FILM COOLING OPTIMIZATION FOR MINIMUM COOLING AIRFLOW IN AIRCRAFT GAS-TURBINES

FILM COOLING OPTIMIZATION FOR MINIMUM COOLING AIRFLOW IN AIRCRAFT GAS-TURBINES G . J. STURGESS University of Technology, Loughborough, England.

Nomenclature Symbols not immediately defined in the text Capitals A^ff A^ ^Re,s R

^s,max

— — — — — — —

slot effective area flametube flow area normal to x-axis coolant Reynolds number based on slot height gas constant wall temperature adiabatic wall temperature maximum permitted wall temperature

Lower Case Cp ^0 rrig mi ρ s t t^ t^x t^ u X Xp y

— — — — — — — — — — — — — — —

specific heat Newton's constant coolant mass flow rate total mass entrained in film mass entrainment rate per unit length parallel to x-axis static pressure slot height time coolant temperature coolent temperature at injection hot mainstream temperature velocity parallel to x-axis distance from slot outlet, or, front of flametube potential core length distance normal to x-axis 347

348

G. J. S T U R G E S S

Greek ΔΡ ρ μ

— delta-P, pressure drop across slot — rho, density — mu, viscosity

Subscripts c m

— denotes coolant stream — denotes hot mainstream Introduction

The relevant heat transfer processes in combustion chamber primary zones have been analysed in some detail by Lefebvre and Herbert^ who showed that flametube temperatures increase with: (a) increase in pressure, (b) increase in inlet temperature, (c) decrease in airflow rate, (d) increase in flametube size. Current trends in both aircraft and engine design are leading to increased inlet temperatures and pressures through higher flight speeds and higher compression ratios, thereby intensifying the problem of coohng the flametube wall to an acceptable limit. The acceptable limit is set by the need to provide a flametube able to withstand the combined effects of oxidation and high buckling load. In general, the temperatures encountered exceed the capabilities of current and likely future materials, hence the interest in cooling techniques. Of recent years heat transfer research in gas-turbines has primarily been directed to the cooling of turbine discs, blades and stators, and the flametube has been neglected. Now, the advent of the supersonic airliner and the so-called '^advanced technology" high efficiency, high pressure ratio engine has forced the combustion engineer to meet an urgent problem and as Lefebvre has pointed out^^^ . . the sum total of knowledge on heat transfer processes in combustion chambers is lamentably shght and is quite inadequate . . for design purposes. Use of existing techniques of flametube cooling in these present and future situations leads to the consumption of inordinately large amounts of cooling air with consequent detrimental effects on chamber outlet temperature distributions through reduction in the amount of air available for mixing in the dilution zone. The prime technique currently available is air cooling, of which film-coohng is the particular form commonly used. It consists of introducing on the surface to be protected, through discrete "spanwise" slots, a thin film of air which acts as a coolant and shield between the hot gas-stream and the wall.

FILM-COOLING OPTIMIZATION

349

To meet the urgent requirement of keeping coohng airflow to a minimum, considerable research is being carried out into more eflicient methods of design­ ing film-cooling systems. The present paper outhnes a calculation procedure for finding the number and position of film-cooling injection slots over the surface of a flametube and hence the required coolant flow to maintain temperatures at or below a stipulated design maximum. A one-parameter optimization on this method is then carried out for minimum cooling airflow. Analysis The temperature of the cooled wall at any point can be found by a heat balance in steady-state, neglecting wall conduction: (^rad)m + (^conv)m — (^rad)ann + (^conv)ann

(0

where ^ is a heat flux and subscripts: rad m = to wall by radiation from hot gases at bulk conditions m, conv m = to wall by convection from w-state, rad ann = from waU by radiation to outer casing, conv ann = from wall by convection to annulus flow. It is permissible to neglect heat flow by conduction along the wall since wall axial temperature gradients are generally small, the wall is thin, and its thermal conductivity is low. In equation (1) the heat flow through the chamber outer casing has been neglected because this is also small in comparison with the other heat flows. The convective flux to the wall can be expressed, (^conv)m =

^effi^rn "

Ό

(2)

where a^ff is the effective local heat transfer coefficient to the wall with film cooling present. Thus, if a maximum permitted wall temperature is specified, and equation (2) substituted into equation (1) the latter can then be solved for a^ff, the remaining heat fluxes being evaluated by Lefebvre and Herbert's method^ for wall tem­ perature, which is now known because is taken as r^,max» the specified value. Hence values of film convective heat transfer coefficient over the surface of the flametube wall to keep the wall temperature just at its maximum permitted value can be found. The equation resulting from the substitution of (2) into (1) strictly cannot be solved over the whole flametube length since it involves two unknowns, the required a^ff and the unknown air temperature in the annulus. This can be overcome by either assuming the bulk air temperature in the annulus remains constant at the compressor delivery value, or assuming some temperature

350

G. J. S T U R G E S S

distribution based on experience. Note that the heat transfer coefficient a^ff so obtained is a net coefficient for the film. Available now are the required, maximum allowable, internal convective heat transfer coefficients for the ñametube if it is not to exceed the permitted temperature limit. The film-cooling system must be so designed that the heat transfer coefficients for the film are always equal to or less than these maximum allowable values. How this can be done is determined by the film characteristics produced by an individual slot. When the wall is non-conducting in the direction of the flow and its rear-face is insulated, i.e. the wall can be considered as adiabatic, the effects of injection are completely described by the ratio between the excess of mainstream over wall temperature to the excess of mainstream over injected air temperature.^ This ratio, the dimensionless abiabatic wall temperature distribution, is termed the film effectiveness ε, and most film-cooling data are presented in terms of this parameter, e.g. refs. 3-6. Thus, t — Τ ε = "7 ^

(no coolant

flow)

(3)

Note that for incompressible flow, (the present case), recovery factor is one and ε corresponds to the normally considered coohng efficiency η, since for an adia­ batic wall in these circumstances, TsM

=

(3A)

Film decay characteristics being conveniently represented in terms of film effectiveness, some relationship is therefore necessary between ε and a^ff. One such relationship has been suggested by Spalding^*^^ who proposed for the film-cooling of a heated plate,

"··

-.i^T

(4)

where a, k and b are unknown constants and μ is evaluated at some appropriate "film" temperature. The form of equation (4) derives from the form of the relationship between Stanton number and Reynolds number for boundary layers. However, it is only at large distances from the slot that the film velocity profile becomes similar to that of the boundary layer. It has been shown^^^ that for the types of injection slot and flow conditions present in the gas-turbine combustion chamber, only the initial regions of the film are important due to the high rates of film decay encountered. In the initial regions of the film (see Fig. 1) the velocity profiles

351

FILM-COOLING OPTIMIZATION WALL

J E TCASE WHEN

U>U

MAIN

REGION

FIG. 1. Model of injected film development.

will be discontinuous and slot geometry will strongly influence flow develop­ m e n t . ^ ^ ' T h e boundary layer approach therefore seems unlikely to be a rewarding one in the present context and in any case, the constants a, k, and b remain unknowns. An alternative approach is presented in Appendix I in the absence of any more exact relationship: the film heat transfer coefiicient could also be related to the adiabatic wall case through

α=

(5)

(^conv) m

where T,^¿ is the local adiabatic wall temperature and T, is the actual local temperature of the wall. Appendix I yields the semi-empirical relationship: ε = exp

-C(x-

x , ) [ l - Ζ)/1·65

Ι^^.,Γ'-'Μα,

cff

(6)

where -b ^N,L —

Pc^c

Re,s

(7)

(μm)L]

b having the value 0 1 5 for slots of the type considered in this paper, and C a n d D being empirical constants dependent on slot geometry. Equations (6) and (7) allow the effects on film entrainment of individual slot geometry and variation of mainstream conditions to be accounted for, in terms of an imaginary slot of the same type as to be used in the design, placed at the point where Λ: = 0, usually the front of the flametube. It would be desirable when more information on film entrainment is available to formulate more exact laws to replace the approximations used here.

352

G. J. S T U R G E S S

Using equation (6) together with the values of a^ff obtained above, the effec­ tiveness distribution over the flametubes surface required of the film-cooling can mow be calculated. An iterative method is thus now to hand for finding the spacing between slots of a given type and the calculation of the amount of cooling air required to maintain a flametube below a stipulated maximum temperature. For each station along the flametube wall under the given chamber conditions, the film heat transfer coefficient can be evaluated. F r o m the relationship linking film decay to its heat transfer characteristics the required film effectiveness distribution over the surface is then obtained using these heat transfer coefficients. Finally, the effectiveness decay curve actually obtainable from the chosen slot type is matched to the required effectiveness distribution, new slots being inserted in the wall where these curves intersect. The process is repeated for the new mass flow distribution so obtained until the successive approximations con­ verge. Optimization It has been shown,^^^ that the most economical and thermally eflicient way of air-cooHng a wall is by effusion of the coolant through the wall using a porous material. That film-cooling by discrete injection is not a very good approximation to this ideal is shown by Fig. 2. The method is of course in­ herently inefficient and expensive in air since from the point of injection u p to

T W O - D I M E N S I O LN AF L OW [ D T S C R EET

I D E AL P O R O US

S L O T ]S

W H O L YL S U R F A EC

I P O R O U S M E T A SL | P R A C T I C LA F I LM C O O L I GN

I G A U ZE

C O M P A C TI S

T H R E E - D I M E N S I OLN A F L OW

D I S C R E ET S I N G EL R OW P E R F O R A T I SO N

U N I F O R MYL D I S C R E ET

DISTRIBUD TE P E R F O R A T I SO N

FIG. 2. Classification of film cooling flow systems.

the point where the wall reaches its maximum permitted temperature, the wall is over-cooled. Where a large number of slots have to be employed to satisfy the wall temperature restriction it is worth while investigating methods of minimizing the amount of coolant to be provided. It has been shown that for the gas-turbine flametube^^^ only the initial regions of the film are relevant. It is therefore worth while to consider development of the injected film in some detail with reference to Fig. 1, which represents twodimensional flow from a slot of finite outer wall thickness.

FILM-COOLING

OPTIMIZATION

353

Boundary layers will build up on the flametube wall and on slot outer wall inner and outer surfaces, and a velocity defect is thus introduced into the flow because of these latter layers and the finite thickness of the slot wall. This defect is gradually filled by mixing of the two streams and the mixing layer so formed grows until its inner (wall-side) edge reaches the flametube boundary layer; the distance to this point from the slot outlet is the potential core length Xp. The flow region between the mixing and boundary layers is conditionally termed potential since, in general, the turbulence there will be less than that in the bounding layers.^"^^ A long way downstream from the slot, no matter what the initial conditions, the flow will have the character of a thick, turbulent boundary layer with the familiar universal velocity profile; this is termed the main region of the film. Obviously, between this main region and the end of the potential core the velocity profiles will be non-similar and changing rapidly; this is termed the transition region X j . As the initial regions of the film, consisting of Xp and x^, have been shown to be so important^^^ it is worth while considering how they may be extended. A theory has been developed^^^) to predict the potential core length for the situation described above and iUustrated in Fig. 1 . The approach is based on Prandtl's mixing length theory and uses the basic concepts of Appendix II. From these concepts it is shown db

\ui - 1 / 2 I

*

where b = width of mixing layer, ε* = degree of turbulence generated, u = characteristic velocity of the mixing layer. On the above basis, when the velocity difference between the two streams is neghgible or zero, the growth of the mixing layer will also be small or zero, in which case Xp will tend to infinite length. In practice, however, when the turbulence ε* falls to the same order as that inherent in the two streams them­ selves, equation (8) is no longer valid and mixing continues at this particular rate. In Fig. 3 are the experimentally measured values of potential core length for two typical modern cooling devices and it can be seen that Xp tends to a maximum value for unity velocity ratio. The method used to obtain these measured lengths is outlined in ref. 9. Both theory and experiment indicate that potential core length is a maximum when the velocity ratio for the mainstream and injected coolant is unity. Using these facts, a simple, one-parameter optimization is possible to minimize required coolant flow by locally matching slot injection velocity to equal that of the combustion chamber.

354

G. J. S T U R G E S S \—I

π

I I II I I

"Ί

I

J

1 I 1 II U

1

TYPE 0.)

I

-I

•2

-3

I

I I I I

- 4 -5 -6-7 Μ 1 - 0 VELOCITY

8 _i < 61

Π

1—I

\

2 RATIO

I I I II I

3

4

5

6

7Θ9ΙΟ

^*/U

I I II I^

1—I

1

I I I I Lj

" 4 O

TYPE

( 0

-I •4

-5 - 6 7 - 8 - 9 K ) VELOCITY

2

3

I

I

I

4

5

6 7 θ 910

I I I

RATIO

FIG. 3. Experimentally measured potential core lengths.

Calculation Procedure To study the value of such an optimization as proposed, the cooling of a combustion chamber for a reheated turbo-jet suitable for operation in a Mach 2-2 cruise supersonic airliner has been investigated as being typical of the sort of problem facing the combustion engineer at the present time. The general assumptions (the author's own, based on current practice) made for this hypothetical engine are given in Appendix III, where it can be seen that the specification approximates fairly closely to that of the early Bristol Siddeley B.S. 593D engine for Concorde. Two types of cooling device were selected for the study, and correlation studies of film-cooling data^^°^ had yielded the following equations: Type (i)

ε = [1-0 - 0-22432 5^^·^^]

Type (ii)

ε = M O [1-0 - 0-2218 5^^·^^]

(9) (10)

Equations (9) and (10) were derived from data obtained on a two-dimensional research rig^^^^ and the assumption was therefore made that if the ñametube radii were large in comparison with the slot height, then the film in the chamber

355

FILM-COOLING OPTIMIZATION

could also be considered two-dimensional; this was taken as the case. These equations provide the film decay characteristics to be matched with the required effectiveness distribution (see Fig. 4), and, in addition, the constants C and D for equation (6) to enable this distribution to be calculated (see Appendix I).

NON

OPTIMISED

.01

2

3

T Y P E (ii) C O O L I N G , SLOT

4

5

6

DISTANCE

7

INNER F L A M E T U B E ,

eOO<»C.

SLOT

3 FROM

9 FRONT

lO OF

SLOT

II

12

13

FLAMETUBE , χ

14

15

16

INCHES

FIG. 4. Matching of real film performance to required performance.

Due to the incomplete knowledge of detailed conditions inside combustion chambers, and the extreme difficulty of mathematically modelling the complicated structure,^^^'^^^ bulk conditions were used in the calculations. This is of course, a gross simplification but an unavoidable one. It is known from experience that where a strong transverse jet penetrates a film, the film is destroyed by the pressure distribution around the jet and by mass entrainment into the jet; also, where the transverse jet is admitted through the film-cooled surface via a plunged hole, the plunging mechanically deflects the flow, destroying the continuity of the film. In such cases it is necessary to renew the film immediately downstream of rows of primary, intermediate and dilution ports, and this practice has been carried out in the present analysis, regardless of the apparent state of the film as indicated by the calculations. Further, a slot was always placed at the flametube front even when calculation indicated the wall design temperature could be accommodated by convection in the annulus flow alone. This was done because the annulus flow usually separates from the front of flametubes due to the usual layout of chambers, particularly where a target-plate diff*user is employed. For a Nimonic 75 sheet construction, a desirable maximum temperature for the wall to ensure mechanical integrity of the flametube is about 800 °C and this has been made the starting point for analysis. Holland^^^^ concludes that the

356

G.

J.

STURGESS

average increase in permissible metal temperatures in gas-turbines has been 10° per year. Thus, assuming this rate persists, possible growth for the next ten years is covered by raising ^ax to 900°C, whilst step-changes in material properties are covered by going up to a T^^^ax of 1000°C. Beyond a wall tempera­ ture of 1000°C, radiation cooling of the flametube starts to become the dominant mode of heat transfer. The procedure for each T^,^^^ was as follows: (a) Starting with the initial condition of no film-cooling, values of a^ff were worked out at ^ in. stations along the flametube wafl, from equations (1) and (2) and ref. 1. (b) The values of C and D for the slot type chosen were fed into equation (6), together with the values obtained for a^ff, and hence the required effective­ ness distribution over the flametube calculated. (c) Using either equation (9) or (10) as appropriate, the effectiveness decay curve actually obtainable from the chosen slot type was matched to the required effectiveness distribution, slots being inserted in the wall where these curves intersected (see Fig. 4). (d) Knowing the slot effective area and the chamber pressure field (for the non-optimized case), the total coolant flow required and the new chamber mass flow split were calculated. (e) The process was repeated using the new chamber mass distribution until successive approximations converged by the number and position of cooling slots, and the coolant mass flow, becoming fixed. Convergence of successive approximations was found to occur after four or five iterations and obviously the calculations are most conveniently carried out using a digital computer. For the optimization, if we assume one-dimensional flow within the chamber, together with constant pressure mixing, the general expressions for: slot mass flow, =

lb mass/sec ft run

Vcpc

(11)

slot volumetric flow.

V

Pc

coolant density. pc = ~ —

lb mass/cu. ft.

(13)

FILM-COOLING

OPTIMIZATION

357

mainstream velocity, = 1——

ft/sec

(14)

Pm

velocity ratio. (15) coolant Reynolds number based on slot height, NKe.s

=

Γ-Γ-

M e f f

(16)

become with slots optimized for maximum potential core length. 1-0

(17)

fn„,Rj„, = J ~ —

(18)

"TT" =

u

"c

and the calculation procedure can be gone through as before. Results and Discussion of Results The results of the S.S.T. engine chamber analysis are presented in diagram­ matic form in Figs. 5-15. Figure 5 shows how the amount of coolant required depends on the permitted wall temperature and on the design of the slot. The lines linking the data points in this and subsequent figures are not intended to portray the behaviour of the function at intermediate values, but merely to serve as a "line of sight" for the eye. Continuous functions are not possible due to the discrete nature of the injection system. However, for the less efficient cooling device having a low effective area, the greater the number of slots required in a given condition and the less the effect of eliminating one or more slots on the total coolant flow. Thus, continuous functions can be approximated to if the number of such slots

358

G. J. S T U R G E S S ff.

Γ

40

•\TYPE(li)

8 00

M A X I M U M

9 00

P E R M I T T DE

W AL

1 0 00 T E M P E R A T UE R

TS

MAX

FIG. 5. Coolant required for non-optimized slots.

required is large. Type (i) cooling device comes under this category for all but the highest values of permitted wall temperature. F o r the permitted wall temperatures of today, 750-800 °C, the mass flow rate of coolant required to meet these in the chamber under investigation is a significant proportion of the compressor delivery, 30-40 per cent. Increasing the permitted wall temperature to 900 °C (representing 10 years, material growth potential) does not reduce this amount significantly below 30 per cent even for the better of the two cooling devices (Type (ii)). The problems facing the designer are emphasized by this figure. Note that for device (ii) no reduction in coolant flow is possible even though maximum wall temperatures are raised from 800 to 9 0 0 X . This is because of the over-cooling nature of discrete injection, the 900°C case being more over-cooled than the 800°C (see also Fig. 12). As is raised, two effects come into play: above 1000°C radiation cooling tends to

T Y P E( Í Í ) ·

y

ιομ

FIG. 6. Coolant required for optimized slots.

FILM-COOLING

OPTIMIZATION

359

become the dominant mode of heat transfer, and less slots are required due to the less severe design condition to be met; if the number of slots required is small, subsequent removal of one or two of them results in a significant change in total coolant flow. This explains the sudden decreases in at high Γ , „,ax. In Fig. 6 a similar plot is shown for the optimized slots and the improvement in coolant consumption is immediately apparent, falling to values about 23 per cent of compressor delivery and this being relatively insensitive to waU temperature. There is little difference between the performance of the two slots when optimized, as would be expected since we are attempting to approximate to the ideal (Fig. 2), and are doing this now as efficiently as possible. The actual reduction due to optimization is shown in Fig. 7, where it can be seen that there is a greater reduction for Type (i) than for Type (ii). Note the occurrence of a local maximum and minimum for Type (ii). These arise because of the shapes of the respective "curves" in Figs. 5 and 6.

20 Γ

Tc

MAX

'C

FIG. 7. Reduction of coolant flow by optimization.

One can conclude from Fig. 7 that for the types of coohng device currently available and for the present period and the next ten to fifteen years, local optimization of the form considered here appears attractive. This view is strengthened when Figs. 7 and 8 are compared. Figure 8 shows the reduction in coolant flow for non-optimized slots by raising permitted wall temperatures through material improvements. Optimization at 800°C for Type (i) reduces the coolant flow by nearly 16 per cent of compressor delivery, whilst to produce the same reduction by material improvements, the permitted wall temperature would have to be raised by over 230°C, to 1140°C. For Type (ii), optimization at 800 °C reduces by 6 | per cent compressor delivery and would necessitate a 170°C increase in T^^max to produce the same result.

360

G. J. S T U R G E S S

TYPE(I)

Id ^

-

800

1000

900 Ts

MAX

1100

*C

FIG. 8. Effects on coolant flow of material improvement non-optimized state.

If one makes the very reasonable assumption that in the interests of maintain­ ing satisfactorily the following chamber performance requirements: (a) operation over a wide range of overall fuel:air ratios, (b) high hmit of flame stabihty, (c) low minimum operating pressure, (d) high combustion efficiency over all operational cruising conditions, (e) low minimum ignition energy, primary zone conditions must remain fixed irrespective of the film-coohng, the main effects of such cooling will be on the requirement that the chamber has: (f) an outlet temperature distribution which is uniform circumferentially and radially acceptable to the turbine, in other words, upon dilution zone design. Despite an excellent paper on dilution zone design by Lefebvre and Norster^^^^ the choice of the number, size, shape and placing of dilution ports to ensure adequate penetration of the dilution jets and high mixing rates is still largely a matter of practical experience. When designing a dilution zone it is useful to have as much air available as possible so optimization of the film-cooling should be a help in this respect. The total airflow available for dilution after non-optimized cooling, for fixed primary zone conditions, is shown in Fig. 9. The amount of air available increases with maximum wall temperature and Type (ii) cooling device is seen to be better than Type (i) in this respect. The equivalent plot for optimized slots is presented in Fig. 10 and similar conclusions can be drawn, except that there is more air available (about 33 per cent compressor delivery as opposed

FILM-COOLING

361

OPTIMIZATION

T Y PE

(,·,· )

'• T Y PE

Ú

(0

,0-

800

900

MAXIMUM

PERMITTED

lOOO

WALL

TEMPERATURE.

T^^J'C

FIG. 9. Total dilution airflow for non-optimized slots.

_J Y P E

(ί.) TYPE

-

ω

800 MAXMUM

900 PERMITTED

WALL

TEMPERATURE,

lOOO Tj

^^/c

FIG. 10. Total dilution airflow for optimized slots.

(.·)

362

G. J. S T U R G E S S

to 30 per cent or less), and the amount is less sensitive to r^^maxFig- 11, the increase in dilution air as a result of optimization is shov^n, and again it can be seen by comparing Figs. 11 and 9 that optimization is more effective than likely material improvements over the next ten years. The aerodynamic benefits of local slot optimization for unity velocity ratio are seen to be both real and v^orth vv^hile. The drawbacks must now be considered. It is obvious that the optimized cooling system will be more complex than the non-optimized. For the combustion chamber and cooling devices under

20r

o

Q

TYPE

(.·)

" LU _L CC <

Α

TYPE

ζ ^

GO

ol 800

700 MAXIMUM

PERMITTED

900 WALL

TEMPERATURE,

FIG. 11. Increase in dilution airflow due to optimization.

consideration, the velocity ratios uju^ obtained along the flametube in the nonoptimized case were all less than or equal to unity. This is likely to be the case with most chambers due to the typical values of pressure drop across the flame­ tube wall to obtain adequate dilution zone mixing, and the present philosophy of designing slots for mechanical strength and integrity before aerodynamic performance. Thus, to achieve optimization, the flow to the slot will have to be metered, this being done upstream of the slot exit to avoid changing the film characteristics, in an extension of the slot. Individual optimized slots will thus be more complex in themselves than the non-optimized equivalent. With the velocity ratio uju^ being less than or equal to one in the non-optimized case, adjusting this ratio to unity reduces the amount of coolant flowing through the slot resulting in a "weaker" (lower momentum) film as a consequence. The weaker film has a higher rate of decay due to greater entrainment rates and so more of the optimized slots will be required in a given situation than the nonoptimized. As a result of optimization, therefore, flametube complexity increases also. Figure 12 illustrates this effect of optimization on chamber complexity. Complexity is seen to decrease rapidly with increase in maximum wall tempera­ ture, improvement in cooling device, and to increase with optimization. For the

363

FILM-COOLING OPTIMIZATION

^

OPTIMISED TYPE

u)

o

(0

\N0N-0PTIMISED

δ

.RYPE(..)

700

ΘΟΟ MAXIMUM

PERMITTED

900 WALL

lOOO

MOO

TEMPERATURE

FIG. 12. Effect of optimization on chamber complexity.

purposes of this ñgure interport coohng slots (taken where appropriate as covering two-thirds flametube circumference for primary zone supplies and onehalf flametube circumference for dilution zone air supplies) have been taken as equivalent to complete circumferential slots. Flametube cost will follow closely flametube complexity, it being likely that providing metering would double the unit manufacturing cost per foot run of slot. The estimated weight penalties due to optimization are shown in Fig. 13. Increasing Γ^^^^ naturally reduces the weight of the cooling system because of

Τ ΥY ΡP ΕEΓ( .. .. )) T

^ *" ^^ ·- ~ ^ ^ ' I ^ ' S £ O

•

OjJON-OPTIMlSED

700

800 MAXIMUM

900 PERMITTED

WALL

TEMPERATURE.

lOOO T^^^°C

FIG. 13. Estimated weight penalty due to optimization.

364

G. J. S T U R G E S S

the decreasing number of slots required, and optimization increases it because of the greater number. For Type (i) cooling device, the optimized cooling system is about half as heavy again as the non-optimized case, there being little effect of Γ, The optimized system for Type (ii) device is nearly twice as heavy as the non-optimized. Any system based on Type (ii) will be heavier than the equivalent system based on Type (i) even though there will be less slots in the Type (ii) system than the Type (i). This is due to the basic design differences between the two slot types. For example, the weight of an optimized Type (ii) system at 800 °C is almost I J times that of an optimized system based on Type (i) whilst the ratio of slot numbers in the two systems would be twothirds. Comment The conclusion of ref. 8 that the initial regions of the film only need be con­ sidered for application to gas-turbine cooling is confirmed (see Fig. 4). It would be expected that the dilution zone regions of a flametube would be more difficult to cool than those of the primary zone, because: (a) there is generally less air available after the dilution ports, (b) flow velocities in the annulus cannot be allowed to rise much above 200 ft/sec due to keeping skin friction losses low, (c) the coolant towards the rear of the chamber will be higher in temperature than at the front due to heat transfer from the flametube, (d) the hot gases in the dilution zone of the flametube will have a significantly higher mass velocity than those in the primary zone, thus tending to in­ crease entrainment into the film. In the calculation procedure considered here, the cooling was carried out at the expense of dilution air so there was always an adequate supply of coolant made available after the dilution ports; reasons (b), (c) and (d) are still pertinent however. The relative ease of cooling the two regions is indicated in Fig. 14 where the ratio of the number of slots per unit length, dilution to primary zone, is plotted against maximum wall temperature for the two slots. It can be seen that on this complexity basis there is not much difference between the two zones, and a great deal depends on the design of the slot. On a thermal basis, however, it can be seen from Fig. 15 that the dilution zone is most definitely the harder to cool, and that optimizing the cooling slots makes the problem somewhat easier. Another conclusion of ref. 8 is confirmed therefore. The conclusion that the dilution zone is the hardest part of the flametube to cool is strengthened by the study of photographs of temperature-sensitive paint tests where higher temperatures in the dilution zone regions are always observed.

365

FILM-COOLING OPTIMIZATION

TYPE ( i )

ill

Ο

o I < ρ

<

900

_,

i

FIG. 14. Relative ease of cooling primary and dilution zones.

^OPTIMISED

δ

ω α-

μ-, ζ

Q < 900

FIG. 15. Relative ease of cooling primary and dilution zones.

It should be pointed out though, that the flametubes are supported at their rear-flanges and conduction to the surrounding engine structure could play a part in the cooling processes at the very rear of the dilution zone. Conclusions 1. A simple, one-parameter optimization on the basis of local matching of velocity ratio for maximum potential core length produces a worthwhile reduction in the total amount of coolant flow required to limit the maximum

366

G. J.

STURGESS

flametube temperature to a specified value. The amount of this reduction depends very much on the individual slot design used, but such an optimization apparently oflers greater air savings than likely material improvements. 2. By optimizing the coohng system more air is available for mixing in the dilution zone, thus easing considerably the design problems associated with this zone. 3. The drawbacks to the optimized cooling system are that its complexity increases considerably, together with a likely doubling of cost. A significant weight penalty can be incurred for an optimized system, but the extent of this again depends very much on the design of the individual slots. 4. The value of optimizing the coohng system being estabhshed by the present study, it seems worth while extending the optimization to one of at least two parameter, either slot effective area or slot height forming the additional, parameter. Alternatively, it might be worth while to consider also a mixed-slot configuration. Extending the optimization in these ways would certainly reduce the cooling airflow even further, but would increase complexity and cost although the weight penalties might not be so severe with a mixed system as with the single-slot. 5. To successfully apply a velocity ratio-optimized system, considerably more information than available at present on flametube flow conditions will be required, to improve the mathematical modelling techniques used in the calculation process. 6. Slot design should be for maximum potential core and transition lengths in the film. 7. The conclusions of ref. 8 are confirmed by these more detailed calculations. 8. The design of a suitable cooling system is quite plainly tied indirectly to the original design specifications of the particular engine under consideration, and must be tailored to the combustion chamber design just as much as this in its turn is tailored to the individual engine design. General solutions are not possible. References 1. LEFEBVRE, A. H . and HERBERT, M . V. Proc. Inst. Mech. Engrs. {London), 174, 1960. 2. LEFEBVRE, A. Η . Progress and problems in gas-turbine combustion. Paper presented at Tenth Symposium (International) on Combustion, Cambridge, August 1964. 3. SEBAN, R . A . Trans. ASME, J. Heat Transfer, 3 0 3 , 1960. 4. PAPELL, S. S . and TROUT, A M . Experimental investigation of air cooling applied to an adiabatic wall by means of an axially discharging slot. NASA TN D-9, 1959. 5. SAMUEL, A. E. and JOUBERT, P. N. Trans. ASME, J. Heat Transfer, 4 0 9 , 1965. 6. HARTNETT, J. P., BIRKEBAK, R . C . and ECKERT, E . R . G . Trans. ASME, J. Heat Transfer, 2 9 3 , 1961 7. SPALDING, D . B . Unpublished Imperial College report, London (1963). 8. STURGESS, G . J. J.R.Ae.S. 7 1 , 430, June 1967.

FILM-COOLING

OPTIMIZATION

367

9. STURGESS, G. J. Some observations on the behaviour of practical film-cooling devices for aircraft gas-turbine combustion chambers, A R C 27390, HMT 81, 1965. 10. STURGESS, G . J. Bristol Siddeley Internal Report, 1966. 11. COLE, E . H . A procedure for predicting the adiabatic v^all temperature in the film-cooling process, based on the unified theory. ARC 27374, HMT 79, 1965. 12. SPALDING, D . B . A unified theory of friction, heat transfer and mass transfer in the turbu­ lent boundary layer and wall-jet. ARC 25925, 1964. 13. BAYLEY, F . J. Air cooling methods of gas-turbine combustion systems. R. &M. No. 3110, 1959. 14. HiNZE, J. O. Turbulence—An introduction to its mechanism and theory, p. 488. McGraw-Hill, 1959. 15. STURGESS, G . J. Unpublished work, University of Technology, Loughborough, 1966. 16. ScHLiCHTiNG, H. Boundary Layer Theory, p. 477. McGraw-Hill, 1960. 17. PALMER, J. F. Bristol Siddeley Internal Report, 1964. 18. CLARKE, A. E., GERRARD, A. J. and HOLLIDAY, L . A. Ninth Symposium {International) on

Combustion, p. 878. Academic Press, 1963. 19. Unpublished work at Bristol Siddeley Engines Ltd., 1966. 20. HOLLAND, M . Film-cooling in air-breathing engines, ARC 27379, HMT 80, 1965. 21. LEFEBVRE, A. H. and NORSTER, E . R . College of Aeronautics Memo N o . 5, 1963.

Appendix I Required Effectiveness—Heat Transfer Coefiicient Relationship Consider the film formed from a two-dimensional slot as shown in Fig. A l . Let the film exist as a discrete layer over the element AB of length Idx, b u t with a mass rate m entrained upstream of A.

MAINSTREAM

FIG. A l .

If the temperature at χ is t^, the temperatures at A a n d Β are, respectively, dt. t . - ^ d x

and

[tc +

dt.

Y^dx].

and the enthalpy increase of the film in passing from ^ to 5 is ^hg, where,

(Al)

368

G. J. S T U R G E S S

where Cp = a mean specific heat for the element of the film nie

= m'J^x — dx)

m'xldx

0 in the hmit.

The average heat now into element A-Β is given by

^Qs = 2(xdx{t„,- O

(A2)

where α is the local heat transfer coefficient between mainstream a n d film, and t'c is some appropriate mean film temperature over the element. Now, if the wall is assumed adiabatic, the heat is carried away in the film and a heat balance yields for steady-state. =

AQE

(A3)

If t'c is taken as the arithmetic mean temperature over the element and equations (Al) and (A2) substituted into (A3), it can be shown that dt.

— ccdx

(A4)

The boundary conditions for the above differential equation are as follows: (a) atx = 0,t,=: t,u ( b ) a t x = Xp, T, = i , „ (c) if the temperature gradient through the film is small, as it will be as a consequence of the adiabatic wall approximation, =^ Γ,, (d) as a result of boundary condition (c), α becomes the heat transfer co­ efficient between mainstream and wall. Thus, integrating (A4) yields

I.e. In

Τ. - ί Λ

-ci,„dx

(A5)

But a definition of film effectiveness is ε =

ÍZ - t \tci-U

(A6)

Hence, Ιηε =

-a.ffdx

(A 7)

FILM-COOLING

OPTIMIZATION

369

To proceed further suitable mass entrainment laws are required to enable the integration to be made. Cole^^^^ found for a distance downstream of the potential core there was a region where Spalding's recommended entrainment laws^^^) were not valid. He suggested this region was the transition region, where constant values of entrain­ ment might be appropriate. To give a good fit to existing (clean slot) data, he found these values depended upon velocity ratio and the relative magnitude of the free-mixing layer component of the velocity profile at the end of the potential core, i.e. m, + m, = [m, + m^^x^ + m^x - x^)]

(A8)

where m'^^ and m'^ are independent of x. Substitution of laws of this type has been made and the resulting α^^^'^ε relationship examined in the primary and dilution zones of a combustion chamber. Extreme sensitiveness to the actual values assigned to and was observed. It became obvious that the entrainment laws chosen must be closely related in both this transition region and the early parts of the main region of the film, to the geometry of the actual cooling device to be used. It can be shown on the basis of a modified turbulent boundary layer model^^^^ that s =

(A9)

nif

rrif being the total mass flow rate in the film at any point, and, from correlation studies based on this model,-^^hhat the film effectiveness can be described by the semi-empirical relationship, ε = CIVO-DS^^'^']

(AlO)

where C and D are empirical constants depending on slot geometry and .S^ is a theoretical correlation group given by •\-b

(All) where b depends on the wall shear stress law taken for the film and has the numerical value of 0 1 5 for slots of the type and form considered in this paper. Now, ntf

and, using equation (A9),

=

+

nig

370

G. J. S T U R G E S S

Therefore {m, +

= ^

(A12)

This last relationship forms the basis of the semi-empirical entrainment laws in this paper. Substituting equation (10) into (A 12) and the result then into (A7), integrating and rearranging, gives the sought relationship : f-C(x - χ , ) [ 1 Ό - D/L65|5^,,r^-^^]aefr] ε = exp< - - z = >

^^^^^ (A13)

where local variation of mainstream conditions (as occurs in a combustion chamber) is accounted for by use of the subscript L for local, on correlation group .S^, i.e. entrainment is a function of local flow properties in addition t o geometry. Thus, through equation (A13), the effectiveness distribution over the surface required from the film-cooling is described in terms of a single, imaginary slot of the same type as those to be used, placed at the leading edge of the surface. Appendix II Essential Concepts of Potential Core Length Theory From Prandtl's mixing length theory^ du v'azl— dy

(A14)

where / is Prandtl's mixing length, and v' is the perturbation component of transverse velocity, the instantaneous velocity ν being defined, ν = ϋ^υ'

(A15)

Assume dh — ^v'

(A16)

where b is the thickness of the mixing layer. Now, db —

dt

dbdx =

- — 7 -

dx and

dx dt

— =u dt

So, db

\v'\

dx

\u\

T-oc

-

(A 17)

FILM-COOLING

OPTIMIZATION

371

Similarity of velocity and density profiles (plotted in appropriate form) in the mixing layer is assumed and as a consequence, V'

GC - ( w i

-

U2)

(A18)

and 7 = constant b

Thus,

oc

(wi

-

U2)

(A19) (A20)

i.e. the perturbation component of transverse velocity is generated by the velocity difference between the two streams. Therefore, substituting equation (A20) into (A 17), db_ dx

OC

— — — ' = ε*

where ε* is the degree of turbulence generated, and w is a velocity characteristic of the mixing layer, defined thus. pu dy u = pdy

Appendix III General Assumptions made for S.S.T. Combustion Chamber at Design Point 29,300 lb force (dry) Engine thrust 35,000 lb force (reheated) 356 lb mass per sec Engine airflow (compressor delivery) 342 lb mass per sec Combustor airflow 420 lb mass per min Fuel flow Annular vaporizer Chamber type 10-25 lb mass per sec from rear of Bleed for turbine cooling inner annulus Turbine entry temperature 1422°K Compressor delivery temperature 715°K Maximum flame temperature 1726°K Primary zone combustion efficiency 80 per cent Overall combustion efficiency 99 per cent Compressor delivery pressure 217 psia

372

G. J. S T U R G E S S

Overall loss in total pressure

Flametube (axial) length Outer flametube diameter at primary zone

^PjPi = 10 P^r cent, losses made up of 50 per cent in the diffuser, of the total pressure crop across the flametube wall, 53 per cent is due to mixing in the dilution zone. 20-5 in. 3-083 ft

Inner flametube diameter at primary zone

1 -832 ft

The gas constants for combustion products and air were taken respectively as 100 and 96 ft-lb force per lb mass °K. In the primary zone bulk temperatures were calculated from the expression. Tlx

2'p.z. where /p.z. is the length of the primary zone, and, in the dilution zone, was taken as the turbine entry temperature, i.e. the dilution zone rearranged tempera­ ture profiles without changing bulk temperature. Viscosities for combustion products and coolant flow were considered as functions of temperature only. Specific heats for combustion products were found as functions of temperature and fuel/air ratio from standard tables. Chamber geometry was held fixed and it was assumed that redistributions of airflow in the annulii did not significantly change the pressure loss assumptions. Fuel/air ratio in the flame stabihzation region was held constant regardless of the cooling. Mean specific heat Cp was taken as

DISCUSSION J. WINTER:

Since velocity ratios VJVc in some chambers, particularly primary zones of spray chambers, are on the other side of unity compared with those quoted by Mr. Sturgess, does this mean that the rather pessimistic results he obtained where more slots are required would be reversed, i.e. more optimistic with less slots required? G . J. STURGESS:

Firstly, it must be emphasized that the present analysis applies only to an annular, vaporizer-type chamber. However, it is primarily the shape of the potential core length ^ velocity ratio curve which determines the number of slots required for a given slot design (see Fig. 3), and this is usually about the same immediately on both sides of unity velocity ratio. The number of slots required then might not be too different in the two cases; the coolant flows, however, would be. If velocity ratio ujuc is less than unity, raising it to unity reduces the flow of coolant, whilst if ujuc is greater than unity, lowering it increases the coolant flow. The answer to the question is, therefore, that the number of slots required would be about the same but more coolant would be required. J. WINTER:

The mass flow of the cooling film in the primary zone can be a significant proportion of the hot gas flow. This means that the cooling efficiency will never reach zero, and hence ought not the definition of efficiency be modified to include enthalpies rather than temperature ? G . J. STURGESS:

This condition seems only likely to occur where there is a flare to cool, i.e. in a spray-type chamber. The designer is plainly interested in the definition of effectiveness given by equation (3). Where the injected and mainstream gases are taken as the same and temperature diff'erences are such that constant properties can be assumed, and for low stream velocities, then this definition is equivalent to one based on specific enthalpies,

-

π

.

where h denotes a specific stagnation enthalpy and subscript G applies to a station just outside of the boundary layer. In a rigorous development of equation (A9) in Appendix I (development not given in this paper), this equation should in reality read:

nif

In the present paper, it has tacitly been taken that ε = €h In the case Mr. Winter quotes the enthalpy-based definition would have been the one to use and this would have led to slightly more complicated equations in the analysis. Such a refine­ ment has not been used in the present investigation since this of necessity would have posed the question: What is the effect of preceding slots on film development from a succeeding slot? The answer is by no means clear and so the pessimistic assumption that there is no favourable eff'ect has been made. 373

374

DISCUSSION

J. WINTER:

In view of the fact that there are distinct differences between the performance of the two slots given in the paper, ought not the optimization of the slot geometry be given so much emphasis as the optimization of a given number of slots in a chamber. G . J. STURGESS:

If I understand the question correctly, the answer is no, since any practical chamber is not designed with a fixed number of slots in mind. V . SIDDHARTHA:

Three fundamental questions: 1. Does the analysis assume a Prandtl number of unity and by implication the validity of Reynolds' Analogy? 2. What is the basis for the "potential core" hypothesis ? Have any turbulence measurements been made to substantiate this hypothesis ? 3. For ujuc = 1 -0 the only mechanism by which mixing takes place is free stream and slot turbulence. Has this effect been properly evaluated ? G . J. STURGESS:

In the analysis, constant density and fluid properties in the film have been assumed so the velocity field becomes independent of the temperature field. However, these two fields can become similar for a small streamwise pressure gradient and small fluid viscosity; in which case they will be exactly so if the Prandtl number is taken as unity. This assumption is implicit in the derivation and application of equations (A 10) and ( A l l ) of Appendix I, which it is hoped will eventually be presented elsewhere. This represents an approximation of course, and must be recognized as such. Since Reynolds' Analogy is a direct consequence of the general principle of similarity, by assuming similarity it is implied that Reynolds' Analogy is valid also, although it is nowhere used in the analysis. The "potential core hypothesis", defined in the text in terms of velocities, is a fact well established by velocity measurements and too adequately documented in the literature to warrant further comment here. When the coolant is injected at a velocity ratio of unity, it is true that mixing for an idealized slot can only take place as a result of the turbulence inherent in the primary streams them­ selves; this is the whole basis of the present paper. This effect, however, has not yet been properly evaluated although my own experimental programme aims to do just this. P . RICE:

Would the author like to comment on the effect of the wall thickness since most authors usually ignore it in their analysis ? G . J. STURGESS:

It is true that the effects of the slot outer wall thickness are usually avoided in most theoretical and experimental investigations. In any practical slot, however, this outer wall, to preserve the combustion chamber mechanical integrity, will have a thickness which represents a consider­ able proportion of the slot outlet height. The presence of this lip introduces into the mixing layer a velocity defect, as indicated in Fig. 1, which through wake drag, represents a momentum loss, the immediate effect being to shorten potential core length from that expected from a slot with an infinitely thin outer wall. A second effect is to extend the length of the transition region. These effects are automatically accounted for in equations (9) and (10) since they are semiempirical relationships. The theory we are developing to predict potential core length does take into account this finite thickness of the slot outer wall. R. SINGH:

Following a question on optimization in the situation where the coolant injection velocity is less than mainstream velocity, I would like to point out that in such a situation no optimiza-

DISCUSSION

375

tion of the type described by Mr. Sturgess is possible, This is because such an optimization would require an increase in chamber pressure loss and this would be unacceptable. G. J. STURGESS:

Generally speaking, I would agree with this statement, although I have on occasion known flametubes where pressure loss has had to be raised during the development phase, but for other, more urgent reasons than ñlm-cooling! The present study was applied only to annular, vaporizer-type chambers with a pressure loss perhaps a trifle on the high side (see Appendix III), when compared to the Spey for example, where Messrs. Gradon and Miller quoted a brochure ñgure of 4 per cent ΔΡ/Ρ, although I should be interested to hear a measured value, after development, quoted. However, with the pressure loss taken, velocity ratios in the primary zone came out to be very much less than one, indicating that they would probably still have been less than one, thus permitting the optimization, at a value of say, 6 per cent AP/F. Evidence from photographs taken on water-analogy rigs, albeit unreliable, of such chambers indicates that the coolant ñlm is injected in practice at a velocity higher than that of the mainstream locally, over most of the flametube length. As stated under conclusion 5, more information on conditions inside flametubes is required. I would like to query Mr. Singh's emphatic statement that any increase in chamber pressure loss is unacceptable. Surely it depends heavily on how much increase in pressure loss would be required to bring about the optimization, how severe the cooling problem was, what other benefits might be brought about by the optimization, and on the application of the engine concerned? If it is insisted that minimum pressure loss is required regardless of any other considerations, then the optimization might still be possible using, as suggested under conclusion 4, a mixed slot configuration. Indeed, this latter step might possibly be the best solution because then there is no doubt for a given slot system, coolant would always be at a minimum, which is the basic aim anyway. I think the answer to Mr. Singh's question is contained in conclusion 8 of the paper. R . SINGH:

The heat transfer coefficient a^u introduced in equation (6) (also equation (A13) in Appendix I) is the heat transfer coefficient between the mainstream and cooling film for an adiabatic wall. The same heat transfer coeflScient a e f f is also used in equation (2). Here it is the heat transfer coefficient between the mainstream and the wall, and this is a non-adiabatic case. It is diflftcult to see how these two O e f f ' s can be treated as equivalent. An attempt is made to justify this in Appendix I (boundary condition (c)). However, the use of equation (5) Oeff

=

implies a difference between Ts and Ts.ad, and this fact together with the fact that in one case it is the heat transfer between gas and gas (adiabatic wall) and in the other heat transfer between gas and wall (non-adiabatic wall) that is considered, makes the equivalence of a^f as used in equations (2) and (6) difficult to accept. G . J. STURGESS:

The approximation in the derived relationship between required efl'ectiveness and heat transfer coefficient comes in equation (A3) of Appendix I and not in the boundary condition (c). We have assumed a priori that property values in the film can be considered constant (at a station) and it is as a consequence of this that it can be said tc ^ Ts and then α = a e f f . Equa­ tion (A3) does represent a serious approximation and should be recognized as such. It is however, a pessimistic approximation in that it implies a more rapid decrease in effectiveness than would actually occur if some heat were allowed to escape through the chamber wall, and as such is therefore engineeringly acceptable for the present purposes. The relationship used here is not offered as the final solution but as an interim one in the absence of anything more satisfactory. An alternative statement which could have been made as equation (A3) is: Aha

—

aQb

—

. 4 [ ( ^ c o n v ) A n n] B

376

DISCUSSION

but this would have involved considerable difficulties in both manipulation and further assump­ tion for convective heat transfer from the wall to the annulus flow. Miss E. J. MACNAIR:

Mr. Sturgess's analysis assumes coolant flow parallel to mainstream flow. Swirlers may be on the way out, but at present most combustion chambers (e.g. that sketched by Mr. Winter) have swirling mainflow in the primary zone, while wigglestrips and other cooling devices are designed for axial flow down the wall. If the slots were skewed to match the mainflow with its tangential component, not only would the theory be more applicable, but the film should be more effective and persistent because of the centrifuging of the higher density coolant air to the wall. I should be interested to hear Mr. Sturgess's comments on the implications of swirling mainflow on his analysis, and also whether swirled coolant flow to match the mainflow has been tried in practice. G . J. STURGESS:

Miss Macnair's comments apply to tubular and tubo-annular spray chambers only, where swirlers are used to assist in flame stabilization, and, in such situations, raise a valid point: the present theory would be expected to be in error when applied to such systems. For a slot optimized for unity velocity ratio on the assumption of parallel streams, the effect of swirl would be to reduce the velocity ratio by the cosine of the swirl angle, for small angles, thus reducing the potential core length. For large swirl angles, one feels the mechanism of mixing would be fundamentally different from that assumed in Appendix II, involving perhaps the stability of the film more. Some tests were carried out by Bristol Siddeley Engines Ltd., a number of years ago now, with pieces of wiggle-strip set at 30° incidence, and these tests indicated that the cooling achieved was worse than that from a standard, parallel fitting. Whether or not this is a significant effect in practice would depend on the shape of the potential core length velocity ratio curve for the cooling slot under consideration and the magnitude of flow swirl angle at the wall in the particular chamber. A thorough study of this aspect does not seem to have been made. The other point raised by Miss Macnair concerning the use of centripetal force to assist in preserving the film is more difficult to answer. If one considers present flametube design, I feel it is of no importance whatsoever since positioning of slots in the wall depends more on where and how primary, secondary and dilution air is admitted to the flametube (see Fig. 4 in conjunction with paragraph 6 of section entitled "Calculation Procedure"; also ref. 15) than on the stability of the injected film, generally it is necessary to go to another slot before the film loses its stability. Furthermore, it appears that annular, vaporizer flame tubes are coming into vogue, and stabilization in this manner would not be possible on the inner flametube of such chambers. For an unconventional design where an extraordinary amount of coolant is admitted through the flare, as in the case of Mr. Dakin's flametube or, for an injection system as described by Professor Schlader, this might well be significant and worth considering. Application of a skewed cooling system to a chamber might in fact prove rather difficult since the coolant intake of the slot would then be at incidence to the annulus flow, unless the compressor residual swirl happened to be the same in direction and magnitude as that intro­ duced inside the flametube by the swirler! If this were not the case, the slot might not "run full".