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

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

wide variations in cooling-air quantity can occur between seemingly identi-

cal liners, owing to slight differences in wigglestrip material thickness. Even

small variations in metal thickness, within normal manufacturing tolerances,

can have a marked effect on coolant airow rate. Nevertheless, by careful

control of weld quality, and by ow-testing to check dimensional accuracy,

lm-cooling devices of the wigglestrip type have been used successfully on

a large number of American and British aero engines at pressure ratios up to

18–1. Rolls Royce engines featuring wigglestrip cooling include the Avon,

Spey, cannular Olympus, and Pegasus.

8.8.2 Stacked ring

Another cooling device that uses total pressure feed is the “stacked ring,” as

shown in Figure 8.2b. Although it provides a less rigid form of liner construc-

tion than wigglestrips because the air-admission holes are drilled or punched,

their dimensional accuracy is higher, resulting in smaller variations in cooling

airow rate. The total ow area of these holes is calculated to meter the required

amount of cooling air. The aft end of the previous liner panel provides a plenum

in which turbulence is dissipated and the individual jets coalesce to form a sin-

gle annular sheet of air. At its downstream end, the gap width is dimensioned

to give the required cooling-air velocity. Thus, a useful asset of this arrangement

is that the cooling-air velocity can be xed at the optimum value for maximum

cooling effectiveness, regardless of the actual pressure drop across the liner.

Cool air

Hot gas

View A-A

View B-B

Cool air

Hot gas

(a)

(b)

(c)

(d)

Total-pressure air feed

Static-pressure air feed

Figure 8.2

Film-cooling devices: (a) wigglestrip, (b) stacked ring, (c) splash-cooling ring, (d) machined

ring.

Heat Transfer 331

8.8.3 Splash-Cooling ring

This device uses only the static pressure drop across the liner wall as the

driving force for the injection of lm-cooling air (see Figure 8.2c). The cool-

ing air is bled from the annulus through a row of small holes in the wall

and is directed along the inside surface of the liner by means of an internal

deector “skirt” or “lip” that is attached to the wall by riveting or welding.

The function of the skirt is again to provide space in which the separate

air jets can merge to form a continuous sheet at the slot exit. A typical skirt

length is about four times the slot depth, which is usually of the order of

1.5–3.0 mm.

8.8.4 Machined ring

One concern with the stacked ring is the quality of the braze joint where the

rings are connected [1]. Conduction of heat through this joint is essential to

liner-wall cooling, and voids in the braze ller material can lead to local hot

spots. This problem does not arise in the “machined ring” liner, which is

machined either from a single piece of metal or from several rings welded

together. Rows of holes are then drilled to allow annulus air to enter the

cooling slot by either total-head feed, static pressure differential, or a combi-

nation of both, as illustrated in Figure 8.2d.

The machined ring offers advantages in terms of more accurate control of

cooling-air quantity and a marked improvement in the mechanical strength

of the liner, which is particularly important for large annular combustors.

Machined rings have acquired many millions of hours of operational ser-

vice on the Rolls Royce RB211 engine, and are specied for the RR Trent

combustor, where they will be used in conjunction with augmented external

convection and selective angled effusion cooling (AEC).

8.8.5 rolled ring

A drawback to both stacked and machined ring liners is that steep tempera-

ture gradients exist between the slot lip and the metal adjacent to the cooling

air feed holes. The lip inevitably has a high temperature because the cooling

air from the previous slot has lost its effectiveness, entrained hot gas, and is

now heating the liner wall instead of cooling it. On the other hand, the metal

near the cooling holes is immersed in air at combustor inlet temperature.

The resulting thermal gradients produce high stresses that can lead to liner

distortion and cracking [1].

The General Electric rolled-ring liner, shown in Figure 8.3a, is fabricated

from a series of rings that are rolled into shape and welded together. In this

design, the static-pressure fed air jets provide impingement cooling to the

rolled ring before emerging from the slot as an effective cooling lm. Similar

design principles are employed in the Pratt and Whitney “double-pass” ring

shown in Figure 8.3b.

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

8.8.6 Z ring

As discussed above, the function of the skirt or lip is to allow the individual

cooling air jets to coalesce and form a continuous lm. Clearly, any reduction

in the initial diameter of these jets would allow a corresponding reduction

in the length of lip required. The extreme case of zero lip length is the Z-ring

slot, as illustrated in Figure 8.3c. This design was made possible by the

increased availability of EDM and laser drilling (or trepanning) techniques.

Using a large number of closely pitched, small-diameter holes ensures that

the jets coalesce quickly to form a uniform lm without needing the protec-

tion of a skirt.

In addition to its superior cooling performance in comparison to more

conventional cooling slots, the Z-ring design has another obvious advan-

tage in that it eliminates the life limitation due to skirt cracking. It also

lends itself to manufacture using ring rolling techniques, which give

good material utilization and produce contoured shells that need little

machining.

One drawback to the Z ring is the high cost of drilling a large number of

small holes. Improved manufacturing methods should alleviate this prob-

lem. There is also a need to control the land width between adjacent holes

and other critical dimensions to ensure satisfactory mechanical integrity

without loss of cooling performance.

Liners featuring Z-ring cooling have been tted to a number of Rolls Royce

military engines.

(a) (b)

(c)

Figure 8.3

Film-cooling devices: (a) GE rolled ring, (b) P&W double-pass ring, (c) RR Ζ ring.

Heat Transfer 333

8.9 Correlation of Film-Cooling Data

Almost all the theoretical and experimental studies of lm cooling carried

out so far have been aimed at nding parameters to describe the tempera-

ture of an adiabatic wall at any point downstream of the coolant injection.

The results of these investigations will now be examined, and later, it will be

shown how the data may be applied to a liner that is nonadiabatic due to the

heat uxes produced by ame radiation and external cooling.

When a wall is lm cooled by injecting a stream of air between the sur-

face and the hot mainstream ow, three separate ow regions may be iden-

tied, as illustrated in Figure 8.4. According to Stollery and El-Ehwany [9],

the rst ow region comprises a potential core, in which the wall temper-

ature remains close to the coolant-air temperature. This is followed by a

zone where the velocity prole is similar to that of a wall jet. Further down-

stream, the ow conditions approximate those in a turbulent boundary layer.

The relative lengths of the three regions are governed mainly by the veloc-

ity ratio U

. For U

< U

, the second zone is nonexistent, and a turbu-

lent boundary-layer model is appropriate for all regions downstream of the

potential core.

Hot gas

Cooling air

Jet boundary layer

, U

, m

, ρ

, A

1.0

0 x

Figure 8.4

Schematic of lm-cooling process. (Reprinted from Stollery, J.L. and El-Ehwany, A.A.M.,

International Journal of Heat and Mass Transfer, 8(1), 55–65, 1965. With permission from

Elsevier.)

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

8.9.1 Theories Based on Turbulent Boundary-Layer Model

Stollery and El-Ehwany [9] used a turbulent boundary-layer model to derive

the following expression for lm-cooling effectiveness.

η=

−

309

(8.30)

where η, the lm-cooling effectiveness, is

η=

−

gw.ad

(8.31)

and

= Re ,

025

(8.32)

where

s is the depth of the lm-cooling slot, x is the distance downstream of

the slot, m is (ρU)

/(ρU)

, and Re

is the slot Reynolds number = U

s/µ

When Stollery and El-Ehwany compared their theoretical formula with the

experimental data of other workers, they found that a better correlation

could be obtained by increasing the value of the constant from 3.09 to 3.68

and slightly modifying the correlation group to give

























−

368

.Re.

(8.33)

A drawback to this equation and to all others based on the Blasius

skin-friction relationship is that they relate to an idealized turbulent

boundary layer far downstream of the slot. Thus, they cannot satisfacto-

rily describe the ow situation near to the slot, which is of prime inter-

est for the gas turbine. This suggests that a better model for this region

would be one that employed skin-friction coefcients obtained by direct

measurement in this zone. From a study of skin-friction data, Ballal and

Lefebvre [10] derived the following expression for effectiveness in the

near-slot region:

























−

015

.Re.

(8.34)

Heat Transfer 335

This equation was found to predict, to ±5% accuracy, all the available experi-

mental data within the following ranges of conditions:

Parameter Range

m 0.5–1.3

/ρ

0.8–2.5

s 0.19–0.64 cm

x/s 0–150

8.9.2 Theories Based on Wall-Jet Model

If the velocity of the cooling air is signicantly higher than that of the main

stream, the ow emerging from the slot behaves more like a jet than a

boundary layer. This jet model applies, of course, only in regions close to

the slot. Further downstream, the ow conditions revert to the boundary-

layer type.

The wall-jet model of Ballal and Lefebvre [10] leads to the following expres-

sions for effectiveness, for 1.3 < m < 4.0:

For x/ms < 8:

η=1. .0

For 8 < x/ms < 11:

η= +













−

06 005

.. .

(8.35)

For x/ms > 11:

























−

015

.Re.

(8.36)

Values of effectiveness based on these expressions agree quite closely with

published experimental data [10].

Equations 8.35 and 8.36 may be applied to the near-slot regions of all two-

dimensional “clean” slots, provided that the thickness of the slot lip is small

in relation to the slot height. However, for mechanical integrity, the lip is

sometimes made quite thick; in that case, a wake region is created behind

it, which tends to shorten the length of the potential core and extend the

transition zone.

From an analysis of available experimental data concerning the inuence

of slot-lip thickness, t, on effectiveness, Ballal and Lefebvre [11] derived an

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

empirical “correction factor” that, when applied to Equations 8.34 and 8.36,

gives, for 0.5<m <1.3,

































−

110

065

015





−02.

(8.37)

and for 1.3<m <4.0,





































−−

128

015

02 0

(8.38)

It should be noted that Equation 8.38 is recommended for all values of x/ms

because the additional accuracy given in Equation 8.35 for thin-lipped sys-

tems is lost when t/s exceeds 0.2, owing to the inuence of lip thickness on

effectiveness in this very-near-slot region [12]. Thus, the use of two separate

equations for the wall-jet model is unnecessary in thick-lip situations.

A comparison of Equations 8.37 and 8.38 shows that, apart from a

small difference in the value of the constant, the only signicant differ-

ence is in regard to the inuence of m. According to Equation 8.37, an

increase in m should improve effectiveness, whereas Equation 8.38

implies that effectiveness is independent of the value of m. This apparent

anomaly arises because of the contrasting effects produced by a change

in m, which depend on whether the initial value of m is greater or less

than unity. When m<1, an increase in m improves lm-cooling effective-

ness in two ways: (1) through a relative increase in the amount of coolant

air, and (2) through a reduction in the rate of mixing between the cool-

ant and mainstream gases as m approaches unity. However, when m >1,

any further increase has two opposing inuences on cooling effectiveness.

The relative increase in coolant ow is again benecial, but this effect is

countered by a more rapid rate of mixing between the coolant and main-

stream ows as m departs further from unity. This causes an increase in

the thickness of the boundary layer, which consequently embraces a larger

amount of mainstream gas. The net result is that effectiveness is sensibly

independent of m.

In many early designs of gas turbine combustion chambers, unfortunately

the cooling slots are not clean, but contain obstructions of various kinds. These

reduce effectiveness by generating turbulence and enhancing mixing rates.

The effectiveness of such practical lm-cooling slots has been investigated

in detail by Sturgess [13]. His equation for the prediction of effectiveness may

be written in a slightly simplied form for machined-ring devices as

η= −10 012

065

.. ,

(8.39)

Heat Transfer 337

and for stacked-ring devices as

η= −10 0094

065

.. ,

(8.40)

with

−













−

eff

Re ,

015

where x

is the potential core length, A

is the slot outlet area, and A

eff

is the

slot overall effective area.

These equations were found by Sturgess to correlate measured values of

effectiveness from a number of machined-ring and stacked-ring geometries

to an accuracy of within 10%.

To summarize, for “dirty” cooling slots of the type still used in many gas tur-

bine combustors, it is recommended that Equations 8.39 or 8.40, due to Sturgess,

be used to predict effectiveness. For thick-lipped systems in which the slot

geometry is sensibly “clean,” it is suggested that Equations 8.37 and 8.38 be

used for m<1.3 and m>1.3, respectively, over the range of x/s from 0 to 50.

8.9.3 Calculation of Film-Cooled Wall Temperature

In the calculation of lm-cooled wall temperatures, the previously derived

expressions for R

, R

, and C

remain the same, but the internal-convection

component, C

, is altered because the coolant ow changes both the velocity

and temperature of the hot gas near the wall. Dealing with velocity rst, we

have [11] for 0.5<m <1.3,













0069

.Re,

(8.41)

leading to

0069

=−.Re( ),

w.ad w

(8.42)

where

Re .

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

For m>1.3,













010

044

.Re,

(8.43)

leading to

036

010













−

.Re().

w.ad w

(8.44)

The gas temperature, T

w,ad

, at the wall is obtained from the denition of η,

given in Equation 8.31 as:

η=

−

gw.ad

where η is the effectiveness value calculated from Equations 8.37 or 8.38 for

clean slots, and Equations 8.39 or 8.40 for dirty slots.

example

For the combustor of the previous example, let us calculate the liner-wall tempera-

ture at a distance x downstream of the slot, where x/s = 18.

We ﬁrst calculate the slot parameters. From the liner geometry, we know that

s===18 04 0 00145..m,

Sm==×

−

π 59510

Thus

x =× =18 0 00145 0 0261..m,



mUA

saas

kg/s.==ρ 0 289.

Hence

kg msU =⋅485 7./().

For air at 880 Κ and a pressure of 3040 kPa,

kg/ ms=× ⋅

−

38910

.(),

W/(m K).=⋅0 0553.

Heat Transfer 339

Therefore,

Re .,

==×

18110

Re ..

==×

32610

To determine the mainstream parameters, we have,

m= 0 0137

K,= 2280

kg ms=× ⋅

(

)

−

70510

./,

= 005.,



mUA

gggL

kg/s,==ρ 262.

WmK=⋅

(

)

0 157./.

Hence,

kg/(m sU == ⋅

262

0 137

191

To calculate the ﬁlm-cooling effectiveness, we note that

== =

485 7

191

254

Since m>1.3, it is appropriate to use Equation 8.38:

























−

128128

389

015

7705

18 04 0 789

015

(.)..













×=

−

Now

η=

−

g w,ad

w.ad

2280

2280 880

Hence, T

w,ad

= 1176 K.