Experimental and Numerical Study of Transonic Cooled Turbine Blades

Transcription

1 International Journal Turbomachinery Propulsion Power Article Experimental Numerical Study Transonic Cooled Turbine Blades Andrey Granovskiy *, Vladimir Gribin * Nikolai Lomakin Moscow Power Institute, Moscow, Russia; niklomakin@mail.ru * Correspondence: rey.granovskiy@yex.ru (A.G.); gribinvg@mpei.ru (V.G.); Tel: (A.G.) This paper is an extended version our paper published in Proceedings European Turbomachinery Conference ETC , Paper No. 89. Received: 10 February 2018; Accepted: 30 May 2018; Published: 8 June 2018 Abstract: State---art gas turbines (GT) operate at high temperatures that exceed endurance limit material, refore turbine components are cooled by air taken from compressor. The cooling provides a positive impact on lifetime GT but has a negative impact on its performance. In convection-cooled turbine blades coolant is usually discharged through trailing edge leads to limitations on minimal size trailing edge, reby negatively affecting losses. Moreover, injection cooling air in turbine disturbs main, may lead to an additional increase in loss. Trailing edge loss is a significant part overall loss in modern gas turbines. This study comprises investigations unguided angle, trailing edge shape, cooling air injection through trailing edge on prile losses in cooled blades. Some vane blade cascades with different unguided turning angle two shapes trailing edges with without coolant injection were studied both experimentally numerically. This analysis provides a split losses caused by different factors, fers opportunities for efficiency lifetime improvements real engine designs/upgrades. In particular, it is shown that an increase in unguided turning angle use a round trailing edge result in a reduction loss in case a relatively thick trailing edge. Numerical investigation showed that an increase in unguided turning angle at initial transonic vane with a thick blunt trailing edge, without a change in or basic geometric parameters, allowed for a significant reduction prile loss by about 3 4% at exit Mach number M 2is = Experimental investigation four cascades with cooling air injection into through trailing edge allowed us to validate fact that in blades with a low level C pb < 0.1 at m = 0 a non-monotonic dependence change losses against relative cooling air mass m is observed. Firstly, cooling air injection into wake increases decreases losses; n losses start to increase with increasing cooling mass due to interaction between main cooling air (mixing losses), finally, due to cooling mass increase momentum increase losses are decreased. In blades with an increased level coefficient C pb 0.1 at m = 0 cooling air injection results in an increase in losses right from beginning injection n, according to cooling mass increase momentum rise, losses decrease. It is also shown that injection through trailing edge slot parallel to main leads to a neutral loss impact even a loss reduction in subsonic range a loss increase in supersonic range exit Mach numbers. Keywords: cooled transonic vanes blades; prile losses; unguided angle trailing edge (TE) shape impact; TE cooling air injection Int. J. Turbomach. Propuls. Power 2018, 3, 16; doi: /ijtpp

2 Int. J. Turbomach. Propuls. Power 2018, 3, Introduction Modern gas turbines operate at high temperatures that exceed endurance limit material, refore turbine components are cooled by air taken from compressor. The cooling provides a positive impact on lifetime a gas turbine (GT) but has a negative impact on its overall performance. The cooling air bypasses combustor refore provides less work in turbine than hot gas due to lower enthalpy. Moreover, in multistage turbines this coolant provides less work as it is ejected furr downstream path. However, injection cooling air has also a secondary effect an increase in aerodynamic losses. The aerodynamic losses in turbines have been intensively investigated since middle 20th century. Different types losses were identified (e.g., friction losses, trailing edge losses, secondary losses, etc.), several correlations were proposed for each loss type. The results se investigations have been published in numerous papers books, with [1 10] representing most frequently cited works. One source losses is cooling; its impact on turbine aerodynamic is twold. Firstly, cooling requirements lead to restrictions on blade shape, most important factor being limitation trailing edge size. To ensure cooling air injection, blade should have a slot or holes at trailing edge, refore trailing edge thickness cannot be reduced according to aerodynamic requirements. This feature causes additional losses. Secondly, coolant injection disturbs main may lead to increased losses. As coolant is mixed with main, se losses are called mixing losses. The models for se losses are presented in [2,5,7 13]. Many researchers investigated trailing edge losses without cooling air injection (e.g., [1 4,6,14 27]). Basically, se studies show that direct way trailing edge loss reduction is application thin trailing edges, which may be not applicable to cooled blades. However, few reports in open literature have already pointed out that trailing edge thickness reduction is not only way to achieve a reduction in trailing edge loss. Chao Zhou et al. [21] examined effect trailing edge thickness on losses in ultra-high lift turbine blades. These blades had a significant unguided turning angle that allowed a prile loss reduction even with a thicker trailing edge. Granovskiy et al. [22] reduced prile loss in a transonic vane by suction surface curvature redistribution. Vagnoli et al. [23] demonstrated evolution trailing edge as function downstream Mach number (M) on basis highly unsteady character near wake, which directly affects trailing edge. Yoon et al. [24] showed that for uncooled last turbine stages rotor trailing edge (TE) losses represent 44% total losses. For cooled turbine stage, figures are certainly different, but in any case fraction TE losses will be significant. In present work results a combined experimental numerical investigation effect unguided turning angle, TE shape, coolant injection through trailing edge on transonic cooled blade losses are presented. To underst effect unguided turning angle TE shape, four linear vane cascades three blade cascades were tested in a transonic wind tunnel over a wide range exit Mach numbers (M 2is = ). A numerical study se cascades has been carried out using commercial code Fluent. Four vane cascades consist blades having nearly same prile about same basic geometric cascade parameters but differ from each or as regards value unguided turning angle. Three blade cascades correspond to tip, mean, hub sections a real cooled blade with two kinds TE shapes. To underst impact trailing edge injection, one three vane cascades a blade cascade were tested numerically simulated at different rates injected air.

3 Int. J. Turbomach. Propuls. Power 2018, 3, Experimental Numerical Procedures 2.1. Experimental Setup Large-scale plane cascades were tested in a transonic wind tunnel. The air from atmosphere is sucked through test section, refore inlet total total temperature correspond to ambient conditions (typically P bar, T K). Inlet turbulence intensity (Tu) was maintained at level Tu = The exit Mach number (M 2is ) varies in range M 2is = , Reynolds number (Re = c 2is L/ν) d on prile true chord length varies in range Int. J. Turbomach. Re = ( ) 10 6 Propuls. Power 2018, 3, x FOR PEER REVIEW The air , injected through Reynolds trailing number edge (Re = c2isl/ν) supplied d by on aprile separate true chord high length varies line. For simplicity range Re = ( ) 10 this air is called cooling air, although 6. it does not have a cooling function in se tests. More details on this The air injected through trailing edge is supplied by a separate high line. For Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW 3 19 rig can besimplicity found in this [5,20]. air is The called mass cooling air, although injected it does air varied not have ina cooling range function 0 < m in < se 7%, tests. where m is ratio injected More , details air mass on this Reynolds rig can to be number found mainin mass (Re [5,20]. = c2isl/ν). The mass d on prile injected true air chord varied length in range varies 0 in < m The experimental < range 7%, where Re = ( ) m is cascades ratio consist injected air mass seven to nine main aeroils mass. with height h = 125 mm. Basic The experimental cascades consist seven to nine aeroils with height h = 125 mm. Basic geometric parameters The air injected cascades through are illustrated trailing edge inis Figure supplied 1. by a separate high line. For geometric simplicity parameters this air is called cascades cooling are air, illustrated although in it Figure does not 1. have a cooling function in se tests. More details on this rig can be found in [5,20]. The mass injected air varied in range 0 < m < 7%, where m is ratio injected air mass to main mass. The experimental cascades consist seven to nine aeroils with height h = 125 mm. Basic geometric parameters cascades are illustrated in Figure 1. Figure 1. Basic geometric parameters cascade. TE, trailing edge; Δ, width; L, true chord length; d2, Figure 1. Basic geometric parameters cascade. TE, trailing edge;, width; L, true chord length; trailing edge thickness; d1, leading edge diameter; w2, trailing edge wedge angle; w1, leading edge d 2, trailing wedge edge angle; thickness; β1m, intel metal d 1, leading angle; β2m, edge outlet diameter; metal angle; wcx, 2 axial, trailing chord length; edge t, wedge pitch; δ, angle; unguided w 1, leading edge wedge turning angle; βor 1m uncovered, intel metal turning; angle; a2, throat β 2m width;, outlet γ, stagger metal angle; C x, axial chord length; t, pitch; δ, unguided Figure turning 1. Basic angle geometric or uncovered parameters turning; cascade. a 2, TE, throat trailing width; edge; γ, Δ, width; stagger L, true angle chord length; d2, The true chord length (L) varies in range L = mm (L depends on type aeroil). trailing edge thickness; d1, leading edge diameter; w2, trailing edge wedge angle; w1, leading edge The boundary layer accumulated on walls test rig upstream a test section is cut f by wedge angle; β1m, intel metal angle; β2m, outlet metal angle; Cx, axial chord length; t, pitch; δ, unguided special expansion plates located near endwalls cascade. The cooling air is injected through turning angle or uncovered turning; a2, throat width; γ, stagger angle simple slot in trailing edge characterized by one parameter width, Δ. The The total true chord static length (L) varies distributions in range downstream L = mm (L cascade depends are on measured type aeroil). using a combined The boundary probe layer accumulated taps on located walls at distance test z behind rig upstream trailing a edge. test section The relative is cut value f by throat special width/ expansion distance plates between located near cascade endwalls measurement cascade. plane The (z/a2) cooling is in air is injected range through (depending simple slot on throat in size). trailing The edge positioning characterized measurement by one parameter width, planes is shown Δ. in Figure 2. The total static distributions downstream cascade are measured using a combined probe taps located at distance z behind trailing edge. The relative value throat width/ distance between cascade measurement plane (z/a2) is in range (depending on throat size). The positioning measurement planes is shown in Figure 2. The true chord length (L) varies in range L = mm (L depends on type aeroil). The boundary layer accumulated on walls test rig upstream a test section is cut f by special expansion plates located near endwalls cascade. The cooling air is injected through simple slot in trailing edge characterized by one parameter width,. The total static distributions downstream cascade are measured using a combined probe taps located at distance z behind trailing edge. The relative value throat width/ distance between cascade measurement plane (z/a 2 ) is in range (depending on throat size). The positioning measurement planes is shown in Figure 2. Figure 2. Measurement planes downstream cascade. 1, cascade; 2, combined probe; 3, static taps; 4, measurement plane (z, distance between cascade measurement plane). The combined probe comprises a needle probe to measure static, distant from it, a three-hole probe with a central hole for measuring total adjacent holes, Figure 2. Measurement planes downstream cascade. 1, cascade; 2, combined probe; 3, static Figure angled 2. Measurement at 45, for angle measurement. The probe can be positioned different axial planes, taps; 4, planes measurement downstream plane (z, distance cascade. between 1, cascade; 2, measurement combined probe; plane). 3, static taps; 4, measurement distributions plane (z, distance are obtained between by cascade traversing measurement probe along plane). cascade. The static The distribution combined probe in front comprises cascade a needle is probe measured to measure by static static taps located, at distant a distance from ( ) a2 it, a three-hole upstream probe with leading a central edge. hole The for static measuring distribution total along aeroil adjacent holes, angled at 45, on for trailing angle edge measurement. are measured The by probe static can be positioned taps at in different midspan axial section. planes, distributions are obtained by traversing probe along cascade. The static distribution in front cascade is measured by static taps located at a distance ( ) a2 upstream leading edge. The static distribution along aeroil on trailing edge are measured by static taps at midspan section.

4 Int. J. Turbomach. Propuls. Power 2018, 3, The combined probe comprises a needle probe to measure static, distant from it, a three-hole probe with a central hole for measuring total adjacent holes, angled at 45, for angle measurement. The probe can be positioned in different axial planes, distributions are obtained by traversing probe along cascade. The static distribution in front cascade is measured by static taps located at a distance ( ) a 2 upstream leading edge. The static distribution along aeroil on trailing edge are measured by static taps at midspan section. Traversing in spanwise direction showed that total static distributions are uniform within half a span around midspan position, refore at midspan can be considered as two-dimensional (2D). Traversing in tangential direction showed that is periodic over at least three aeroils at middle cascade. The accuracy total static (P) measurements was estimated as follows: δp %, δp %, δp 2 0.5% at M 2is = Moreover, before every test a calibration probes was performed. The mass rate injected cooling air is measured by an orifice. The total temperature injected air are measured in supply line, se parameters are practically same at injection point, since re are no cooling channels inside aeroil, just a hollow cavity with negligible losses. Based on se measurements, prile losses (Loos) are calculated using following expressions (see e.g., [12]): ( ) κ 1 [ ( ) κ 1 ] V 2 2is/2 = c p T 01 [1 P2 κ P ], V 2 cis/2 01 = c p T 0c 1 P2 κ P 0c. Loss = 1 V2 2 V 2 2is 1+m 1+mV 2 cis /V 2 2is (1) Here V 2is is isentropic velocity main air (i.e., velocity air would have after expansion to P 2 without losses), V cis is isentropic velocity cooling air, V 2 is actual velocity at cascade outlet, κ is ratio specific heats, m is relative mass cooling air. This expression is valid if total parameters cooling air are same at all injection points, refore is valid in cases with a single injection slot considered in this work. If total parameters at different injection locations are different, this expression should be modified appropriately. The velocity at outlet is related to total temperature by relationship ( ) κ 1 ] V 2 P2 κ 2 /2 = c p T 02 [1. (2) P 02 In cases without injection (m = 0) Equation (1) can be reduced to Loss = [ ( P01 P 02 ) κ 1 κ 1 ] / [ ( P01 P 2 ) κ 1 κ 1 ]. (3) In cases without injections, coefficient (C pb ) is calculated using following expression: C pb = P b P 2av P 02 P 2av. (4)

5 Int. J. Turbomach. Propuls. Power 2018, 3, Here Pb P2av averaged exit static. This parameter, Cpb, characterizes separation wake width, refore is correlated with losses as shown in [22]. The isentropic Mach number is derived from equation P01 /P = κ 1 2is M 1+ 2 κ κ 1. (5) 2.2. Numerical Model The numerical simulations were performed using commercial solver Fluent (ANSYS, Canonsburg, PA, US). Calculations were conducted over a period several years, so different versions Fluent were used. In most cases Fluent version 14.5 (ANSYS) was used. The calculations are done at mid span, is assumed to be 2D periodic in a spanwise direction. The unstructured numerical mesh was generated using commercial code Gambit. Figure 3a shows this mesh, which contains 50,000 cells. The mesh is stretched within boundary layer according to exponential law, value numerical accuracy criterium (y+) in first cell on wall is below 1. The mesh behind trailing edge Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW 5 19 is also refined to resolve shocks at supersonic exit conditions. In injection, exit exit part part slot included in domain, as shownas in shown Figure 3b. In calculations calculationswith with injection, isslot is included in domain, in Calculations without injections were done using two meshes: unstructured mesh described above, Figure 3b. Calculations without injections were done using(1)two meshes: (1) unstructured mesh where slot is present (2) slot. The latter has value y+ described above, where but not slotactive; is present butstructured not active;mesh without (2) structured mesh without slot.the in first cell on wall below 1, but has two times less cells outside boundary layer. Neverless, latter has value y+ in first cell on wall below 1, but has two times less cells outside boundary results obtained on both meshes are close each or in to following discussion only data layer. Neverless, results obtained on to both meshes are close each or in following for unstructured mesh are shown. discussion only data for unstructured mesh are shown. The simulated using k-ε turbulence model. The turbulence intensity The turbulence turbulencewas was simulated using realizable k-ε realizable turbulence model. The turbulence at inlet equals experimental value Tu = intensity at inlet equals experimental value Tu = Figure 3. View numerical grid around Cascade 1: (a) view two periodic pieces; (b) fragment at Figure 3. View numerical grid around Cascade 1: (a) view two periodic pieces; (b) fragment at trailing edge. trailing edge. In all cases considered, at cascade inlet is assumed to be uniform axial, with a In alltotal cases considered, at inlet outlet is assumed to be uniformis axial, constant temperature. At cascade cascade static specified with a constant total temperature. cascade outletexit Mach staticnumber). is specified (according to Equation (5) it is equivalent to At specified isentropic The no-slip (according to Equation (5) it is equivalent to specified isentropic exit Mach number). The no-slip conditions are applied on solid walls. The walls are considered adiabatic in calculations conditions are applied on cold solid The walls are considered adiabatic in calculations without without injection with airwalls. injection. injection with with cold air injection. In cases injection, total temperature mass injected air are prescribed at In cases with injection, total temperature mass injected air are prescribed at inlet slot. inlet slot. 3. Unguided Turning Angle 3. Unguided Turning Angle The influence unguided turning angle (δ) on losses was studied The influence unguided turning angle (δ) on losses was studied using using four vane cascades with about same basic geometric parameters except for angle δ. four vane cascades with about same basic geometric parameters except for angle δ. These basic These basic parameters investigated cascades are presented in Table 1. This shows that all parameters investigated cascades are presented in Table 1. This shows that all cascades have cascades have exactly same pitch to chord length ratio t/l = approximately same ratio trailing edge thickness to throat width d2/a2 = Table 1. Basic geometric parameters cascades. Vane β1m [deg.] β2e [deg.] t/l [-] δ [deg.] d2/a2 [-] ϒ[deg.] Δ/d2

6 Int. J. Turbomach. Propuls. Power 2018, 3, exactly same pitch to chord length ratio t/l = approximately same ratio trailing edge thickness to throat width d 2 /a 2 = Table 1. Basic geometric parameters cascades. Vane β 1m [deg.] β 2e [deg.] t/l [-] δ [deg.] d 2 /a 2 [-] Υ [deg.] /d 2 Cascade Cascade Cascade Cascade B 2e, outlet effective angle; deg., degree. Figure 4 shows measured prile loss coefficient as functions exit Mach number for Cascade 1 Cascade 4. There is a correlation between coefficient prile losses. In Cascade 1 (see Figure 4a), with practically a flat suction surface after throat (δ = 2.3 ), coefficient decreases from C pb = 0.1 to C pb = 0.49 over exit Mach number range At same time, prile loss increases from Loss = to Loss = At Int. MJ. 2is Turbomach. = 0.98 Propuls. Power 2018, coefficient 3, x FOR PEER reaches REVIEW minimum prile loss is at its maximum Figure 4b shows measured prile loss coefficient as functions exit Mach number exit for Mach Cascade number 4 with for Cascade a maximal 4 with unguided a maximal turning unguided angleturning δ = 15.9 angle. Inδ this = casein this case coefficient increases coefficient from increases valuesfrom closevalues to zeroclose to positive to zero values to positive C pb > values 0 Cpb prile > 0 loss goes prile down loss over goes down exit over Mach number exit Mach range number range Over range Over M 2is range = M2is = coefficient coefficient decreases decreases prile lossprile grows. loss grows. (a) (b) Figure Figure Measured Measured losses losses (Loss) (Loss) coefficient coefficient (C (Cpb). (a) Cascade 1 with δ = 2.3 ; (b) pb ). (a) Cascade 1 with δ = 2.3 ; (b) Cascade Cascade4 4with withδ δ = = Symbols. Symbols are are measured measuredvalues, values, curves trend curves trendlines. lines. The calculated structure (isolines Mach number) surface isentropic Mach number The calculated structure (isolines Mach number) surface isentropic Mach number distributions for Cascade 1 Cascade 4 are presented in Figure 5. The data, which correspond to distributions for Cascade 1 Cascade 4 are presented in Figure 5. The data, which correspond to same exit Mach number (M2is = 0.9), illustrate change structure with variation in same exit Mach number (M unguided turning angle. 2is = 0.9), illustrate change structure with variation in The Mach distributions in Figure 5a,b show that with an increase δ unguided turning angle. The Mach distributions in Figure 5a,b show that with an increase δ throat shock strength is significantly reduced. That is also seen in Figure 5c,d. As a result, throat shock strength is significantly reduced. That is also seen in Figure 5c,d. As a result, thickness thickness boundary layer on suction surface is reduced as well. In Cascade 1 on suction boundary layer on suction surface is reduced as well. In Cascade 1 on suction surface (SS) surface (SS) significant acceleration up to throat is terminated by a strong shock. After significant acceleration up to throat is terminated by a strong shock. After this shock this shock starts accelerating again up to TE, where local Mach number becomes Mis starts accelerating again up to TE, where local Mach number becomes Mis = 1.0. This is = 1.0. This is followed by a Prtl Meyer expansion around thick TE. This expansion fan on followed by a Prtl Meyer expansion around thick TE. This expansion fan on SS near TE is SS near TE is seen in Figure 5a. Thus leaves prile with a high velocity, which leads a decrease by up to Cpb = 0.4 an increase in prile losses up to Loss = in Cascade 1. A different pattern is observed in Cascade 4. On SS, after a weak second shock, continues deceleration up to TE downstream TE becomes higher than averaged static downstream Cascade 4. Therefore, coefficient becomes Cpb > 0 loss reaches a minimum at M2is = 0.9. Moreover, in Cascade 1 interaction

7 Int. J. Turbomach. Propuls. Power 2018, 3, seen in Figure 5a. Thus leaves prile with a high velocity, which leads a decrease by up to Cpb = 0.4 an increase in prile losses up to Loss = in Cascade 1. A different pattern is observed in Cascade 4. On SS, after a weak second shock, continues deceleration up to TE downstream TE becomes higher than averaged static downstream Cascade 4. Therefore, coefficient becomes Cpb > 0 loss reaches a minimum at M2is = 0.9. Moreover, in Cascade 1 interaction shock on surface (PS) with wake leads to a much thicker wake than in Cascade 4 (this feature can be seen in Figure 5a,b). At same exit Mach number, similar changes in structure were observed, also in medium range unguided turning angle (Cascades 2 3), although y are less pronounced. Similar variations structure are also observed at a lower transonic Mach number (M2is = 0.8). At supersonic exit Mach number influence unguided turning angle is reduced, structures in all variants are similar to those in Cascade 1. Similar experimental numerical results have been obtained for various cooled vanes blades with thick trailing edges over transonic range exit Mach number M2is. These results motivated a change design philosophy for cooled blade design at exit Mach number M2is = In particular, an aft-loaded approach with an increased value unguided turning angle is preferable to traditional approach, where for blades with thin trailing edges decreased values unguided turning angle have been recommended at transonic range. However, in this case it is necessary to check behavior friction coefficient to avoid separation, especially at a low Reynolds number. The friction coefficient has to be c f > 0. Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW 7 19 Figure 5. Comparison calculated structure in variants 1 4 at M2is = 0.9 (a) isolines M = Figure 5. Comparison const in Cascade 1; (b) calculated isolines M = const structure in Cascade in4; variants (c) isentropic 1 Mach 4 number at M 2is distribution = 0.9 (a) in isolines M = const in Cascade Cascade 1; (d) 1; isentropic (b) isolines Mach number M = const distribution in Cascade in Cascade 4; (c) 4. isentropic Mach number distribution in Cascade 1; (d) isentropic Mach number distribution in Cascade 4. The results coefficient prile loss measurements for all vane cascades listed in Table 1 are summarized in Figure 6. In order to make this chart easier to read, only trend lines are presented measured points are not indicated. Figure 6a shows that coefficient is a non-monotonic function exit Mach number in each variant it has a minimum. The point minimum moves from M2is = 0.98 in Cascade 1 (δ = 2.3 ) to M2is = 1.1 in variant 4 (δ = 15.9 ). The comparison coefficient for different variants shows that in transonic range (M2is = ) with a constant value relative trailing edge thickness (d2/a2 = 0.115) coefficient Cpb strongly depends on unguided turning angle (i.e., it depends on curvature SS after throat). The results coefficient prile loss measurements for all vane cascades listed in Table 1 are summarized in Figure 6. In order to make this chart easier to read, only trend lines are presented measured points are not indicated. Figure 6a shows that coefficient is a non-monotonic function exit Mach number in each variant it has a minimum. The point minimum moves from M 2is = 0.98 in Cascade 1 (δ = 2.3 ) to M 2is = 1.1 in variant 4 (δ = 15.9 ). The comparison coefficient

8 The results coefficient prile loss measurements for all vane cascades listed in Table 1 are summarized in Figure 6. In order to make this chart easier to read, only trend lines are presented measured points are not indicated. Figure 6a shows that coefficient is a non-monotonic function exit Mach Int. J. Turbomach. Propuls. Power 2018, 3, number in each variant it has a minimum. The point minimum moves from M2is = 0.98 in Cascade 1 (δ = 2.3 ) to M2is = 1.1 in variant 4 (δ = 15.9 ). The comparison coefficient for different variants shows that in transonic range (M (M2is 2is = ) with a constant value relative trailing edge thickness (d(d2/a2 2 2 = 0.115) coefficient CCpb strongly depends on unguided turning angle (i.e., it depends on curvature SS after throat). (a) (b) Figure Figure Measured Measured coefficients coefficients (a) (a) prile prile losses losses (b) (b) (trend (trend lines). lines). Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW 8 19 Thus, test data show that in transonic range (M2is(M = ) an increase in vane unguided turning angle causes an anincrease in in coefficient (it can (it can become become positive positive Cpb > C0) pb > 0) a reduction a reduction prile prile losses losses by 3 4%. by 3 4%. The losses in incascades were were also also numerically calculated at at exit exit Mach Mach numbers numbers equal equal M2is = M0.77, 2is = 0.77, 0.88, 0.88, 1.06, 1.06, respectively. Figure Figure 7 shows 7 shows comparison between measured calculated prile loss over a range unguided turning angles from 2 2 to 16.. There is a reasonable agreement between numerical measured data. Both experimental numerical data show that as unguided turning angle increases, prile losses decreases by 2 4% over exit Mach number range Figure7. Measured calculated prile losses vs. unguided turning angle (δ) M2is. M 2is Trailing Trailing Edge Edge Shape Shape Most Most vanes vanes blades blades state---art state---art cooled cooled turbines turbines have have thick thick trailing trailing edges edges to to allow allow injection injection cooling cooling air air into into path. path. The The shape shape trailing trailing edges edges may may differ differ depending depending on on applications but two main types are used: round trailing edges blunt trailing edges. Figure 8 shows blunt trailing edge real cooled blade.

9 Figure 7. Measured calculated prile losses vs. unguided turning angle (δ) M2is. 4. Trailing Edge Shape Int. J. Turbomach. Propuls. Power 2018, 3, Most vanes blades state---art cooled turbines have thick trailing edges to allow injection cooling air into path. The shape trailing edges may differ depending on applications applications but but two two main main types types are are used: used: round round trailing trailing edges edges blunt blunt trailing trailing edges. edges. Figure Figure 8 8 shows shows blunt blunt trailing trailing edge edge real real cooled cooled blade. blade. Figure Figure 8. The 8. The blunt blunt TE TE real real cooled cooled blade. blade. A simple A simple correlation correlation for for estimation estimation trailing trailing edge edge loss loss was was proposed proposed by by Flugel Flugel in his in his monograph monograph [19], [19], where where k isk anis empirical an empirical coefficient: coefficient: Loss TE = k d 2 /a 2, (k = ). (6) Numerous experimental studies confirmed primary importance trailing edge thickness, but at same time showed that k is not constant. Different researchers tested various turbine cascades with different geometric parameters different boundary conditions. They obtained a large scatter coefficient k values in range indicated in Equation (6). In current engineering practice for assessment subsonic s, k is ten assumed to be constant equals 0.18 or 0.2, but in transonic s this assumption may lead to high inaccuracy. The experimental investigation trailing edge shape effect on prile losses has been conducted on three plane cascades corresponding to tip, middle, hub sections transonic cooled blade. The main geometric parameters se cascades are shown in Table 2. Trailing edges tested cascades are quite thick d 2 /a 2 = priles have large unguided turning angles δ = Every experimental cascade had two set blades, one with round TE one with blunt TE. Figure 9 shows measured prile losses in Tip, Mean, Hub cascades in wide range exit Mach number M 2is = In general, experimental investigations showed that prile losses in cascades with round trailing edges are lower than prile losses in cascades with blunt trailing edges. For Tip cascade (Figure 9a) difference prile losses in cascade with blunt TE with round TE is δ Loss = 0.8 1%. This difference increases in Mean cascade to δ Loss = % in Hub cascade to δ Loss = 3 3.5%. The increase in prile loss difference in se cascades is connected not only to change trailing edge shape. The prile loss difference increases also due to increase in d 2 /a 2 ratio from 0.15 to 0.21 decrease unguided turning angle from 17.5 to 12.8.

10 tested cascades are quite thick d2/a2 = priles have large unguided turning angles δ = Every experimental cascade had two set blades, one with round TE one with blunt TE. Figure 9 shows measured prile losses in Tip, Mean, Hub cascades in wide range exit Mach number M2is = In general, experimental investigations showed that prile Int. losses J. Turbomach. in cascades Propuls. with Power round 2018, 3, trailing 16 edges are lower than prile losses in cascades with blunt trailing edges. Figure 9. Measured losses in cascades with different trailing edge thickness; round blunt TE. Figure 9. Measured losses in cascades with different trailing edge thickness; round blunt TE. Table 2. Basic geometrical parameters blade cascades. Blade Cascades β 1m [deg.] β 2e [deg.] t/l [-] δ [deg.] d 2 /a 2 [-] Υ [deg.] Tip Mean Hub The data presented in Figure 9 are overall prile losses. The trailing edge loss is about one-third overall prile loss [6]. Extracting this part from overall loss one can estimate influence trailing edge shape on pure TE loss. Using data in Figure 9, one can come to conclusion that blunt trailing edge practically doubles TE loss (i.e., coefficient k in Equation (1) should be increased by a factor two for blunt TE). Thus trailing edge shape has a significant effect on overall loss. This factor should be taken into account in analysis degradation impact on loss because not only size but also shape trailing edge will change depending on degradation blades in operation.

11 Int. J. Turbomach. Propuls. Power 2018, 3, Loss Reduction The simplest technical approaches are ten most complicated ones in practice. One simplest ways prile loss reduction is trailing edge thickness decrease. However, realization this measure is complicated enough, especially for cooled vanes blades with holes or slots for cooling air injection through trailing edges. Despite well-known alternative injecting cooling air through slots on surface near cutback trailing edge, cooling air injection through thick trailing edge still remains most popular measure. As decrease trailing edge thickness cooled vanes blades has limited potential, it is worth investigating anor way to obtain prile loss reduction in blades with thick trailing edges. As shown in [21], thick trailing edge in ultra-high lift blades with significant uncovered turning is not necessarily a disadvantage. Based on this observation experimental numerical results discussed in previous sections, authors performed loss optimization using unguided turning angle as a control parameter. The vane with thick blunt trailing edge investigated in [25] was taken as a reference. The main geometric parameters this vane are presented in Table 3. Then two new variants with same basic geometric parameters, except unguided turning angles, have been generated compared with original version. Based on se geometric data, reference geometry has been regenerated using an in-house blade generator. The main geometry parameters recreated vane are presented in Table 3, view this variant is shown in Figure 10. Two additional cascades have been generated using same basic geometric parameters but with higher unguided turning angles. The main geometry parameters se cascades are presented in Table 3 a view se geometries are shown in Figure 11. Table 3. Basic geometric parameters cascades. Vane Cascades β 1m [deg.] β 2e [deg.] t/l [-] δ [deg.] d 2 /a 2 [-] Υ [deg.] Cascade 1 (initial) Cascade Int. J. Turbomach. Cascade Propuls. 3Power 2018, 3, 90x FOR PEER REVIEW Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW Figure 10. Initial Cascade 1 with δ = 22 ( same as vane cascade from [25]). Figure 10. Initial Cascade 1 with δ = 2 ( same as vane cascade from [25]). Figure 11. View Cascades 3. Figure Figure View View Cascades Cascades Cascades 1, 1, 2, 2, 3 have have been been computed computed by by a 2D 2D Navier Stokes Navier Stokes code. code. Two Two cases cases with with exit exit Mach Mach number Cascades M2is 1, 0.82, (Re 32.3 have 10been 6 ) computed M2is 0.89 by(re a 2D 2.4 Navier Stokes 10 6 ) were considered. code. Two cases The isentropic with exit Mach number blade M2is 0.8 (Re ) M2is = 0.89 (Re = ) were considered. The isentropic blade number Mach number M Mach number 2is = distributions 0.8 (Re = 2.3 are 10 distributions are presented presented 6 ) M 2is in = Figure 0.89 (Re 12. = The 2.4 Mach 10 in Figure 12. The Mach 6 number ) were considered. distribution The for isentropic number distribution for Cascade Cascade 1 blade in Figure Mach 12a number corresponds distributions to one arepublished presentedin in[25]. Figure The 12. rapid Theacceleration Mach number on distribution front suction for in Figure 12a corresponds to one published in [25]. The rapid acceleration on front suction Cascade side is followed 1 in Figure by 12a strong corresponds deceleration to in one throat published region in before [25]. reaccelerating The rapid acceleration smoothly furr on side is followed by a strong deceleration in throat region before reaccelerating smoothly furr front downstream. suction side At is end followed by suction a strong surface deceleration accelerates in throat sharply regiondue before to reaccelerating downstream. At end suction surface accelerates sharply due to expansion expansion smoothly around furr downstream. around trailing trailing edge. At edge. This end This is is a typical suction typical feature surface feature for for leaving accelerates leaving blade, sharply blade, with with small due small unguided unguided angle. angle. Usually Usually it it leads leads to to large large negative negative values values coefficient. coefficient. Computed Computed values values coefficient coefficient prile prile losses losses for for se se cascades cascades are are presented presented in in Table Table In In Cascade Cascade 1 coefficient coefficient is is Cpb= Cpb= prile prile loss loss is is Loss 8.5% at M2is Loss = 8.5% at 0.8. The increase unguided turning angle to 8 in Cascade leads to M2is = 0.8. The increase unguided turning angle to δ = 8 in Cascade 2 leads to a flattening flattening deceleration deceleration zone zone on on suction suction surface. surface. In In Cascade Cascade 2 coefficient coefficient

12 Int. J. Turbomach. Propuls. Power 2018, 3, to expansion around trailing edge. This is a typical feature for leaving blade, with small unguided angle. Usually it leads to large negative values coefficient. Computed values coefficient prile losses for se cascades are presented in Table 4. In Cascade 1 coefficient is C pb = 0.27 prile loss is Loss = 8.5% at M 2is = 0.8. The increase unguided turning angle to δ = 8 in Cascade 2 leads to a flattening deceleration zone on suction surface. In Cascade 2 coefficient is C pb = 0.19 prile loss is Loss = 7.3% at M 2is = 0.8. A furr increase unguided turning angle to δ = 16.2 in Cascade 3 results in a nearly optimal velocity distribution on suction surface without any deceleration, Figure 12c. In Cascade 3 coefficient becomes positive C pb = prile loss decreases to Loss = 6% at M 2is = 0.8. The same calculations were conducted at M 2is = Computed coefficients prile losses are summarized in Table 4. Figure 13 shows computed prile losses over unguided turning angle δ range from 2 to 16.2 for two values exit Mach number, M 2is = 0.8 M 2is = This plot shows that prile losses in Vane with thick blunt trailing edge (d 2 /a 2 = 0.2) are decreased by 3.5 4% with an increase unguided turning angle from δ = 2 to δ = Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW Figure 12. Isentropic Mach number distributions in Cascades 1, 2, 3 at M2is = 0.8. SS, suction surface; PS, surface. Figure 12. Isentropic Mach number distributions in Cascades 1, 2, 3 at M 2is = 0.8. SS, suction surface; PS, surface.

13 Int. J. Turbomach. Propuls. Power 2018, 3, Table 4. Results calculations. Cascades [deg.] M 2is = 0.8 M 2is = 0.89 C pb Loss C pb Loss Cascade 1 (initial) Cascade Cascade C pb, Base coefficient. Figure 12. Isentropic Mach number distributions in Cascades 1, 2, 3 at M2is = 0.8. SS, suction surface; PS, surface. Figure 13. Computed prile losses vs. unguided turning angle. Figure 13. Computed prile losses vs. unguided turning angle. 6. Trailing Edge Injection This part paper presents results on effect coolant injection. The basic geometrical data are presented in Table 5. Note that, contrary to real engines with differences in densities due to temperature differences between coolant main, experimental tests reported here are performed with same medium, air, at same total temperature. This simplification was justified by some tests using CO 2 N 2 as coolant to simulate density effects, which did not show any noticeable effect. Similar results were already reported by Sieverding [13], Deckers Denton [7], working effectively with correct temperature ratios between coolant main, concluded that effect coolant total temperature ratio on loss was very small. Table 5. Basic geometric parameters cascades. Vane β 1m [deg.] β 2e [deg.] t/l [-] δ [deg.] d 2 /a 2 [-] Υ [deg.] /d 2 Cascade Cascade Cascade Cascade Three cascades, 1, 2, 4, are typical cooled vanes with axial in. These three variants have similar turning unguided angle but different trailing edge thickness. These parameters have a strong influence on losses structure behind blade (see, e.g., [22]). The slot size, refore injection parameters, also varied in se tests. Cascade 3 is a typical cooled blade with different turning a relatively low, unguided turning angle. At same time, trailing edge thickness belongs to same range as in vanes.

14 Int. J. Turbomach. Propuls. Power 2018, 3, To evaluate effect injection, delta between losses with without injection Loss was calculated: Loss = Loss with cooling Loss without cooling. The test results for all investigated cascades are presented in Figure 14. In Cascade 4 injection leads to additional losses at supersonic exit Mach number, while at M 2is = 1.05 injection leads to a small reduction loss. The latter can be explained by additional momentum that injection air with high velocity introduces to main. At supersonic conditions same amount injected air has a lower momentum than main, refore creates losses. In Cascades 1 2 losses without injection are higher than in Cascade 4, which is related to lower unguided turning angle a thicker trailing edge. At same time, effect injection is weaker in this case. In Cascade 2, even at M 2is = 1.22 additional losses are close to zero because shock losses are dominating in this case y are less affected by injection. In Cascade 1 re is a clear effect loss reduction in subsonic range exit Mach number. Considering that behavior loss in blade cascade 3 has a similar trend as in vanes, one could expect same trend for injection. The measurements confirm this expectation, this cascade also shows a loss reduction due to injection in subsonic range loss increase in supersonic range. Thus one can conclude that for cascades with a moderate unguided turning angle (δ < 15 ) TE thickness in range d 2 /a 2 < 0.2 injection through TE slot parallel to main leads to a neutral loss impact even a loss reduction in subsonic range a loss increase in supersonic range exit Mach numbers. Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW Figure 14. Loss change caused by injection cooling air (symbols: measured values, curves: trend Figure 14. Loss change caused by injection cooling air (symbols: measured values, curves: trend lines). lines). In general, In general, all cases all cases changes losses due to cooling air injection through TE TE into into can be can split be split into into two two groups. groups. The The first first group consists cascades with with a low a low level level coefficient Cpb < 0.1 large TE losses at m 0. Usually se are vanes blades with coefficient C pb < 0.1 large TE losses at m = 0. Usually se are vanes blades with low value unguided turning angles δ < In second group re are cascades with an low value unguided turning angles δ < In second group re are cascades with an increased level coefficient Cpb 0.1 low TE losses at m = 0. These are blades increased with level a large value unguided turning coefficient angles C pb δ > Figure 15 low demonstrates TE losses at two m possible = 0. These scenarios are blades with a large change value unguided losses versus turning change angles δ relative > 10. Figure cooling 15 mass demonstrates m. Blue two line possible corresponds scenarios to blades with low level Cpb < 0.1. First, cooling air injection into wake downstream TE increases losses decrease. Then losses start rising as cooling air mass increases due to interaction between main cooling air (mixing losses). Finally, with a furr increase in cooling mass a corresponding rise in momentum, losses are decreased. The brown line corresponds to blades second group. The cooling air injection causes an immediate increase in losses. Subsequently, increase in cooling

15 Figure 14. Loss change caused by injection cooling air (symbols: measured values, curves: trend lines). In general, all cases changes losses due to cooling air injection through TE into can be split into two groups. The first group consists cascades with a low level Int. J. Turbomach. coefficient Cpb Propuls. Power 2018, < 0.1 3, 16 large TE losses at m = 0. Usually se are vanes blades with low value unguided turning angles δ < In second group re are cascades with an increased level coefficient Cpb 0.1 low TE losses at m = 0. These are blades change with a large losses value versus unguided change turning angles relative δ > cooling 10. Figure mass 15 demonstrates m. Blue line two possible corresponds scenarios to blades with low level change losses versus C change pb < 0.1. relative First, cooling cooling mass air injection m. Blue intoline corresponds wake downstream to blades with low level Cpb < 0.1. First, cooling air injection into wake TE increases losses decrease. Then losses start rising as cooling downstream TE increases losses decrease. Then losses start rising as air mass increases due to interaction between main cooling air (mixing losses). cooling air mass increases due to interaction between main cooling air Finally, with a furr increase in cooling mass a corresponding rise in momentum, losses are (mixing losses). Finally, with a furr increase in cooling mass a corresponding rise in decreased. momentum, The brown losses line are decreased. corresponds The tobrown blades line corresponds second group. to blades The cooling second air group. injection The causes an immediate cooling air increase injection incauses losses. an Subsequently, immediate increase increase losses. in cooling Subsequently, mass increase momentum in cooling leads to a decrease mass in losses. momentum leads to a decrease in losses. Figure 15. Possible scenarios change losses vs. relative cooling air mass. Figure 15. Possible scenarios change losses vs. relative cooling air mass. Int. J. Turbomach. Propuls. Power 2018, 3, x FOR PEER REVIEW Calculations Calculations were were performed performed cold for main cold main cooling cooling conditions conditions (isormal (isormal conditions), whereconditions), boundary where conditions boundary correspond conditions to correspond experimental to conditions. experimental The blade conditions. surface The in se blade cases is assumed surface adiabatic in se cases without is assumed heat transfer. adiabatic The without heat drop transfer. overthe blade is maintained, drop over blade is mass at maintained, outlet is increased mass according at to outlet is amount increased injected according air. to The amount calculations injected without air. injection The were calculations performed over without a wide injection rangewere exit performed Mach numbers. over a wide Therange comparison exit Mach lossnumbers. calculations The with measurements comparison is presented loss calculations in Figure with 16. measurements There is a reasonable is presented agreement in Figure 16. data, There although is a reasonable calculations agreement data, although calculations somewhat underestimate losses in subsonic range somewhat underestimate losses in subsonic range overestimate m in supersonic range overestimate m in supersonic range with moderate exit Mach numbers. At high supersonic with moderate exit Mach numbers. At high supersonic Mach numbers, losses are underestimated. Mach numbers, losses are underestimated. It is necessary to mention that in supersonic range It is necessary position to mention shocks that is in sensitive supersonic to geometry range variations, position some difference shocks is sensitive in calculated to geometry variations, measured geometry some difference may lead into calculated differences in losses. measured Neverless, geometry may trends leadin toloss differences behavior inare losses. Neverless, captured correctly. trends in loss behavior are captured correctly. Figure 16. Measured calculated losses in Cascade 1 in cold conditions for uncooled priles. Figure 16. Measured calculated losses in Cascade 1 in cold conditions for uncooled priles. The structure at subsonic (M2is = 0.78) relatively high supersonic Mach numbers (M2is = 1.43) are shown in Figure 17, this picture demonstrate that numerical mesh used in this calculations is able to resolve wakes shock structures quite well. The picture for supersonic conditions also illustrates shock boundary layer interaction on suction surface, evolution this shock explains trend in loss curve in transonic range.