Current Technology of Radial-Inflow Turbines for Compressible Fluids

P AP E R N UMBER

Current Technology of Radial-Inflow

Turbines for Compressible Fluids

HOMER J. WOOD Consulting Mechanicol Engineer, H. J. Wood and Assodates, West Los Angeles, Calif. Mem . .A,SME.

Efficiencies up to 94 per cent may be achieved with radial, mixed, or axi·al-flow turbines using ei.ther compressible or i™=omp•ressitble fluids. Such high performances are possible only if specific speeds are within certain limits and criteria with respect to Reynolds number and Mach number are favorable. All three types a·re applicable with no efficiency disadvan1'age at low and medium specific speed�. For specific speeds above certain limits, radlial-inflow turbines tend to be less efficient. In the medium-specifk-speed range, a form of radial-infl·ow turbine having straigh' radi1al blade elements has special interest for compressiblefluid applications. Efficiencies in the 90-94 per cent regime have been demonstrated. Stress characteristics are such that for high temperatures an·d proper specific-speed ranges, higher heads per stage may be used efficiently in one stage than is possible with a single-stage axial turbine.

Contributed by the Gas Turbine Power Division for presentation at the Gas Turbine Power Conference and Exhibit, Houston, Tex., March 4-8, 1962, of The American Society of Mechanical Engineers. Manuscript received at ASME Headquarters, January 9, 1962.

Written discussion on this paper will be accepted up to April 9, 1962.

Copies will be available until January 1, 1963.

Copyright © 1962 by ASME

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Current Technology of Radial-Inflow

Turbines for Compressible Fluids

In spite of there having been a number of excellent publications on radial turbines in turbomachinery literature, there seems to be a common impression among designers of flow paths for compressible-fluid turbomachinery that radial turbines should be selected only when considerations of cost outweigh the desire for high performance. In considerable measure, this attitude has been fostered by the undeniable fact that large gas turbines of high performance have, without exception, used axial turbines. There are valid reasons why these machines utilize axial-flow paths, but efficiency considerations should not be among them. In fact, a search of the published performance of all types of turbines reveals that a radial-inflow machine holds the record with 94.57 per cent.1

Technologies have a way of becoming compartmentalized to such a degree that nrutually exclusive conclusions can be reached in different industries by failing to place a particular line of evolution in its proper perspective. Thus, water turbines and steam turbines both long antedate gas-turbine technology as we know it today, and there has been surprisingly little cross-fertilization of information. In consequence, some myths have been established with respect to the usefulness of radial turbines which are long overdue for exposure.

The building of water turbines is a very ancient art indeed, and many of the trends which are expressed in today's machinery had their origin at least 100 years ago. Reference (!)2 provides an excellent description of three classes of hydraulic turbines in general use, known as the Pelton, Francis, and Kaplan. In broad terms, the Francis machines have radial inflow rotors with adjustable nozzles; Kaplan turbines have axial-flow rotors, and both rotor and nozzle bladings are adjustable. Pelton turbines have a special geometry which has no true counterpart in compressible-fluid turbomachinery (because efficient operat'ion of a Pelton rotor requires that it not be submerged in water, and this concept can have significance only where the rotor is exposed to some medium which is much less dense and has mu.ch less drag effect than the main working fluid). 1 The James Leffel and Company. 2 Underlined numbers in parentheses designate References at the end of the paper.

1

HOMER J. WOOD

Going back in history, Francis turbines evolved as counterparts of centrifugal pumps; the Pelton wheel evolved from paddle wheels propelled by mining nozzle jets in the California gold fields; Kaplan turbines evolved from submerged propellers (which were probably derived from early water-screw devices). Each found its proper market application through competitive evolution, and it was largely a process of rationalization which caused the Pelton wheel to be associated with very low specific speeds, the Francis turbine with medium specific speeds, and the Kaplan turbine with very high specific speeds. There is little question that these discriminations ·are valid from an economic viewpoint, but they certainly are open to some debate as to whether they represent fundamental fluid dynamics limitations.

Dr. O.E. Balje (_g) has presented a recent and comprehensive picture of the turbine-performance spectrum. Although primarily devoted to compressible-fluid systems, most of the arguments presented therein apply to incompressible fluids as well. It is noteworthy in showing that axial turbines (with proper design parameters) can cover the entire specific-speed range of practical interest, and provide efficiencies equal to those of any other turbine form. Taken literally, this would mean that Kaplan turbines could be designed for the same specific-speed range as is normally covered by Francis turbines. [rt is interesting to note that something of the sort has been done in the 11Deriaz11 mixed-flow turbine (l). J Whether such a procedure would make economic sense is not of concern here. However, carrying the analogy further, there is difficulty in attempting to use the design methods o� reference (.g.) for water turbines having specific speeds normally covered by Pelton designs. In this case, the analogy fails because the Pelton wheel solves the problem of high disk friction associated with low specific speeds by avoiding submergence of the disk in the working fluid. Thus, although it would be possib.le to build water turbines corresponding to the partial-admission axial stages of very low specific speed described in reference (.g), their performance would be inferior to that of Pelton wheels.

In broad terms, turbines which must operate with rotors submerged in the working fluid tend to have efficiency losses. dominated by disk friction


Fig. l Inward-flow radial turbines

and leakage in the low specific-speed range, and by losses associated with high throughflow velocity in the high specific-speed regions. The basic technology behind these assertions may be found in reference (2); furthermore, it brings out the point that �ome types of radial turbines properly are limited to a medium specific-speed range by their relatively high disk friction (as compared with impulse axial turbines) at low specific speeds and by high throughflow losses at high specific speeds. Within its limited range, the best radial-flow turbines can match but not exceed best axial-flow-turbine performance. This specificspeed range, then, is not exclusive to any of the three flow paths, nor can any part of the entire specific-speed spectrum be held exclusive to radial turbines. It is the author1s firm conviction that from Ns = 3.0 to limits of practical interest, no other form of turbine flow path will exceed the peak performance capability of the axialflow turbine. Furthermore, this applies to incompressible-fluid turbines as long as the specific speed is higher than the applicable range of Pelton turbines. This does not necessarily mean that axial turbines always represent the best design solution, but it does mean that the specificspeed criterion alone cannot'be used to rule explicitly in favor of a radial-flow path.

comparisons are made herein between turbines of grossly differing sizes and working fluids. If true geometric similarity is maintained (including surface roughnesses and clearances proportional to n2), the only real "size effects" are included in Reynolds number, which contains both size and fluid properties. Unfortunately, absolute Reynoldsnumber effects vary with specific turbine configuration and Mach number. Some insight may be gained by treating water and gas turbines as if they were geometrically similar. In such case:

2

Fig. 2 Flow path of mixed-flow turbomachinery

1/2 ( 2gHt) D2

Re V = Reynolds factor

Comparing typical Francis and 90-deg inward-flow radial turbines:

N y D2

Ht

Reynolds factor s

Francis � 107 (water) • • . 65 1000 8 400 10.6 •

90° IFR 0.16 . 107 (air) • • • • • 65 1000 l 60,000 1.2

It is seen that the Reynolds factors lie in the same order of magnitude.

WHAT IS A RADIAL TURBINE?

In the introductory remarks, reference to "radial" turbines was made with deliberate vagueness, and there are serious difficulties in attemptiqg to define Just what the classification term really means. References (�) and (.!2_) cover the variety of geometries which have been used, and also note the comparison with water-turbine practice. Using the same terminology as reference (�), it is the intention of this paper primarily to cover the 90-deg inward-flow radial turbine.3 As used herein, "radial" turbines are those which have no appreciable axial component of fluid velocity entering the rotor. Fig.l shows the fundamental 90-deg IFR

�nward-flow radial" hence abbreviated to IFR.


Fig. 3 Mixed-flow "Deriaz" hydraulic turbine rotor with

adjustable blading (Ns = 220)

turbine geometry involved, as contrasted with a cantilever radial turbine (which has blades rather similar to those of low-specific-speed axial turbines).

Reference (.�) brings out very clearly the low ratio of blade height to disk diameter which is optimum for low-specific-speed axial turbines. When these low blade-height ratios are utilized, the flow-path efficiency is quite independent of whether the meridional flow at rotor entrance is axial, radial or mixed; thus a cantilever radial turbine of low specific speed, such as appears in Fig.l(a), 4 could be expected to produce the same performance as its axial-flow counterpart, since the blade geometries would, for all practical purposes, be identical and the disk frictions similarly equal; fluid dynamics considerations do not then favor one sort of turbine or another, and matters of stress or flow-path convenience may be regarded as determinate. On the other hand, the axial turbine dominates the high-specific-speed regime, and there is no radial counterpart in general use.

Selection of the 90° IFR turbine for concentration of interest is based upon a number of practical considerations. Primarily, this rotor form has the highest structural strength, and in many compressible fluid applications - specifically in gas turbines -stress considerations are dominant; for equal specific speeds, the cantilever radial turbine is a much less favorable structure for high tip speeds.

4 Which would perform equally for radial outflow as well as inflow.

Fig. 4 Typical Kaplan turbine profile

The long history and variety of evolutions of turbomacbinery have left us with inconsistent and conflicting terminology. There are those who would call the 900 IFR turbine shown in Fig.l(b) a "mixed-flow" type in that the discharge from the rotor is axial even though the entrance is radial; whereas the cantilever type has the blade flow· path entirely radial. Somewhat arbitrarily, the author insists that the 90° IFR rotor illustrated is a "radial" turbine. R. Birmann (.2.) has written a number of papers on what he calls a 11centripetal11 turbine, which has a rotor system like Fig.2. The author would term this a "mixed-flow" type, since the meridional flow has both axial and radial components at the rotor entrance. Its counterpart in water turbines would be the Deriaz machine shown in Fig.3. (If this were not sufficiently confusing, Fig.4 illustrates a typical Kaplan turbine flow path in which the nozzle flow is radial, but the rotor flow is axial.) It should be noted that the mixed-flow rotors favored by Mr. Birmann have the same excellent structural integrity as the 90° IFR rotor, since the major blade elements lie along radial lines; his terminol�gy would cover any turbine in which convergence of the meridional flow path occurred; this can include geometries with specific speeds as high as any axial types, but the flow paths are scarcely to be described as 11radial.11

Fig.5 shows a typical high-head Francis-turbine flow profile, and selection of the 90° IFR turbine as being the geometry of primary interest immediately invites comparison with Francis turbines for water power service. Figs.6 and 7 show two extremes of the geometries that are found in

3

•


""

-

�

'

t

.. . �!le ;

WHllL PIT DRAIN

;•;�· -----

.: .. '-:: �·-.,.

,, .. "-· >'f) :::7 I =i :.•,··· :-:�:. 'J.�� .·!·'.

� �·� ·,;. ·� ·:_p:·: . � :.·· . , . ; ·;_.<> .•."'. • ��::I � ��-��-._,.;� I " : .•:

1li::: -..._ I �

"· . ..-1 . ---r----

· . .-.:

l'.•f., :::.-_:r •,::.� ·.; .. ·,

��NTROL � RANGE

-I

TAIL WATER D£PllE$SION Fl.OAT CONTROL

Fig. 5 Typical Francis turbine flow profile (Ns = 62)


Fig. 6 High-head Francis turbine flow profile (Ns = 62)

Francis-turbine designs, and it is evident that the blade forms of the high-specific-speed rotor bear little resemblance to Fig . l(b) and would have a poor structural integrity for high tip speeds . Also, it can be seen that the high-specific-speed water turbine has an outlet diameter greater than its inlet diameter, which is far from what is implied by the 900 IFR terminology. This suggests that the 900 IFR turbine may not be capable of covering the specific-speed range traditionally associated with Francis turbines, although, as Fig.5 shows, there are water turbines which, for all practical purposes, are identical in flow path to the 90° IFR concept.

In water-turbine practice, the 11degree of reaction, " which is reflected in the value of U/C0 at the best efficiency point, is ·a free variable, although there is a consistent trend toward higher values of U/C0 with higher specific speeds . Thus Fig . 7 shows a rotor of higher reaction than Fig . 6 . 90° IFR turbines have very little variation of reaction with specific speed (see the following section) and cannot cover as broad a range of specific speed as Francis turbines for this reason .

Fig. S(a) illustrates a 90° IFR rotor of modern

design which would be suitable for gas-turbine service at high tip speed and high temperature . For structural reasons, the rotor is unshrouded, and the back disk is deeply scalloped. The mating nozzle is shown in Fig.S(b). This nozzle provides for variations in blade angle, and represents laboratory equipment. Stage performance with this rotor is shown in Fig.9 . It was designed for Ns =

99, and this specific speed is seen to pass through the best efficiency zone of Fig.9.

Although the b�sic intent of this presentation is to describe current technology for a fairly restricted class of turbine geometries, it is important that the insights of the 11big picture" of reference (�) are not lost; to the extent found practical, parameters and symbolism are the same, and the characteristics of competitive flow paths are covered for orientation purposes .

HOW HIGH IS HIGH EFFICIENCY?

To a surprising degree, gas-turbine designers are unfamiliar with the accomplishments of water turbines ( and vice versa) . Furthermore, a great confusion has arisen as to just what is an "hon-

5


Fig. 7 Low-head Francis rotor (N5 = 160)

est11 efficiency. It is pointed out in reference (2) at some length that there are differences between total-to-total and total-to-static efficiency ratings. There seems to be a rather common attitude that the total-to-static rating with measured shaft power is a morally superior parameter since it is "conservative." Total-to-static efficiency has the fundamental flaw that a perfect isentropic machine so rated would not have 100 per cent efficiency unless its throughflow were zero. This is a logical absurdity, and it is further absurd to presume that the kinetic energy of the flow leaving a turbine rotor is necessarily lost or not otherwise useful; yet this is what the total-to-static rating really means, unless the machine is equipped with an exhaust diffuser and rated at the end of the diffuser. Properly, the total-to-total rating is rigorously correct when the turbine is rated for conditions at its rotor exit, but such an efficiency should always be accompanied by a statement as to the amount of residual kinetic energy in the exhaust flow. This is frequently expressed as a ratio of the exhaust velocity head to the total-to-total applied head ( C3/C0)2• If the turbine is to be rated with an

6

exhaust diffuser, then it is proper to use the total-to-static rating since, if the diffuser performs its function properly, there should be no measurable difference between total-to-total and total-to-static efficiency rated at the end of the diffuser.

For purposes of this discussion, a total-tototal rating must refer to an exhaust pressure corresponding to the stream ("static") pressure plus a dynamic pressure corresponding to the summation kinetic energy of the meridional velocity components (which are axial vectors in the geometries of int€rest). This is tantamount to assuming that the exhaust flow has no tangential coinponent or that any swirl energy would not be recoverable. In practice, swirl energy may also be recovered in diffusers or following stages, but the classification and generalization of design methods for turbines having appreciable amounts of recoverable swirl energy is too formidable a task for this presentation. Accordingly, there is a presumption in these arguments that, at the best efficiency points, the machines considered will have swirl-free exhaust flow (or nearly so). In all cases, quoted efficiencies are 11isentropic


Fig. 8(a) Model test 90° IFR rotor in rig (Ns =99)

COURTESY CONTINENTAL AVIATION

A.ND ENGINHRIN8 CORP,

)

Fig. 8(b) Adjustable nozzle for test rig

90" I. F. R. TURBINE PERFORMANCE

5f--��---flll:-::;;;:;::::;;;t��:,......."'-f�-t-'l\t�-t--t---;:;::;::;:::;;::::::-'( Ns•99l CORRECTED TO P • 14.7 Psi

T • 519 "R

0 00 U/Je -

300 400

Fig. 9

shaft power11 efficiencies, as defined in 11 Parameter Groups.11

The designers of water turbines having submerged rotors have long since recognized the importance of an exhaust diffuser which, in the terminology of that industry, is called a 11draft

700 800 900 1000

tube.11 Much attention is paid to attaining high draft-tube efficiencies, and the normal rating of a water turbine quotes efficiency on a total-tostatic basis at the end of the draft tube. It is therefore remarkable that both Francis and Kaplan turbines so rated have produced over-all efficien-

7


TWO STAGE AXIAL TURBINE PERFORMANCE Ns• too

30 CORRECTED TO P • 14.7 ��si.'-----�'J.-"7'-tio-=-�t-. T = 519 "R

COURTESY CONTINENTAL AVIATION AND ENGINEERING CORP.

� 7789 OUTPUT HEAD

(B TU/LB.)

200 300 Fig.10

cies of 94 per cent or slightly better . The best comparable compressible-fluid data directly available to the author are a total-to-static efficiency, without an exhaust diffuser, of a 90-deg IFR turbine which made 89 per cent at a pressure ratio of 6:1. This particular turbine had an exhaustenergy factor ( C3/C0)2 of 0 . 05, which would then give it a total-to-total efficiency of 93 per cent. 5 However, it is quite likely that, with an exhaust diffuser, this same turbine would have produced a total-to-static efficiency of 92 per cent. Fig.9 shows a performance map of a 90° IFR turbine which developed 93 per cent total-to-total efficiency without an exhaust diffuser.6 In three separate programs, the author has had direct access to authentic test data on 90° IFR compressible-fluid turbines with efficiencies above 90 per cent. It is no coincidence that this figure checks well with comparable water-turbine performance.

Very little has been published on the performance of the best compressible fluid axial turbines ( 1, 8). One difficulty is that the best machines have been designed for gas-turbine service where a high throughflow velocity usually is desired, and a large difference llUlSt then exist between totalto-total and total-to-static ratings without diffusers. Furthermore, there has been a concentration on minimizing diameter in aircraft gas tur-

5 Hamilton Standard Division, United Aircraft Corp. Data from UAC Research Laboratories. 6 Continental Aviation and Engineering Corp., Detroit, Mich.

8

400 (fps)

500 600 700

bines, which has tended to result in efficiencies somewhat less than might be expected at the corresponding specific speed. Refer to (£) re the "Specific-Diameter" influence. These circumstances, combined with security restrictions and some reluctance to release information, have provided very little published high-performance axial-turbine data. Nonetheless, the author has seen several instances of axial turbines showing total-to-total efficiencies above 90 per cent, and there is every reason to believe that the 94 per cent figure for radial turbines can be matched.

Emphasis is placed on these high-efficiency numbers, since, even in reference (£) there is a reluctance to state positively that such represents current state-of-the-art. Fig.107 shows a performance map of a two-stage axial turbine which did exceed 90 per cent, and Fig.117 shows a single-stage machine which made 90 per cent. It is noteworthy, in Fig.11, that a total-to-static efficiency of only 77 per cent would be implied if there were no exhaust diffuser, and the specific speed of this turbine lies within a range which would be reserved for a Francis configuration in the water-turbine tradition.

Controversy regarding total-to-total versus total-to-static efficiency ratings really can be resolved only in terms of functional analyses of the exhaust flow. In water turbines, where only single stages are used and the need for most efficient use of available hydraulic power is domi-

7 Continental Aviation and Engineering corp., Detroit, Mich.


7ttHt 7780

OUTPUT HEAD <BTU/LB)

CORRECTED TO P, • 14.7 psi li • 519 °R

COURTESY CONTINENTAL AVIATION AND ENGINEERING CORP.

SINGLE STAGE AXIAL TURBINE PERFORMANCE { N1 • 128)

(0

Fig.11

nant , it is natural to regard turbines without diffusers as essentially incomplete. Accordingly , although one might deduce that total-to-total efficiencies (rated at the rotor outlet) of 95-96 per cent have been achieved, this is properly regarded as of little significance, since compatibility with draft-tube flow is essential. A high total-to-total efficiency measured at the rotor outlet does not necessarily imply that the exit flow will diffuse efficiently. Fig.5 shows the flow path of a modern high-head Francis turbine designed for Ns = 62. Note the right-angle bend in the draft tube. Peak efficiency is 93 per cent.

Compres sible-fluid turbines may be required to provide a flow compatible with many arrangements (such as following stages , a jet nozzle festooned with structure, or a piping system catering more to space limitations- than efficiency) . In consequence, the motivation for exhaust diffusion as a standard rating procedure is not strong, and the tendency has been to pay insufficient attention to this matter. In many instances diffusers have been left off systems where the performance benefits would be substantial, and the result has been too much emphasis on reduction of rotor-exit velocities. As described in another section, high specific speeds require exhaust velocities which represent serious kinetic energy losses if not diffused efficiently.

The same line of reasoning leads to the conclusion that medium-to-high specific-speed turbines should be developed to have unifo.rm flow velocities at the rotor exit with little or no

swirl, and design methods which ignore exhaust flow can be quite wasteful. When diverging conical exhaust diffusers are used, some swirl in the fluid next to the outer wall can be helpful in improving performance. Such normally occurs in a nominally zero-swirl exhaust flow from a turbine rotor because the peripheral leakage always has a substantial tangential-flow component.

In comparing "best available" performance data of compressible and incompressible-fluid turbines, it must be recognized that specific cases have specific inhibitions on design configuration which may reduce performance. Reynolds-number effects may be prominent in either case, and Mach-number influences have first-order significance in compressible fluid-flow paths. Detailed analyses of the physics of boundary-layer flow show subtleties related to fluid properties to a degree that it might well be concluded that water and gas turbines would not show similar performances; but the recorded facts support the conclusion from simple flow theory to the effect that, for equivalent specific speeds, optimum specific diameters , and high Reynolds numbers, the best water and gas turbines have equivalent efficiencies. Furthermore, the "best available" data show total-to-total efficiencies of 90-94 per cent for specific speeds ranging from 60 to 600. This is in agreement with Fig.12 of reference (.£), noting that the text thereof allows for values 8 per cent higher than shown in that.figure.

As illustrated in Figs.9, 10 and 11, axial and 90° IFR turbines for compressible fluids have demonstrated total-to-total efficiencies above 90 per

9


PLOTTED POINTS 1.00 I. 90" l.F.R., O.• 0.Z9'

P,IP,•9.0 IAIRl

/

3 8 4 7 • '\ •5 6 \

2. AXIAL, D,_•0.42' P,IP, • 6.0 (AIR) .80

AXIAL v /1,2 3. FRANCIS (WATERJ T URBINE> /' 90" l.F.R.

4.90" l.F.R. P,IP, • 2.l !GAS> <FIG.9) oto.01r.60 /

TURBINES

��EU��

FUL (' s s ss s SS SI 90• 1.F.R. TURBINES 5. AXIAL, O.• 1.16

'

!AIR> VALUES OF N & s s S s S\S\\SS! FRANCIS

6. AXIAL (FIG. II l TURBINES (AIR) .40

7. KAPLAN ( WATER)

8.90" 1.F.R., 0.•0.625'

P,IP, • 6.0 !AIR) .20 9. FROM REF. 2

0

�t TOTAL EF F ICIENCY

Ns = NrV• H"4 •

10 100 SP ECIFIC SPEED - N,

1000

Fig. 12 Specific-speed characteristics - turbines (best current data for "submerged rotors"

cent, with 92-94 per cent being probably consistent with ubest availableu state-of-the-art. These values are entirely consistent with water-turbine performance.

HOW SPECIFIQ IS SPECIFIC SPEED?

Dr. Balje (.f) has given an extensive mathematical treatment to the specific speed (Ns) and specific diameter (Ds) concepts. It is presumed that this reference is available so that the mathematics are not repeated here.

For 90° IFR turbines it is helpful to factor Ns as follows :

The term

( 2)

is found to vary only over a small range for the complete spectrum of practica'1 90° IFR turbines at the best efficiency point if the best efficiency point occurs with zero exhaust swirl. Thus, in practice, at the best efficiency point :

0. 69 < ..!!... < 0 . 72 5 Co

�hydraulic-turbine practice, specific speed (Ns)1 is commonly quoted as (Ns)l

= N( HP)l/2/ Ht5/4. To convert (Ns)1 for water turbines to Ns, the following relationship may be used : Ns/( Ns)1

=

3/7J.tl/2.

10

or

( 3)

(It is to be emphasized that Ht is the total-tototal head, but V3 is the actual volume flow leaving the turbine).

It now becomes apparent that, to a close approximation, for 90° IFR turbines

N ac ( V 3 ) 1/2 ( 4) s ND)

( No such simplification would be possible if C0 were based on a total-to-static head) .

Analysis of a 90° IFR turbine on an isentropic basis ( which presumes zero exit swirl, shockless entry, no disk friction, and no leakage) shows that this ideal case should have U/C0 = 0.71. It is remarkable that real machines check so closely, and seems to indicate that the meridional flow path efficiency is very high. This conclusion and the data quoted are in disagreement with reference (10), which indicates that U/C0 is a variable related to over-all efficiency. The author1s data experience, from Ns = 30 to Ns = 100, shows no important trend in U/C0 at best efficiency, although efficiency does vary, as indicated in Fig.12. The evidence is that disk friction and leakage are the major loss factors in 90° IFR turbines.

To see the practical significance of equation ( 1) we write :

Since

v3 = c3A3 (presumes c3 is uniform) (5)

2 C0 = 2gHt (6)

N (, ) 1(2 N ( 2 ) 3/4 ( 7) s \

C3A3 CJ1'Z g 0

N s

1/2 2 1/2

= G3) (;�: ) , 2g) 3/4

, 8) 0

- 22.7 G:( (·tz2t (�J (91

1 -:-r72 for 90° IFR turbines 2

1/2 (C )1/2 (.A N2) 16 04 _]. -3-.

c u2 0 2 2 2

( 10)

Since u2 1T N D 3600

N s

1/2 1/2

271. 5 G:) ( :;) ( 11)

Since (c3/c0)2 represents the ratio of exhaust


1000

500

100

50

I =SPECIFIC SPEED I I _FUNCTION _ 90° I. F. R. TURBINES

,_____ u I c. • i12:

0 uJ LrJ -� a. If) !::! LL.. ---u --

-w a. -If)

,... I -"'

�z

i-------i----�

,_

� � � � o� --

___g,1.-

-- l----------l--

------

--

----"°

t � )i_ N5 = 271.5 (e. 2 � I 11 I ( 111 I I

---

-

2 (?-)=EXHAUST ENERGY

10 . 03 .o+ .Cl'.'i

I I oi I I FACTOR I I .10 .2.0 .30 .40 .50

Fig. 13

kinetic energy to total head, we can write: 2

'Jlt Zl + (�3) (12) l/s o

In gas-turbine practice, .2

O.O!J. < G�) < 0.30 (13)

2

Flow tends to be unstable with (��) ( O .O!J. ( l!J.)

Also, practical geometries generally yield A3

0.1 < - (0. 5 Ad

A3 c )'

Using 0 .1, ( c� = o.o!J. Ad ( 15)

N 38.7 s

Using A3

0.5, (:�)' 0.30 Ad

N l!J.2 s

Fig .13 plots

N, "} [(:J GJ] for U/C0 0.71

(applicable to 90° IFR turbines)

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2 3.0

2.8

2-6

2.4

2.0

a: w f-w :E "' a: � (/) (/) w a: f-(/) w 0 "' ...J ID '%"

=

�� <(

1.0

a.,. o:;

2.0

CENTRIF UGAL STRESS PAR AMETERS FOR RADIAL-ELEMENT BLADING

3. 0 4.0

Fig. 14

Noting that (�)

Since U/C0

D s

0.71 (a constant) 1

( 16)

( 17)

In 90° IFR turbines, specific diamete� is inversely proportional to specific speed.

From the foregoing line of reasoning, a state-of-the-art plot using available test data can be plotted as in Fig.12 . The envelope line represents 11 best available" performance of all types of turbines and, as stated previously, can be achieved entire�y with axial turbines . The limit line of 90° IFR turbines also is shown, and � bar chart indicates general ranges of applicability. Thus specific speed can define the range of applicability of 90° IFR turbines, and is " specific" to that extent. However, other turbine flow paths can be equally efficient for these same ranges. Although there are logical trends, a given specific speed does not abs olutely define rotor geometry (see Fig.19).

STRESS CONSIDERATIONS

Stres s patterns in 90° IFR turbines are quite complex, but may be analyzed by treating the main

1 1


IOOO I I I II � �SPECIFIC SPEED FUNCTION t- TYPICAL AXIAL TURBINES v-� ( u,.. ... (c)=- 0.47 _ II 0 95 i-----

II� -+-500

i---- __Eft-.---

� -1--.....

1--- 1----Ns

� --

SPEC If IC 1---SPEEll --1-- _,... -----1-- _y$-100 - 0$-= --

�

v------,_-

� -1--

� ) --� N5 -1s1 (�:J (A� - I

I I I ��0�-EXHAUST ENERGY FACTOR

0 .03 .04 .05 .10 .20 .30 .40 .50 Fig. 15

disk and exducer as separate, even if a one-piece construction is used. As Fig.8(a) illustrates, the exducer really is an axial-flow member and may be treated as such. Centrifugal stresses in axial blading may be related to the parameter A3N2 as illustrated in Fig. 14 and in the Appendix.

Main disk stresses are more complex, particularly due to thermal gradients. The deeply scalloped construction shown in Fig. 8(a) permits drastic tapering of the radial blades to hold down centrifugal stresses . It also serves to minimize thermal stresses (which can be very high in a full disk wheel). Use of these techniques permits tip speeds (U) of over 2000 fps with high gas temperatures, and many gas turbines have been built in the last decade with tip speeds of 1700 fps and 1650 F inlet gas temperature. However, it is necessary to cool the hub, since this zone is highly stressed. Failure to use hub cooling seriously limits the 900 IFR turbine for gas-turbine service, and this point has been overlooked in several engines using 90°. IFR stages.

Specific speed can be written in stress-limiting terms as follows (repeating equation 10):

or

'C3)1/2 (Al

2)l/2 N 16 . 04 / - -2- (10) s \

c0 u

N s

IA N2\l/2 1/2 � (c ) 16. 04 u c�

( 18)

In 90° IFR turbines, main disk stresses primarily are determined by the tip speed (U), and

12

2 exducer blade-root stresses by the factor A3N In gas-turbine practice, an upper limit value

of A�2 would be about 3.8 · 108, and a value of (U) of about 1800 fps is well justified. Using (C3/C0)2

= 0. 30, a value of specific speed is obtained of

N s

1/4 16 . 04 (. 30)

1800

128. 5 1 Note that Ns er u

8 1/2 (3.8 . 10 )

Since exducer and main disk represent separate structural problems, it often can be established that the use of high tip speeds to match high heads per stage reduces the value of specific speed which can be utilized. The numerical example is to illustrate an analytical technique rather than to set a finite limit.

Noting that (A3N2/u

2) = 57l(A3/Ad) (19)

Fig.13 may be used to solve equation (18).

AXIAL VERSUS RADIAL-STAGE LOADINGS

Although the many variables of detail design make direct comparisons of axial and radial turb ines difficult, some insight may be gained, noting that axial-turbine blade-root stresses in gas turbines also are directly related to the parameter A3N2 and disk stresses are related to UAR' where U is the tangential velocity of the blade AR roots. For efficient axial turbines, UAR/C0 � 0.47, which means that the roots run at 1 1 impulse1 1 conditions, or with some 1 1 reaction. 1 1

Equation (8) is valid for axial turbines and equation (9) may be rewritten as:

Using

Since

N s �c:r (:�:r c�) 12·)314

22•

1 Cf2

(:�:r G�

N s

Co 0. 47,

1/2 2 . 1/2

10.1 (:3) (;3\ )

o AR

(20)

( 21)

( 22)


0 10 'i>O eo 70 60 50 40

·-2

..!i R 3

0 9 8 7 6 �

4

3

z

I

and

/ / /

/ / / // / PRESSURE RATIO / / j LIMIT FUNCTION / v

�. Y •1.4 / I/ "'lr -o.so

/ � � /

\� � V-M,&1.0 � /

II / v / v / '(/

/ .04 v l,.,Y / / lllllN.\/ ><> / \_..,..,'/ > I// / \ // r-<c / /

v // /

�/ / /

M3•.70p � v

/ / /

� ----

; h EXHAUST ENE.RGY FACTOR � Co I I I I I

0 ·°"' .10 .20 .30 ."40 .�o

N s

Fig. 16

1T 2 Ad = A3 + 4 DR

181 (c3

)1/2 ( 1

)1/2

C A /A3 - 1 0 d

-

(24)

Equation (24) may be compared with equation (11)

Using 2 c3

0.5, c

-0

N = 134 s Fig.15 plots equation (24).

0.30

Comparing equations (21) and (10), it is fair to assume that , for a fixed design requirement, (c3/c0

)2, Ns' and A3N2 would be the same for either an axial or a 90° IFR turbine. In such cas e

I 16.04 u u = -- = 1. 5 AR l0. 7

�is ignores the difference between geometric and effective exhaust flow areas. The approximation is close enough for purpos es of this argument.

7Q•TORQU AT 8E$T EFFICl�NCV POINT

No= RPM AT Sf:.ST 1---\---1---+--+- EFFICIENCY POINT

00 1.0 N/No

2.0

Fig. 17 Comparison of axial and radialturbine torque characteristics

( Remember, U is the tip speed of the radial turbine and UAR is the blade-root speed of the axial turbine!)

This implies that the tip speed of a 90° IFR turbine must be 50 per cent higher than the blade-root speed of an axial turbine. In practice , this can be achieved with lower stres s es in the radial turbine! Accordingly , for equal specific speeds, the radial turbine can handle a higher head efficiently in a single stage.

In more general form: U (U/C0) radial

UAR = (UAR/c0) axial ( 25)

This is an obvious relationship, but the practical values are important. The comparison has been much obscured by failure to recognize the common factors established by Ns, (c3/c0)2, and A3N2• In other words, the comparison really is bas ed on main disk structural integrity.

As long as (c3/c0)2 is the same for all turbine geometries considered, the power output per stage can be higher for the radial turbine, since it can match a higher head. However, if disk stres s es to match a specified head are not critical , the turbine which can tolerate the higher

value of (c3/c )2 IllllSt have higher power. For • 0

thes e and many other reasons , generalities are dangerous . Convenient comparison equations have

13


COMPARISON OF AXIAL ANO 90• l.F.R. TURBINES

-- AXIAL TURBINE FROM FIG. I I

7ltHt/77e9 OUTPUT HEAD (BTU I LB. l

0

(2.60)

(1.84)

(i.4.3)

ROTOR SP:E�Tf.f B��E

�FFICIENCY = SPEED FACTOR 0.5 0.7� 1.0 l.Z5 1.5

Fig. 18

been presented for consideration of specific problems.

2 The (C3/C0) parameter ls important, since there can be no doubt that it can be larger for an axial turbine than for a 90° IFR turbine because of the meridional turning losses in the latter. In practice (c3/c0)2 = 0.20 seems to produce no measurable performance loss in the totalto-total efficiency of a 90° IFR machine, and the upper limit has not been explored in data available to the writer. Probably (C3/C0)2 = 0.30 is somewhat high for the 90° IFR flow path, whereas many axial gas turbine stages run at or near this value. If exhaust diffusion is necessary to achieve a high net total-to-static efficiency, values of (C3/C0)2 above 0.20 are questionable in either case.

The term "stage loading" has no generally accepted rigorous definition. Sometimes it refers to the head per stage, and sometimes to the horsepower. Thus, for equal available heads within single-stage capacity, the higher maximum Ns of the axial turbine implies a higher horsepower per stage. On the other hand, the 90° IFR turbine can handle a higher head per stage, so stage-loading comparisons can be quite ambiguous.

Another stage-loading criterion is pressure ratio, For equal inlet temperatures, higher pressure ratios are related to higher heads, and this favors the radial turbine. However, it ls easy to show that, for any class of turbine, increasing pressure ratios must mean higher relative Mach numbers, and there are certain limits entailed thereby.

14

For equal specific speed, (C3/C0)2, and pressure ratio, a radial turbine will have relative

Mach numbers equal to or lower than an axial turbine. Futhermore, relative Mach numbers tend to increase with increasing specific speed. It can be argued that a 90° IFR turbine is thus better suited to operation at high pressure ratios, and data are available showing efficiencies above 80 per cent at pressure ratios up to 20:1 at Ns = 30. Under these conditions, absolute tangential velocities of the gas entering the rotor are supersonic, but relative velocities throughout the rotor are subsonic. Also, converging nozzles are used, and gas acceleration to supersonic speeds occurs by free-vortex action or oblique expansion shock patterns in the nozzle-to-rotor clearance space. It is thus true that a 90° IFR turbine avoids supersonic turning passages at pressure ratios which would require supersonic turns in axial-flow paths. A few years ago this was important, and it could be claimed that 90° IFR turbines were superior at high pressure ratios, but is ls now well established that high-angle supersonic turning passages are at least as efficient as subsonic turns (provided an adequate supersonic design technique ls used). Accordingly, it ls the authoris conclusion that, for equal specific speeds, properly designed axial and radial turbines are equally capable of utilizing high pressure ratios per stage.

All forms of turbine have pressure-ratio limits imposed by the exhaust 11choking11 limit, which occurs when C3 approaches sonic velocity (for simplicity, only the no-swirl case is considered). This condition is expressed by the equation:

(;f which

pl P3

1 - 1/t it:.! Gj �

1-

reduces

CJ2

+

(��2

to:

.r-1 2 -2-M3

1 - ;)'-1 2 -2-M3

J'-1 2 2 M3

l - 3'-1 2 -2-M3

�-1 M 2 -2- 3

(26) l'-1 2

1 2 M3

1.. 3'-1

11t

( 27)

( 1 - "l'ftl

Fig.16 plots this function for J?t = 0.90, ·r= 1. 4 and M3 = 1.0 and 0.7. In practice, effective exhaust choking occurs at nominal values of M3


60 70 Ns 80 100 120

.� �-� �-� � (�}o• �-� �-� � ti

.16 �-� �-� �-� �-� � Fig.19 Influence of N5 and (C3/C0)2-on 90° IFR rotor profile geometry

equal to 0.7 or slightly higher instead of the ideal case of M3 = 1.0. It is seen that (c3/c0)2

has a first-order effect on pressure-ratio limits of single-stage, full-admission turbines, EXhaust swirl, if present, lowers the pressure ratios at choke.

Fig.16 also demonstrates that high pressure ratios tend to force the use of lower specific speeds, since, as illustrated by Fig.13, Ns follows the trend of (C�C0)2. This is an important case where the water turbine analogy breaks down.

As used herein, "choking" refers to a condition where further decrease in exhaust pressure produces no increase in output torque with exhaust conditions at or near zero swirl. In a plot like Fig,9, choking sets an upper limit on the ordinate parameter. The phenomenon � occur when rotor exit relative velocities (w3) are sonic, which means that c3 must be subsonic. However, when the turbine rotor is suitably designed, w3 may be supersonic, with efficient performance. In all cases, M3 �1.0 sets a design limit, since the rotor cannot then sense further decreases in exhaust pressure. In practice, boundary layer, wake, and distribution effects result in sonic velocity when

M3 = 0.7 for the ideal (no blockage) case.

OPERATING CHARACTERISTICS

Much confusion seems to exit regarding the off-design operating characteristics·of all turbines, and the 90° IFR class is no exception. Occasionally one or another particular design is claimed to have a "broader operating range," but the terminology is misleading.

Turbines using incompressible fluids can have their basic characteristics illustrated on single

maps, provided there is only one element of vari� able geometry, As soon as compressible fluids are used, only fixed geometry can be represented on a single map, and a three-dimensional plot is required for even a single element of variable geometry. The picture is further complicated by questions as to whether or not the exhaust swirl which may exist at off-design operation is recoverable. Diffusers can be designed which can recover a substantial portion of swirl kinetic energy. Again we must face the neces.sity of defining the exhaust flow path to present rational data.

If it is presumed that the exhaust-flow path is not capable of either recovering swirl energy or developing abnormal losses with swirl (as occurs with a converging flow path), some generalizations may be made. An axial turbine of fixed geometry operating at constant head has less variation of efficiency with speed than its 90° IFR counterpart, and this is true for either compressible or incompressible fluids. Fig.17 shows torque and power qurves for both types to illustrate this point. The linearity of the axialturbine torque curve is confirmed by a great deal of data, although supporting theory is lacking. The extent to which the 90° IFR torque curve lies below the axial torque curve is largely determined by the ratio of the mean effective diameter of the exducer blading to the outside diameter of the radial turbine rotor; the lower off-design torque is really due to the lower angular momentum of the fluid leaving the 90° IFR rotor when swirl is present.

On the other hand, fixed geometry axial and 90° IFR turbines using compressible fluid show a different trend with pressure ratio when both are

15


designed for the same best efficiency point. The best obtainable efficiencies at off-design pressure ratios are higher for the 90° IFR turbine, and· this is shown in Figs.9 and 11 . Again the reason relates to exhaust swirl, with internal flow compatibility also being involved. In effect, at off-design pressure ratios, both 90° IFR and axial turbines develop peak performance with some exhaust swirl , but the swirl energy is les s in the 90° IFR flow path. In this case, a small exducer mean diameter minimizes swirl energy losses .

From the foregoing, it can been seen that a "broader operating range" may be claimed for either type machine, depending upon the off-design variable. Fig.18 illustrates the basic trends in a single plot by over-plotting Figs.9 and 11.

With either radial or axial turbines, but particularly with axial turbines, exhaust diffusers capable of recovering swirl energy improve off-design performance. Similarly, following stages with blading insensitive to inlet angle of attack can recover exhaust swirl energy.

It was noted above that 90° IFR off-design performance is sensitive to the meridional-flow diameter ratio. Thus a 90° IFR turbine of a given specific speed may have various meridionalflow configurations of equal "best" efficiency, as illu.strated in Fig .19. The large-hub-exducer machine would behave very like its axial-flow counterpart, and 90° IFR turbines can have surprisingly different performance maps. On the other hand, single-stage axial turbines show an amazing similarity when their maps are reduced to common parameters. Contrary to widely held opinions, blunt versus sharp leading edges and de.sign-point relative Mach numbers have very little influence on performance deterioration at off-design conditions, if exhaust axial Mach numbers are below 0.7.

Figs.9 and 11 bring out clearly that the optimum values of U/C0 and UAR/C0 shift with pressure ratio in fixed-geometry turbines . Whether lines of constant U/C0 or lines of optimum efficiency are followed, the 90° IFR turbine shows les s variation of efficiency with pres sure ratio than does the axial machine. This trend is more marked at lower specific speeds.

INTERNAL FLUID DYNAMICS

Dr. Stepanoff (11) makes the following observation: "Considering the high degree of perfection of modern pumps, as demonstrated by pump gros s efficiencies of over 90%, it is remarkable that so little exact knowledge is available on the loss es of centrifugal pumps . '' For turbines, and

16

9 0° IFR turbines in particular, a similar statement is applicable. Traditionally, water turbines have been developed by long evolution of scale models, but the end products show strong evolutionary convergence between independent firms. 10° IFR turbines for compressible fluids were first evaluated by running compressors backward, and the results,10 showing about 90 per cent efficiencies, were generally disbelieved. It was not until later that the importa.nc.e of exducer design was appreciated, since designers were misled by the predictably small swirl los ses. However, the exducer flow strongly influences conditions at the rotor tip, and these los ses are significant. Also, the relative importance of internal flow losses with respect to disk friction and leakage at lower specific speeds often have been ignored or misunderstood (�).

It is significant to note that a one-dimensional analysis of an isentropic 90° IFR turbine with an infinite number of blades on a total-tototal basis shows that, for zero exit swirl and shockless rotor entry, U/C0 = 0.707. All data available to the author, which cover a wide range of specific speeds and best efficiencies, show U/C0 -- o . 71 as long as the rotor is capable of providing near zero swirl and uniform exhaust flow at the best efficiency point. This strongly suggests that the hydraulic efficiency of the main flow is very high. Surprisingly, the rotor internal flow path is not very significant as long as the ratio Cm2/C3 is greater than unity at the best efficiency point and the exducer has converging helicoidal pas sages of high solidity. Also, deeply scalloped wheels are at least equal to full disk wheels. This is a definite departure from waterturbine practice.

Reference (12) represents a recent theoretical and laboratory study of radial turbines. It notably makes no attempt to draw on established turbine technology, but efficiencies of 90 per cent were achieved in an air turbine of Ns = 63. In spite of this fine performance, the author must take exception to portions of the design theory used, the salient point of which was a nonuniform { but swirl-free) exhaust velocity which tended to crowd flow toward the exducer hub.

In the reference (12) design analysis, only total-to-static performance was considered, and the possibility of exhaust diffusion was not mentioned. Furthermore, rotor internal-flow energy losses were taken as proportional to the relative velocities of the gas leaving the exducer. Inevitably, these mathematics must penalize turbines with high values of ( C3/C0)2 and A3/Ad. Both lO Reference (_!±) Fig.18, Yfs = 0.85, ( c3/c0)2 � 0 . 08 - 0.10 .


factors tend to raise exit relative velocities, and the total-to-static analysis treats (C3/C0 ) 2

as a direct loss. The section on " Efficiency" gives the arguments for a total-to-total analytical base, but the significant error in reference (12) is the assumption that internal flow losses are proportional to the square of the exit relative velocity.

Consistent with the observation that U/C0 =

0 . 71 at the best efficiency point, rotor-entrance relative velocities must be nearly equal to Cm2 . Exit relative velocities must represent the vector sum of c3 and the rotor tangential velocity at the exit point. This means that the ratio (w3/w2 ) = (w3/Cm2l must increase as the exducer radial station increases, and that the acceleration of the relative velocity must be more pronounced as the exducer tip is approached. Since a loss coefficient in ·a cascade decreases with increasing acceleration ratio, the assumption of a constant loss coefficient in reference (12) is not justified. The best test information available to the author indicates that rotor internalflow losses are nearly constant from exducer hub to tip, except for deviations due to leakage and spillover at the blade tips . Thus, on both theo retical and test grounds, the author must reject the analysis and conclusions of reference ( �) with respect to rotor losses.

Further support of the author ' s opinion can be found by noting that Fig.9 shows a 93 per cent peak efficiency for Ns = 99. Such performance at this speciftc speed would be impossible according to reference (12 ) . Also, proven Francis-turbine performance at much higher specific speeds demonstrates the invalidity of the reference (12) design methods, and emphasizes the point that a grossly nonuniform turbine exit flow would not permit efficient draft tube operation.

Although Fig.9 represents tests of a builtas-designed 90° IFR turbine with a design objective of swirl-free uniform exhaust flow, it is probably true that uniform exhaust velocity is not an absolute optimum. However, deviations from uniform flow are not justified in basic design theory , and the needs of a diffuser or following stage must influence any empirical corrections. The importance of such corrections becomes greater at higher specific speeds.

Another aspect of reference (12 ) is in complete agreement with the author ' s experience. This refers to turbine nozzles. In general, radial inflow turbine nozzle blading needs no profile camber, and most water turbines follow this practice . In other words, some curved nozzle vanes are very good, but are no better than straight vanes.

Radial clearance between nozzle and rotor is not critical if the centripetal vortex angle is above 10 deg . Kaplan turbines, with radial nozzles and axial rotors, represent an extreme case, but similar results are found in 90° IFR air turbines. With vortex angles below 10 deg, sidewall friction losses do become prominent with large clearances. Similarly, there is no "optimum" nozzle angle between 10 and 45 deg as long as a total-to-total analysis is used. The nozzle angle is determined by the ratio cm2/u, and cm2 is related to (C3/C0 )2, which is a basic parameter.

In the spirit of Dr. Stepanoff i s quoted comment, it must be admitted that an adequate description of 90° IFR rotor internal flow conditions which would account for coriolis effects and three-dimensional gradients is not known to the author, but it would seem to be of limited merit to spend the time and money to acquire that knowledge. The key factors lie in designing for

2 reasonable values of Ns and (c3/c0) and recog-nizing the following points :

(a) Straight nozzle blades of proper solidity have nozzle efficiencies of 97-99 per cent.

(b) Nozzle clearance is not critical. { c ) Rotor internal hydraulic efficiency is

94-97 per cent. (d) C3iCm2 should be between 1.0 and 1. 5. (e) Best efficiency can be obtained with

zero exhaust swirl, uniform exhaust velocity, and 0 . 69 < u/c0 <0. 725.

(f) Exducer blading should be of high solidity and match desired exhaust conditions.

With these simple rules and reasonable attention to avoiding unduly abrupt changes in flow path contours, high efficiencies will be obtained as predicted from Fig.12.

WHY USE A RADIAL TURBINE?

It has been stated positively herein that, at any design point, ,an axial turbine can equal or better the performance of a 90° IFR machine. Naturally, the question heading this section arises. Actually, there are cases where design-point performance of the 90° IFR turbine would be superior, and they relate to operation at very low Reynolds number with 30 < Ns (120. The high degree of reaction and reduced blade numbers of the 90° IFR flow path render it less sensitive to Reynoldsnumber influences, but very low Reynolds-number conditions are seldom found in compressible fluid design requirements for turbines.

The most common motivation for using 90° IFR turbines relates to production cost factors. Particularly in small .rotor sizes, it is very expen-

17


sive to maintain the profile accuracies of axialrotor blading compatible with high efficiency. To a surprising degree, 90° IFR turbine performance is ins ensitive to flow surface deviations as long as basic flow-area relationships are maintained . This, combined with the small number of blades required, permits relatively inexpensive fabrication for radial machines.

Evolution of automotive turbochargers over the past decade demonstrate conclusively the superior production cost feature of 90° IFR turbines, since virtually all such supercharger units in service now are of that type . A number of attempts to use axial turbines have been unsuccessful in this economic competition.

In larger rotors, the cost advantage of radial turbines is les s significant unless a single-stage 90° IFR unit can substitute for two axial stages. Forging or casting of large radial turbine rotors presents formidable production problems, but Fig.6 indicates that this has not inhibited the hydraulic industry.

In another section, the point has been made that, where pres sure ratio and/or flow rates representing off-design conditions are important, the 90° IFR turbine has a broader range characteristic. Therefore, when variable-nozzle stages are considered, a 90° IFR design can have significant performance advantages. A less widely appreciated factor relates to geometric difficulties in pivoting axial-flow nozzle blading. Efficient axial turbines of Ns) 60 normally use nozzle blades having high camber and some twist, seeking to generate free-vortex flow entering the rotor . When large changes in blade angle are required, serious geometric incompatibilities arise which distort the vortex flow. Radial nozzle vanes like those of Fig.8(b) introduce no such problem when they are pivoted. This is consistent with the use of radial inflow nozzles and axial rotors in Kaplan water turbines. (A similar arrangement should work with compres sible fluids.)

In many cases, the flow path of a 90° IFR stage can have mechanical design advantages in a turbomachine. This cannot be. generalized, but all too often it has been presumed that the us e of the radial flow path entailed a performance penalty ; such certainly need not be the case. On the other hand, multiple staging of 90° IFR turbines has never proven attractive within the author 1 s experience. A more natural arrangement is to use the 90° IFR stage as a first stage followed by axial stages. This reflects the trend toward higher specific speeds in the latter stages and permits a smooth meridional flow path.

In general, weight, bulk, and diameter are greater for radial than axial turbines, but the

18

differences are not as large as reputed, and mechanical design compatibility can reverse the difference for the complete turbomachine. In gas turbines, preferable combustor arrangements and/or reduction of stage numbers can favor a 90° IFR flow path.

The insensitivity of the 90° IFR turbine to flow-profile deviations also can be advantageous where erosion or deposit formation must b.e tolerated. This is particularly evident in automotive applications, where 11 dirty" exhausts are all too common. Turbochargers in diesel trucking service have an outstanding record in spite of these conditions.

CONCLUSIONS

Use of radial turbines in compressible-fluid turbomachines has been inhibited by lack of knowledge of structural and gasdynamic characteristics. In the specific-speed range from 60 to 100, peak efficiencies have been demonstrated in the 90-94 per cent regime. Furthermore, 90° IFR stages can handle higher adiabatic heads and pressure ratios efficiently than are pos sib le with axial turbines. The real criteria for s electing the basic flow path for a given turbomachine must depend upon cost, design compatibility, off-design performance, and other secondary factors. It is the author ' s belief that, although the radial turbine is not the best for all turbomachines, it often has been overlooked for applications where its use would be advantageous .

ACKNOWLEDGMENTS

The author wishes to acknowledge the helpful co-operation of the following persons and organizations:

1 Continental Avaiation and Engineering Corporation, Detroit, Mich., for the majority of the compressible-fluid turbine information utilized. Mr . E.H. Benstein of CAE has been especially helpful.

2 Hamilton Standard Division, United Aircraft Corporation, Windsor Locks, Conn., and Mr . S.G . . Best of that organization for co-operation and permis sion to publish certain performance information.

3 Mr . I.M. White, Vice-President and General Manager, The Pelton Water Wheel Company, San

Francisco, Calif . , for comment and as sistance in the hydraulic-turbine field.

4 Mr . J, Robert Groff, President and General Manager, The James Leffel & Company, Springfield,

Ohio, for as sistance and comments with respect to hydraulic turbines.


5 D�. O.E . Balje, Consulting Mechanical Engineer, Hollywood, Calif., for his continuing cooperation and commentary.

6 Messrs. A.H. Fink and W . C. Shank of H.J . Wood and Associates, west Los Angeles, Calif., for assistance in preparation of the paper itself.

REFERENCES

1.. "Hydraulic Turbines, " Marks " Handbook, 6th Edition , pp . 9-207 .

2 O .E. Balje, "A Study on Design Criteria and Matching of Turbomachines : Part A, " ASME 60-WA-

230 . 3 A.E. Aeberli, "Deriaz Type Reversible Pump

Turbine Installation at Sir Adam Beck - Niagara Forebay Pumped Storage Project, 11 ASME 58-A-77.

4- W.T . von der Nuell, "Single-Stage Radial Turbines for Gaseous S ubstances with High Rotative and Low Specific Speed, " Trans. ASME, vol. 74-, no . 4- .

5 R . Birmann, "The Elastic -Fluid Centripetal Turbine for High Specii'ic Outputs, 11 Trans. ASME, vol . 76, No. 2.

6 G .A . Bovet, "Modern Trends in Hydraulic Turbine Design in Eu.rope, " ASME 52-A-92.

7 F. Baumgartner and R. Amsler, "Presentation of a Blade-Des ign Method for Axial-Flow Turbines, Including Design and Test Results of a Typical Axial-Flow Stage, 11 ASME 59-GTP-4-.

8 L.B . Mann, A.H. Bell and G.W. Thebert, "Determination of Turbine Stage Performance for an Automotive Power Plant, " ASME 57-GTP-10.

9 L. Brown, "High-Head Francis Turbines for Mammoth Pool, 11 ASME 61-HYD-21.

10 O. E. BalJe, " A Contribution to the Problem of Designing Radial Turbomachines, 11 Trans. ASME, vol. 74-, no . 4-.

11 A. J. Stepanoff, " Centrifugal and Axial Flow Pumps, 11 John Wiley &: Sons .

12 N. Mizaumachi, "A Study of Radial Gas Turbines , 11 University of Michigan Report UM IP4-76 ( translation).

APPENDIX

Centrifugal stress es in rotor blading with

ner . For a rotating blade,

s r

a = f ( r)

a P dr ( 28)

( 29)

Two forms of the blade-section-area function are commonly used. Highest structural efficiency is achieved by holding ar constant from the tip down to a �adius ( rx) where the desired or limiting stres s is reached. From this radius down to the root the section area is then increased to hold the stres s level constant .

w2 p [1 -(�fJ s - - - r 2 r - 2 g t

-w2

E. r 2 [1 - (:j 2] x

s - 2 g ln � r at

Adding equations

s (1 + ln ::) � 2 r 2) r 2g ( rt r

For the case of linear blade tapering,

a rt - r --- ( ar - at) + at rt - rr

Substituting and integrating, we obtain

( 30)

( 31 )

( 32)

( 33)

( 34-)

( 35)

( 36)

mainly radial elements, such as commonly found on Fig . 14- plots equations ( 34-) and ( 35) in convenient axial turbines, may be calculated in a simple man- form .

19


A3

Ad a a r at c 0 c 0 C3 cm2 cm3

Dz DR D s g H t

H s

� N

N s N 0

pl p3 P3s R

Re r r rt s r Tl

Ts3 u

UAR

y3 wz

20

NOMENCLATURE

turbine rotor exit area normal to meridional flow path - ftz

total disc area of blade section area blade section area blade section area

'1T z rotor - 4 Dz - ftz

normal to radial element at blade root - ftz at blade tip - ftz

isentropic spouting velocity - ft /sec (25H� \

absolute gas velocity at rotor exit - ft /sec

- ftz

meridional gas velocity at rotor inlet - ft 1sec meridional gas velocity at rotor exit - ft /sec outside diameter of rotor - feet hub diameter of blade root diameter of axial rotor -specific diameter (see Reference [z] )

acceleration o f gravity - ft/secz

feet non-dimensional

isentropic or hydraulic head across turbine stage , based on t otal pressures at both s tations - feet

head across stage based on inlet total and exhaust static pressure - feet

exhaust flow Mach number - non-dimensional rotative speed - revolutions per minute specific speed - non-dimensional rotative speed at best efficiency point - revolutions per mir · . '

stage inlet total pressure - psia

stage outlet total pressure - psia stage outlet static pressure - psia

ft- lbs gas constant of working fluid - lb 0F Reynolds number - non-dimensional radius of rotor blade root - feet radius of rotor blade tip - feet blade root stress - psi stage inlet total temperature - 0R absolute exhaust static temperature - 0R absolute rotor tip speed - ft /sec tangential velocity of blade roots of axial flow

rotor - ft/sec exhaust volume flow from turbine rotor - ft3/sec rotor inlet relative gas velocity - ft/sec

rotor outlet relative gas velocity - ft/sec W gas f low - lbs/sec

"(' ratio of specific heats - non-dimensional E) = P1/14 . 7 - non-dimensional

11'/s stage efficiency, based on inlet total and exhaust s tatic pressures - non-dimensional*

IJ'/t s tage efficiency, based on inlet and exhaust total

e =

.f' =

'I= T' = 0

uAR/co

A NZ 3

H s

WNZ

pressures - non-dimensional*

T1/519 - non-dimensional

specific weight of blade material - lbs/in3

torque lb-inches torque at best efficiency point - lb-inches rotative speed - radians/sec kinematic viscosity - ft2/sec

PARAMETER GROUPS

exhaust energy factor

rotor velocity ratio - radial

rotor velocity ratio - axial

centrifugal stress factor

rotor exhaust area ratio } for com-pressible fluids

RT )\ s3 exhaust Mach number

flow factor cs<e>\ S/lj --

z

A3N

/Y/ t

IY/s

/Ti t - 1 fl? s

blade stress parameter

550 (ou�put horsepower) w . H t

550 (output hbrsepower) W • H s

=� z[ {�)� .lo!_ / xf�:) ' 1 -Rlt[1

- �;�� ,. 15

N(y�\ H't �

* See "Parameter Groups"


Current Technology of Radial-Inflow Turbines for Compressible Fluids

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