance can be

derived from this equation.

3.4.1 Pressure-recovery Coefficient

The pressure-recovery coefcient C

is calculated as

Cppq

=−

(

)

211

(3.10)

3.4.2 ideal Pressure-recovery Coefficient

In an ideal diffuser, there are no losses and Equation 3.9 becomes

pp qAR

21 1

11−

(

)

=−

[]

ideal

(3.11)

A nondimensional coefcient of ideal static pressure rise, C

pideal

, is derived

directly from this equation as

Cppq AR

ideal

=−

(

)

=−

[]

21 1

11 .

(3.12)

Diffusers 85

This equation shows that C

pideal

is dependent solely on area ratio to which it

is related by a law of diminishing returns.

3.4.3 Overall effectiveness

This is the ratio η of the actual pressure rise to the maximum theoretically

obtainable, i.e.,

η=CC

measured ideal

(3.13)

η= −

(

)

=−

[]

ppqAR

211

11 .

(3.14)

Thus, η is related to C

by the equation

η= −

[]

CAR

(3.15)

Typically η varies between 0.5 and 0.9, depending on the geometry and ow

conditions [6].

3.4.4 Loss Coefficient

This is usually dened as

λ= −

(

)

PPq

121

(3.16)

where the overbar denotes a mass-ow weighted value derived from a

detailed traverse across the duct.

The value of λ depends largely on the type of diffuser employed. Typical

values of λ for combustor diffusers range from around 0.15 for “aerodynami-

cally clean” faired diffusers to around 0.45 for dump diffusers of high liner/

depth ratio (D

) containing a normal complement of support struts and

fuel injectors. For vortex-controlled diffusers (VCD), reported values of λ

range from 0.05 to 0.15.

Some researchers also measure local values of temperature and static pres-

sure and so are able to calculate local values of density, which are then used to

obtain accurate mass ow distributions across the duct. This procedure is not

normally justied except when the static pressure variations in a cross section

are large, for example, just downstream of the compressor outlet guide vanes.

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

3.4.5 Kinetic-energy Coefficient

With nonuniform ows, the kinetic energy ux is greater than it would be

for the same ow rate under uniform ow conditions. To take account of this,

a velocity prole energy coefcient α is dened as

∫

uudA



(3.17)

The value of α varies from 1.0 for completely uniform ow, up to around

2.0 for ow on the point of separation. For fully developed turbulent ow, its

value is about 1.05.

The kinetic-energy coefcient may be incorporated into Equation 3.8 to

give

pqpqP

111222

+=++αα∆

diff

(3.18)

The relevant performance parameters then become

ideal

=−













(3.19)

−

(3.20)

αα

−

(

)

qAR

11 2

(3.21)

λ= −CC

ideal

(3.22)

3.5 Performance

Although considerable progress has been made, no method exists for accu-

rately predicting the quantitative performance of a diffuser with arbitrary

shape and ow. In practice, this means that the designer usually resorts to

model tests carried out on each particular conguration. However, it is pos-

sible to predict with reasonable accuracy the performance of an important

Diffusers 87

range of diffusers that Cocanower et al. [7] have described as “Class A” and

that have the following characteristics:

1. The ow is subsonic, but not necessarily incompressible

2. The inlet Reynolds number is greater than 2.5 × 10

, so that problems

of transition from laminar to turbulent ow are avoided

3. The inlet velocity prole is symmetrical

4. Flow within the diffuser is essentially unstalled

5. The diffuser itself is symmetrical and nonturning

6. The diffuser is either of two-dimensional, conical, or annular geometry

3.5.1 Conical Diffusers

A performance chart for conical diffusers is provided by Figure 3.5, in which

the pressure-recovery coefcient is plotted as a function of area ratio, AR,

and nondimensional length, Ν/R

. It was constructed by Sovran and Klomp

[1] from the experimental data of Cockrell and Markland [8] for one particu-

lar value of boundary-layer thickness.

Figure 3.5 includes two lines that are useful for design purposes. One

(line

) is the locus of points that dene the diffuser area ratio producing

maximum pressure recovery in a prescribed nondimensional length. The

other (line

) is the locus of points that dene the nondimensional length

producing maximum pressure recovery at a prescribed area ratio. Although

the divergence angle varies along the

line, it is very nearly equal to 6° all

along the

line.

N/R

0.4

5.0

2.0

AR – 1

1.0

0.5

2510 20

0.6

0.8

–

= 0.2

Figure 3.5

Performance chart for conical diffusers at 2% inlet blockage. (From Sovran, G. and Klomp, E.D.,

Fluid Mechanics of Internal Flow, Elsevier, Amsterdam, 270–319, 1967. With permission.)

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

3.5.2 Two-Dimensional Diffusers

Perhaps the best known study on two-dimensional diffusers of the type

illustrated in Figure 3.6 is that of Reneau et al. [5], who carried out a series of

tests on two-dimensional diffusers with divergence angles 2θ ranging from

5° to 30°, corresponding to variations in Ν/W

from 1.5 to 25. Figure 3.7 shows

contour plots of overall effectiveness as a function of area ratio and nondi-

mensional length for an inlet blockage of 1.5%. Similar plots, constructed for

other inlet conditions, reveal that effectiveness is diminished by an increase

in inlet boundary-layer thickness.

Sovran and Klomp [1] examined all the data obtained by Reneau et al.

and made the interesting observation that the location of the

line is con-

stant and independent of inlet blockage. This fortuitous result means that

although pressure recovery is affected by inlet boundary-layer thickness, for

a wide range of area ratios the optimum geometry can be chosen without

regard for inlet boundary-layer conditions.

Two-dimensional diffusers have been widely used in combustor develop-

ment because they offer three useful advantages:

1. Flow visualization is easy to apply and helps to identify and avoid

regions of ow separation

2. Geometrical changes are relatively simple, which facilitates experi-

mental studies on the inuence of geometric parameters on ow pat-

terns and performance

3. Airow requirements are appreciably less than for a fully annular

system

However, as pointed out by Klein [9], measured values of losses and pressure

recoveries obtained from two-dimensional or sectoral models are inaccurate

for two main reasons:

Figure 3.6

Two-dimensional diffuser.

Diffusers 89

1. The boundary layers growing along the side walls and the second-

ary ows created by them have considerable inuence on the main

ow. Little and Manners [10] have shown that these effects cannot

be ignored either in two-dimensional models, even for aspect ratios

higher than 10, or in 90° sectors.

2. In two-dimensional models, the radial velocity prole diffuses only

in the direction of the ow, whereas in a fully annular model it also

diffuses in the circumferential direction. This creates additional

mixing and, therefore, higher pressure losses.

3.5.3 Annular Diffusers

Diffusers of the annular type are widely used in aircraft engine combustors.

Their characteristics have been studied by Sovran and Klomp [1], Howard

et al. [3], Klein [9], Kunz [11], Adkins et al. [12,13], Takehira et al. [14], and

Stevens and Williams [15].

Extrapolated data

Diffuser

effectiveness

0.4

0.6

0.7

0.8

0.85

0.875

0.9

1.1

1.2

1.4

1.6

1.8

2.0

3.0

4.0

5.0

6.0

Area raito, W

Nondimensional length, L/W

6810 20

0.90

0.85

Figure 3.7

Two-dimensional-diffuser data at 1.5% inlet blockage. (From Reneau, L.R., Johnston, J.P., and

Kline, S.J., Journal of Basic Engineering 95, 141–50, 1967. With permission from ASME.)