ISSN 00406015, Thermal Engineering, 2015, Vol. 62, No. 5, pp. 329334. Pleiades Publishing, Inc., 2015.Original Russian Text E.V. Mayorskiy, B.I. Mamaev, 2015, published in Teploenergetika.

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Proven methods are presently available for aerodynamic designing of turbine blade cascades withsubsonic and supersonic velocities ([13] and someother works). However, no methods are known usingwhich cascades with transonic flow velocity at 2 0.91.1 could be designed in an efficient manner.With such outlet velocities, a crisislike growth oflosses is observed, which is due to the occurrence ofcompression shocks and flow separation zones.These phenomena are caused by an extremely intricate streamlining pattern, when there is a mixed flowmode on the profile suction side, i.e., when there arealternating sub and supersonic zones with a complexwave structure at their boundaries. Under these conditions, viscosity has a great effect on the current inthe external flow, and it should be noted that thestructure of shocks and rarefaction waves depends onthe interaction between the boundary layers andexternal flow [1, 2].

For reducing excessive flow expansion and compression shock intensity, it is usually recommended todecrease the suction side outline curvature in the outlet area between the throat and trailing edge (todecrease its skew angle) and even to make the suctionside outline rectilinear in the entire in the outlet area

between the throat and trailing edge or in its small section at the trailing edge [1, 4]. It is also known that theabovementioned flow worsening phenomena can beminimized by imparting an inverse (negative) curvature to the suction side outline in the outlet areabetween the throat and trailing edge [1].

Nonetheless, in designing a cascade the efficiencyof which does not degrade under transonic streamlining conditions, problems are encountered that havenot been resolved in principle. The intricate structureof such flow is poorly amenable to a numerical analysis. Therefore, the use of an experimental approachcan be helpful in solving the problem of perfectingtransonic turbine blade cascades.

It is exactly such an approach that was used foraerodynamically elaborating an aircraft turbines firststage rotor blade cascade (the full pressure ratio in thestage is approximately 2.6). The flow parameters forthe blade middle section along the radius are as follows:the inlet angle 1 = 41, the outlet angle 2 = 28.9, and2 1. Initial cascade 1, which was designed accordingto the method suggested in [5] (Fig. 1a) had the following geometrical parameters: the chord b = 36.4 mm, thethickness c = 6.4 mm, the leading and trailing edge

Aerodynamic Development and Investigation of Turbine Transonic Rotor Blade Cascades

E. V. Mayorskiya and B. I. MamaevbaMoscow Power Engineering Institute National Research University, Krasnokazarmennaya ul. 14, Moscow, 111250 Russia

bSiemens, Bolshaya Tatarskaya ul. 9, Moscow, 115184 Russiaemail: boris.mamaev@siemens.com

AbstractAn intricate nature of the pattern in which working fluid flows over transonic blade cascades generates the need for experimentally studying their characteristics in designing them. Three cascades havingidentical main geometrical parameters and differing from one another only in the suction side curvature inthe outlet area between the throat and trailing edge were tested in optimizing the rotor blade cascade for thereduced flow outlet velocity 2 1. In initial cascade 1, its curvature decreased monotonically toward thetrailing edge. In cascade 2, the suction side curvature near the trailing edge was decreased, but the section nearthe throat had a larger curvature. In cascade 3, a profile with inverse concavity near the trailing edge was used.The cascades were blown at 2 = 0.71.2 and at different incidence angles. The distribution of pressure overthe profiles, profile losses, and the outlet angle were measured. Cascade 1 showed efficient performance inthe design mode and under the conditions of noticeable deviations from it with respect to the values of 2 andincidence angle. In cascade 2, flow separation zones were observed at the trailing edge, as well as an increasedlevel of losses. Cascade 3 was found to be the best one: it had reduced positive pressure gradients as comparedwith cascade 1, and the relative reduction of losses in the design mode was equal to 24%. The profiles withinverse concavity on the suction side near the trailing edge were recommended for being used in heavilyloaded turbine stages.

Keywords: blade cascade, profile, suction side, curvature, concavity, transonic velocity, streamlining pattern,efficiency

DOI: 10.1134/S0040601515050080

STEAMTURBINE, GASTURBINE, AND COMBINEDCYCLE PLANTS AND THEIR AUXILIARY EQUIPMENT

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radiuses r1 = 2.4 mm and r2 = 0.35 mm, the relativepitch = 0.664, the blade inlet and outlet angles

= 47 and = 28, the effective angle =arcsin(a2/t) = 28.9, the skew angle = 17, and thewedge angle 2 = 14. The profile suction side in theoutlet area between the throat and trailing edge is madewith monotonically decreasing the curvature toward thetrailing edge, just as is recommended in [1, 6].

Cascade 1 made on a scale of 1.4 : 1 was investigated in the big wind tunnel available in the MoscowPower Engineering Institute (MPEI) Department ofSteam and Gas Turbines. The blade height is equal to70 mm. With 2 increased from 0.7 to 1.2, the Re number varied in the range (0.51.2) 106. In the experiment carried out at 2 = 1, the average relative error of

the loss coefficient = 3% (or at = 0.03, the absolute error 0.001). The angle 2 measurementerror is 0.5.

The obtained dependences for the profile loss coefficient and at 2 = 1 are shown in Fig. 2,and the dependences (2) and 2(2) at 1 = 41 areshown in Fig. 3. It can be seen that at 2 = 1 the cascade (see Fig. 1) streamlining pattern remains stable ina wide range of angle 1: a significant growth of lossesbegins at 1 < 32 (at the incidence angle larger than15), and it should be noted that a simultaneous

=t t b b1 2b 2eff

( ) 1 ( ) 2 1

growth of angle 2 takes place. Less efficient performance is due to an unfavorable suction side streamlining pattern (Fig. 4): it can be seen that the flow distribution curves where is the relative curvilinearcoordinate along the profile outlines, are characterized by essential stratification only at the inlet, and at1 = 29 the value of is significantly greater thanunity ( = 1.27 at = 0.47). However, the unfavorablestreamlining region is not very large, and at < 0.35the streamlining pattern is approximately the same fordifferent values of angle 1.

At 1 = 41, the decrease of with increasing 2 inthe range from 0.7 to 0.9 (see Fig. 2) can be attributedto a growth of positive gradients of on both sides ofthe profile [1]. This follows from an analysis of thedependence shown in Fig. 5a. It should bepointed out that at all studied values of 2 there are twodivergent sections on the suction side in the outlet areabetween the throat and trailing edge. At 2 < 1 the firstsection locates near the cascade throat ( = 0.22), andthe second one is in the trailing edge zone ( < 0.08).With increasing 2 at 2 > 1 the first divergent sectionshifts along the flow toward the trailing edge, and boththese sections are ended with compression shocks.This is clearly seen from the velocity distributions inFig. 5a. Here, the streamlining pattern is essentiallymore intricate than that obtained from calculations carried out according to the pseudoviscosity method [7](see Fig. 4a).

Thus, the suction side profile streamlining structurein the outlet area between the throat and trailing edge at2 > 0.9 consisting of two systems of shocks and of atleast two rarefaction wave systems, and transforming as2 increases determines the pattern of dependence(2) [1]. The compression shocks appearing at 2 > 0.9cause a crisislike growth of the loss coefficient from0.02 to 0.035 at 2 = 1 (see Fig. 3). Flow separation inthe trailing edge zone ( < 0.05) is not observed in this

( ) ,s s

ss

( ) s

ss

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r1 1

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10, 1/mm

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(b)

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Fig. 1. Investigated cascades and curvature distributions(x) on their profiles. (a) Cascade 1, (b) cascade 2,(1) profile suction side, and (2) pressure side. A is thethroat section point.

330 34 38 42 46 50

4

5

6

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30

32

34 1

24

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2, deg, %

Fig. 2. Influence of flow inlet angle on the characteristicsof cascades. (1) Cascade 1, (2) cascade 2, (3) , and(4) 2(1).

( ) 1

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AERODYNAMIC DEVELOPMENT AND INVESTIGATION 331

case. Here, at 2 = 1, the pressure ratio in the shock= 1.4, which is considerably smaller than its critical

value. The results of flow visualization by painting theblade surface also confirmed that the flow streamlinesthe profile without separation.

No essential changes occur in the outlet areabetween the throat and trailing edge in the range2 = 1.001.11 (see Fig. 5a). The flow becomes moreconvergent in nature, and the compression shock atthe trailing edge becomes even less pronounced (upto = 1.3). Therefore, the value of first decreasesto some extent and then approaches a stable value. As2 increases in this range, the angle 2 shows asmooth growth (see Fig. 3).

p

p

A drastic growth of was noted at 2 > 1.15. A morethan twofold growth of with a simultaneous increaseof angle 2 is connected with the occurrence of developed flow separation in the trailing edge zone on thesuction side ( 0.075): at 2 > 1.2, the ratio 2.3,which is greater than the critical value and confirmsthat there is flow separation.

Thus, the initial cascade version was found to be ahighly efficient one in the design mode and in case ofnoticeable deviations from it with respect to the valuesof 2 and 1 at 2 < 1.15 and 1 32.

The first attempt to improve the cascade wasaimed, first, at decreasing the angle 1b to some extentand, second, at redistributing the suction side outlinecurvature, mainly in the outlet area between the throatand trailing edge. It was expected that the latter measure would yield better streamlining of the profile inthe design mode with 2 = 1.

Cascade 2 and its parameters are shown in Fig. 1b. Itcan be seen that the suction curvature value adoptednear the trailing edge is somewhat smaller than it is inthe initial version. However, an extended section nearthe throat is available with constant curvature, the valueof which is larger than it is in the initial version. Thischange of curvature was made with a view to achievemore uniform distribution of velocity in the section with

= 0.200.12 by eliminating divergent flow in it (seeFig. 4a). The calculations of profile streamlining patterns carried out according to the pseudoviscositymethod confirmed that this effect indeed comes intopicture (see Fig. 4b). The parameters of cascade 2 are asfollows: b = 35.8 mm, = t/b = 0.677, 1b = 45, andangle = 19. The other geometrical parameters are thesame as in cascade 1.

The experimental dependences (1) and 2(1) at2 = 1 for cascade 2 are shown in Fig. 2. It can be

s p

s

t

0.7

2

8

4

6

0

0.8 0.9 1.0 1.1 1.2

32

38

34

36

30

1

2

3 45

2, deg

2

, %

Fig. 3. Dependences of the coefficient and angle 2 onthe flow outlet velocity 2. (1) , (2) 2, (3) cascade 1,(4) cascade 2, and (5) modernized cascade 3.

0.4

0.20 0.2 0.4 0.6 0.8

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0.20 0.2 0.4 0.6 0.8

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5

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6

s s

() (b)

Fig. 4. Velocity distribution over the profile of investigated cascades at 2 = 1. (a) Cascade 1 and (b) cascade 2. Values of 1, deg:(1) 29, (2) 35, (3) 41, and (4) 51, (5) calculation at 1 = 41, and (6) throat.

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pointed out in reviewing these results that, first, theeffectiveness of cascade 2 is close to the maximalvalue, and, second, that at incidence angles larger than15 (i.e., at 1 < 30) the level of losses in this cascadeis lower than it is in cascade 1. Thus, the changes madein the profile inlet section turned to be rational.

At 1 = 41, both of the blades have approximatelythe same efficiency in the zone of subsonic velocities;however, at the design value of 2, the level of wasfound to be by approximately 0.004 higher than it wasin cascade 1 (see Fig. 3). This growth of can beattributed to the distribution (see Fig. 4b): thevelocity variation pattern on the suction side in theoutlet area between the throat and trailing edge indeedbecame smoother; however, the outlet divergent section has a large extension = 00.1 (in cascade 1 suchsection has the extension = 00.08). In addition, adivergent section has emerged in the interprofile channel on the suction side ( = 0.250.30), which did notexist in cascade 1 with a small pressure gradient.

However, the main drawback of version 2 lies in thegeneral pattern of the dependence (2) in the zone oftransonic velocities (see Fig. 3) rather than in a somewhat increased level of . At 2 1, the cascade streamlining pattern is mixed in nature: sub and supersonicvelocities alternate near the throat and in the cascadeoutlet area between the throat and trailing edge (divergent and convergent flow regions, respectively). As arule, with such flow modes, the compression shockslocate on the profile suction side near the throat andedge, a factor that just determines the growth of energylosses [1]. It can be seen that losses grow intensely inmodes very close to the design one (at 2 > 1.03). Ananalysis of the distributions obtained in the experiments (see Fig. 5b) shows that, for example, at 2 =

( ) s

ss

s

( )s

1.071.11, transonic velocities appear in the channelon the profile suction side ( = 0.250.30), and thedivergent effect becomes more pronounced. Such aphenomenon was not observed in cascade 1. In the outlet area between the throat and trailing edge, the valueof at 0.13 has an increased level as compared withthat in the initial cascade, and the divergent regionoccupies approximately half of the suction side extension in the outlet area between the throat and trailingedge, which is unfavorable. In addition, the appearanceof the profile in the section = 00.03 confirmsthat there is flow separation at 2 > 1.07.

It should be pointed out that two fundamentallydifferent transonic cascade streamlining patterns areknown [1]. In the first one, there is no flow separationin the trailing edge zone. Such a streamlining patternis typically observed in cascades with a moderate orsmall skew angle . Although the value of increasesin cascades like cascade 1 in the range 2 = 0.951.05,the level of losses in them is on the whole is fairlysmall. The profile cascades similar to cascade 1 can bestreamlined efficiently enough in the rotor bladebucket at 2 1.1 (see Fig. 3). The second streamliningpattern, which is inherent in cascades with increasedvalues of angles , is characterized by developed separation extending along the flow, which emerges in thetrailing edge zone at 2 1. Such a streamlining pattern is accompanied by higher values of and by a crisislike growth of losses as in cascade 2 (see Fig. 3). Inparticular, in using cascade 2, a noticeable drop of turbine stage efficiency should be expected at 2 > 1.03.

Thus, the distribution of curvature over the suctionside that was adopted in cascade 2 did not yield a positive effect in the zone of transonic velocities at asomewhat higher value of . It was also determined

s

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0.4

0.20 0.2 0.4 0.6 0.8

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s s s

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7

Fig. 5. Velocity distribution over the profile at 1 = 41. (a) Cascade 1, (b) cascade 2, and (c) cascade 3. Values of 2: (1) 0.7,(2) 0.9, (3) 1.0, (4) 1.07, (5) 1.11, (6) 1.2, (7) calculation at 2 = 1.0, and (8) throat.

(a) (b) (c)

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that in the presence of compression shocks the negative effect could not be predicted or explained bymeans of optimization calculations carried outaccording to the method [7] that does not take theinfluence of viscosity into account.

The results of the performed investigations haveshown once more how much important is the way inwhich the curvature is distributed over the suction sideoutline [1]. For example, an attempt to increase thesuction side curvature in the throat zone in version 2resulted in an unfavorable distribution of velocity inthis region. At the same time, some reduction ofenergy losses can be achieved in this range of operatingmodes only by organizing a smooth distribution ofvelocity in the outlet area between the throat and trailing edge and decreasing the level of local velocities inthe trailing edge zone. This means that efforts shouldbe taken to decrease the suction side outline curvaturein the outlet section (up to introducing inverse concavity) with trying not to increase, at least considerably, the curvature in the throat zone. All the more so,the suction side curvature in the channel should not beincreased.

In the second attempt of improving the cascade,the main attention was paid to the design mode, inwhich some degradation in the efficiency of versions 1and 2 was noted. The objective of extending the rangeof working modes of operation with respect to thevalue of 2 was also set forth. It was recognized thatinitial cascade 1 was the best base for modernization.In so doing, the following constraints were fulfilled:the profile inlet part remains unchanged, the suctionside outline remains unchanged to the throat point,and the thickness of the new profile in its rear part(from the throat line to the edge) remains the same asin the initial profile.

Thus, the changes in the outline were made only inthe profile outlet part and primarily by altering the

suction side. In making changes to its outline in theoutlet area between the throat and trailing edge, wetook into account unfavorable velocity distributions incascade 1 in the sections = 0.180.15 and = 0.080.02 with divergent flow (see Fig. 5a). It was also takeninto account that the level of and the velocity distribution pattern in the trailing edge zone are almostindependent on the flow inlet angle (see Figs. 2, 4). Inview of this, the changes of suction side shape favorable at the design inlet angle give a positive effect alsoat other values of angle 1.

In view of what was said above, it was decided tomake the suction side section = 0.220.15 locatingimmediately after the throat with a somewhat increasedcurvature in order to eliminate the divergent zone in thispart. However, such a change could yield a negativeeffect in the trailing edge zone, in which the compression shocks might become more intensive. Therefore,inverse concavity was applied on the suction side nearthe trailing edge concurrently with increasing the curvature near the throat with a smooth transition to inverseconcavity (Fig. 6). Expectedly, such profile shape withinverse concavity in the suction side outlet sectionoccupying approximately onethird of its outline in theoutlet area between the throat and trailing edge shouldyield decreased positive pressure gradients at the edgeand exclude the possibility of flow separation due toincreased velocities on the suction side.

It should be pointed out that profile cascades withsocalled inverse concavity have been known sincelong ago [8]. As a rule, such profiles are used in nozzlevane cascades with the interprofile channels havingsome degree of expansion, which are designed forsupersonic outflow velocities [9]. The principles usedto develop the profiles of such cascades are based onthe conditions of interaction between the suction sideand compression shocks from the neighboring profile,and the inverse concavity on the suction side locates

s s

( )s

s

1 2

2

1

t

A

0.5 0 0.5

x

x

10, 1/mm

2 +

r 2

(a) (b)

Fig. 6. Profile rear part (a) and suction side outline curvature in the outlet area between the throat and trailing edge (b).(1) Cascade 1 and (2) cascade 3.

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close to the throat. Thus, these cascades differ essentially from modernized profile 3 both in the shape ofprofiles and in the profile development principles.

The adopted approach to profiling opens the possibility of radically changing the suction side curvature inthe outlet area between the throat and trailing edgewithout changing the suction side outline in the channeland without affecting the profiles entire inlet part.However, in order to retain the thickness of the profileoutlet part, it had to be duly increased on the pressureside (see Fig. 6). The maximal change of thickness thatin fact had to be compensated is 0.25 mm. With theadopted changes in the profile outlet part implemented,the wedge angle 2 decreased and the angle 2bincreased by approximately 2 as compared with theirvalues in cascade 1.

The streamlining calculation results showed thatthe adopted changes of the profile shape led, as shouldbe expected, first, to a growth of flow convergencedegree on the suction side downstream of the throatand, second, to a more pronounced divergence effectin the suction side outlet section and to a higher velocity in the pressure side outlet section (see Fig. 5c).However, the calculation carried out according to [7]does not take into account the viscosity effects, whichmanifest themselves primarily in the divergent sections. Therefore, under real conditions it can beexpected that the streamlining pattern would becomemore intricate and would even be qualitatively different from the calculated one.

Figure 5c shows the experimental dependences At 2 1 the divergent zone on the suction side

downstream of the throat ( 0.2215) is suppressed,and only one such zone at the trailing edge is noted( < 0.1). However, even at 2 > 1, positive pressuregradients in this zone are smaller than they were in theinitial cascade (see Fig. 5a). Only small changes of thedependence as compared with the initial versionsare noted on the concave side, which locate mainly inthe trailing edge zone: some growth of is noted in therange 0.750.95, and on the contrary, in the interval 0.951.0 the velocity gradients became somewhat smaller. However, an important thing is that theflow in the interprofile channels outlet part remainsconvergent in nature.

The obtained experimental dependences confirm the soundness of the approach used fordesigning the cascade: at the design value of 2 = 1,the value by which decreases as compared with theinitial version is 0.008, which is equal to approximately 24% of the loss coefficients initial value (seeFig. 3). An assessment shows that with such modernization of a number of cross sections along the bladeheight, the value of can be decreased by 0.50.6% on

the average. As a result, the efficiency of a particularturbine stage can be increased by 0.20.3%.

At the same time, it should be pointed out thatoptimization matters remained beyond the scope ofthe performed investigation because only one fundamentally new version of the profile outline was considered. Therefore, a positive result from the viewpoint ofthe fundamental approach to profiling has beenobtained. Possibly, with some correction of theadopted shape of modernized profile 3, a more substantial gain in efficiency could be obtained.

Thus, the performed experimental investigation ofturbine cascades intended to operate at transonic flowoutlet velocities and featuring high efficiency hasshown that their further aerodynamic improvementcan be achieved using a new approach to profiling,according to which an inverse concavity of the suctionside outline is introduced near the trailing edge. Thisapproach can be recommended in designing heavilyloaded stages.

REFERENCES

1. M. E. Deich, Gas Dynamics of Turbine Machinery BladeCascades (Energoatomizdat, Moscow, 1996) [in Russian].

2. V. Kh. Abiants, A Theory of Jet Engine Gas Turbines(Mashinostroenie, Moscow, 1979) [in Russian].

3. B. M. Aronov, M. I. Zhukovskii, and V. A. Zhuravlev,Designing the Profiles of Aircraft Turbine Blades (Mashinostroenie, Moscow, 1978) [in Russian].

4. E. A. Gukasova, M. I. Zhukovskii, A. M. Zavadovskii,L. M. ZysinaMolozhen, N. A. Sknar, and V. G. Tyryshkin, Aerodynamic perfection of the steam and gas turbine blade systems (Gosenergoizdat, Moscow, Lemingrad, 1960) [in Russian].

5. B. I. Mamaev and E. K. Ryabov, Designing the turbineblade cascade profiles using the dominating curvaturemethod, Therm. Eng. 26 (2) (1979).

6. B. I. Mamaev, On selecting the blade profile suctionside curvature in the turbine transonic cascade, Izv.Vyssh. Uchebn. Zaved., Aviats. Tekhn., No. 2, 2932(2011).

7. A. B. Bogod, A. V. Granovskii, and A. M. Karelin,Achieving better accuracy and shorter computationtime in numerically studying the flows in turbinemachinery blade cascades, Therm. Eng. 33 (8) (1986).

8. M. E. Deich and B. M. Troyanovskii, Investigations andCalculations of Axial Turbine Stages (Mashinostroenie,Moscow, 1964) [in Russian].

9. M. E. Deich, A. V. Gubarev, L. Ya. Lazarev, andA. Jachanmohan, New nozzle vane cascades for ultrasonic velocities developed at the Moscow Power Engineering Institute, Teploenergetika, No. 10, 4152(1962).

Translated by V. Filatov

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