Shengchng ZHANG, Qinqin WANG, Xioming TAN,*, Jingzhou ZHANG

a College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

b School of Energy and Power Engineering, Beihang University, Beijing 100191, China

c AECC Sichuan Gas Turbine Research Establishment, Chengdu 610500, China

KEYWORDS Aerodynamics;Perforated rib;Squealer tip;Tip injection;Tip leakage flow

Abstract A novel perforated-rib configuration is proposed for controlling the tip leakage flow at the rotor tip of an axial turbine.Three perforated-rib layouts are considered, wherein a perforated rib is installed at(A)the Suction-Side squealer(SS-rib),(B)the Pressure-Side squealer(PS-rib),and(C) the additional squealer along the blade Camber Line (CL-rib).A numerical method is used to show how the novel rib layouts affect the aerodynamic performance of the tip leakage flow.Results show that the coolant jets issuing from the perforated-rib injection holes penetrate deeper into the tip clearance than those in the baseline squealer-tip case,and how the perforated-rib coolant injection affects the tip leakage flow depends strongly on the rib layout.The PS-rib and CL-rib layouts appear promising for controlling the tip leakage flow,playing a significant role in reducing the total pressure loss and improving the turbine blade’s isentropic efficiency.In particular, under an injection mass flow ratio of 1%and a tip clearance of 1%blade span,the PS-rib layout reduces the leakage mass flow rate by 27%and increases the isentropic efficiency by 1.25%compared with those in the baseline squealer-tip case.Meanwhile,the advantages of the PS-rib layout in tip leakage control are confirmed under small and large tip clearances.

1.Introduction

In the turbine section of a gas turbine, an appropriate clearance between the casing surface and the tips of the rotor blades is necessary to avoid direct interference during operation, but this tip clearance induces the primary flow to enter the gap and form a Tip Leakage Flow(TLF).The latter then interacts with the crossing primary flow near the blade Suction Side(SS)and rolls up to generate a highly complex flow structure,referred to as the Tip Leakage Vortex (TLV).The TLV dissipates a great deal of kinetic energy,which is highly detrimental to the aerodynamic performance of gas turbines1–3and the energy utilization efficiency of power and energy conversion systems.4–6.

Over the past decades, there has been extensive research into flow control for blade-tip leakage in gas turbines, and many control strategies have been proposed.One category is passive control methods (e.g., cavity squealers, tip winglets,curved tips, and casing treatments).Accordingly, Zou et al.7numerically studied the aero-thermal performance of a highpressure squealer tip and illustrated that the Scraping Vortex(SV)inside the tip cavity was one of the main flow mechanisms for controlling the TLF relative to the flat tip.In a low-speed turbine cascade test,Zeng et al.8also identified the existence of an SV with a relative casing motion by Particle Image Velocimetry (PIV).For the tip winglet scheme, Coull et al.9demonstrated that the tip winglet played an important role in reducing the driving pressure ratio across the blade tip,which was its primary mechanism for tip leakage control.Considering the role of winglet width, Lee et al.10reported that there was an optimal winglet width to achieve the lowest aerodynamic loss, and beyond this value, the aerodynamic loss changed slightly.Moreover, Zhou et al.11studied the aerodynamic performance of a complex winglet tip configuration with a pressure-side winglet,a suction-side singlet,a winglet cavity,and a gutter.Results found that this winglet tip performed even better than a squealer tip in terms of aerodynamic loss.For curved tip and casing treatment schemes, the design concept is to reasonably organize the flow inside the tip gap by modifying the blade tip and casing,thus reducing the heat load and leakage flow at the blade tip.For example,De Maesschalck12and Maral13et al.adopted the numerical optimization method to adjust the blade-tip shape, and their results found that an optimal blade-tip configuration could achieve a significant reduction in the blade-tip heat load(～18%reduction by De Maesschalck et al.12).Jiang et al.14,15proposed a bending clearance design method by combining blade-tip and casing treatments, and results showed that an optimal curved tip could reduce the total pressure loss by ～11%.Gao et al.16studied three casing layouts (step, trench, and arc casings)and their aerodynamic performances in an unshrouded turbine.They found that the arc casing layout performed the best at the design incidence,whereas the other two casings achieved the greatest increases in efficiency at the off-design incidence.After that, Wei et al.17estimated the aerodynamic performance of an axisymmetric casing contour in a two-stage turbine cascade, and found that this casing design could increase the overall efficiency by ～0.14%.Another category is active control methods (e.g., injection and actuators).For the coolant injection technique, the two most common schemes are blade tip injection and casing injection.For example, Behr et al.18demonstrated that casing injection at 30%rotor axial chord could achieve a 0.55% increase in turbine efficiency with an appropriate injection flow rate.Wang19and Gao20et al.found that tip injection had a significant impact on the TLV, and both the location and breakdown of the TLV were tightly associated with the injection mass flow rate.Regarding actuators, Bae et al.21adopted fluidic actuators to control the TLF and found that the loss reduction was ～30% of the introduced power from a steady directed jet actuator.Matsunuma22and Yu23et al.estimated the aerodynamic performance of Dielectric Barrier Discharge (DBD)plasma actuators in suppressing the TLF.Their results found that the mass flow rate of the TLF was significantly reduced due to a generation of plasma, and the blocking effect could be enhanced by increasing the number of actuators.To the best of our knowledge, cavity squealers and coolant injection are the most common of these strategies.

With a squealer tip, complex vortices are generated inside the concave cavity to dissipate fluid kinetic energy and block the over-tip flow, thereby improving the aerodynamic performance of the turbine blade compared to that with a flat tip;for example, Krishnababu et al.24found a reduction of approximately 8%in the leakage mass flow,and Zhou25found a decrease of 13% in the aerodynamic loss in a transonic turbine cascade.Because of the role of squealers in reducing TLF,many researchers have considered how the squealer geometry(e.g., height, width, SS, Pressure Side (PS), cutback, and location) affects the aerodynamic performance of the blade-tip flow.In this regard, Camci26and Lee27,28et al.performed experiments to study the effects of a partial squealer rim and its location on TLF, and their results indicated that the SS rim produced a less tip-leakage loss relative to that of the PS rim.Zhou and Hodson29performed numerical and experimental studies on the aerodynamic performance of squealer tip flow in a subsonic linear cascade by considering different rim widths and heights; results showed that reducing the squealer width helped minimize the tip-leakage loss because the vortex in the tip cavity was enlarged and the flow separation over the SS squealer became slightly stronger.Increasing the squealer height increases the scale of flow separation over the SS squealer but weakens the mixing between the cavity vortex and TLF,thus making the effect of the squealer height on the tip-leakage loss very complex.Senel et al.30performed a numerical investigation to show how the squealer width and height affected the aerothermal performance of an axial turbine blade with an E3 (Energy-Efficient Engine) design; they showed that increasing the squealer height or decreasing the squealer width reduced the TLF rate because of the increased vortical structures inside the tip cavity.Recently, Zou et al.31reported a detailed numerical investigation of the physical mechanism for how a squealer tip controls leakage loss, and they concluded that the scraping vortex formed inside the squealertip cavity played a dominant role in leakage-loss reduction.The casing’s relative velocity is an important factor in the scale of the scraping vortex, so it should be considered in an accurate evaluation of the aerodynamic performance of a squealer-tip turbine.They also identified an optimum squealer height whereby the scraping vortex is organized reasonably to provide remarkably effective control of the TLF.

With the use of air injection, because coolant jets act like flow obstructions to the tip channel flow, both the tip leakage and the interaction between the TLF and primary flow are weakened effectively.The blade platform’s thermal load is also alleviated effectively by the convective and film cooling effects.Therefore, active coolant injection plays a dual role in the aerothermal performance of a turbine blade.Couch et al.32studied the blowing effect of tip injection from purge holes,identifying that coolant injection had a strong blocking effect on the TLF when the tip clearance was small.Furthermore,from numerical simulations, Li et al.33showed that coolant injection could improve turbine efficiency by 0.41% under a small tip clearance; they suggested that this performance improvement was due to three main aspects: stronger obstruction,weaker mixing,and less entropy production in the tip gap.Rao and Camci34,35performed experimental investigations of an axial turbine tip desensitization by injection from a tip trench, considering mainly the effects of the injection flow rate and location.Niu and Zang36,37studied experimentally and numerically how the tip injection angle and location affected TLF characteristics, showing that coolant injection affected the TLF more when the injection holes were closer to the PS corner.Wang et al.38investigated the TLF for a turbine blade with a cutback squealer and air injection.Mercan et al.39experimentally investigated the effects of camberwisevarying tip injection on the tip leakage loss for a low-pressure turbine blade, for which triangular, reversed-triangular, and uniform injection patterns were considered.For a given mass injection from the tip, it was found that the reversedtriangular injection pattern reduced the overall loss the most.Gao et al.40examined the effect of tip injection on the aerothermal performance of the TLF for both flat- and squealer-tip unshrouded turbine blades; they concluded that the tip injection was dominant at a smaller tip clearance,whereas the cavity tip geometry was dominant at a larger tip clearance.Liu et al.41presented a novel method of using secondary flow injection from a slot over the turbine shroud;through a series of numerical simulations, they suggested that the injection velocity was the main factor affecting the turbine performance, with the injection yaw angle being another critical factor.Sarallah and Afshin42reported a numerical simulation of coolant injection from the casing to identify how injection parameters(i.e.,mass flow rate,angle,location,and diameter)affect the turbine performance.Wang et al.43performed a numerical study to show how the injection orientation and position affected the TLF of a honeycomb-tip blade, and the injection orientation was suggested as the main factor influencing the aerothermal performance.

To enhance the labyrinth-seal role of cavity squealers in TLF, El-Ghandour et al.44proposed a novel turbine blade tip shape─referred to as a triple squealer─for an axial flow turbine:two concave cavities are formed on the blade tip with the use of an additional or third squealer.Through a numerical evaluation, they demonstrated that the triple squealer was more effective than the double squealer in reducing the TLF.Park et al.45proposed a multi-cavity squealer tip by installing an additional rib on the blade tip, with a 90° angle relative to the blade chord;from experiments involving different installation locations and rib shapes, they showed that a multi-cavity tip achieved a less total pressure loss than that of a double squealer,especially when the rib was installed near the leading edge of the squealer cavity.Volino46investigated experimentally the characteristics of TLF for a new ribbed configuration in which the blade tip ribs were staggered with the endwall ribs.It was shown that this configuration reduced the strong tip leakage vortex when compared to a squealer tip blade;however, using ribs increased the total pressure drop.Arisi et al.47investigated the aerothermal performance of a transonic squealer-tip turbine blade with ribs and purge flow within the tip cavity, stating that ribs made the TLF in the tip passage more complex.Jiang et al.48used a numerical method to assess the aero-thermal performance of four rib layouts (full rib, SS half rib, PS half rib, and half rib in the rear squealer cavity).They suggested that the last layout provided the optimal overall performance in terms of blade-tip heat transfer and aerodynamic loss.More recently, Wang et al.49subjected a composite honeycomb tip in a turbine cascade to parameter optimization; it was shown that there was always an optimal cavity depth for any such tip structure, and the optimal structure reduced the tip leakage mass flow rate by about 16.81%.

Herein,we propose a novel perforated-rib configuration for controlling the TLF of an axial turbine blade.This concept evolved from the original ribbed tip configuration by integrating a coolant injection scheme.Considering that tip injection plays a stronger role at a smaller tip clearance, to make full use of coolant injection regarding leakage-flow reduction, this composite configuration uses a perforated rib.With this design,the distances between the injection holes and the casing surface are reduced effectively,which is expected to benefit the blocking effect of coolant injection on the TLF.The present work uses a numerical approach to investigate the aerodynamic performance of the TLF.Three perforated-rib layouts are designed, in which the perforated rib is installed at (A)the SS squealer, (B) the PS squealer, and (C) the additional squealer along the blade Camber Line(CL).The present study shows how the novel rib and its layout affect the aerodynamic performance of the TLF.

2.Computational methodology

2.1.Computational domain and model

As shown in Fig.1, the computational model has three subdomains: (A) the linear axial turbine cascade passage, (B) the coolant plenum, and (C) the injection holes.The rotor-blade profile used in the present study was obtained from that of Behr,50and its section profile is shown schematically in Fig.2.The blade span(H),blade axial chord(Ca),and cascade pitch (P) were 70 mm, 43.14 mm, and 46.54 mm, respectively,the absolute inlet angle(α1)was set as 17°,and the average outflow angle (α2) was approximately 130°.The present study involved the effect of the tip clearance (t), so three tip clearances were selected, i.e., 0.35 mm (t/H = 0.5%), 0.70 mm(t/H = 1.0%), and 1.05 mm (t/H = 1.5%).In the present numerical modeling, to reduce the number of computational grid points, the computational domain was selected as being one cascade pitch with the span of half a blade.

Fig.1 Schematic of computational domain.

Fig.2 Schematic of blade profile.

Herein, a novel perforated-rib configuration was proposed for controlling the TLF of an axial turbine blade.Four composite squealer-tip coolant injection configurations were designed,as shown schematically in Fig.3.Referred to as Case 1(see Fig.3(a)),the baseline configuration is the common one with a full squealer cavity and a row of injection holes arranged uniformly on the tip cavity floor along the CL; the squealer rim has a width (Ws) of 0.7 mm and a height (Hs)of 2.5 mm, and the diameter of the injection holes (D) is 1 mm.Regarding the perforated-rib configurations, the perforated design is effective for reducing the distances between the injection holes and the casing surface, and the present study involved three perforated-rib layouts.In what is referred to as Case 2 or the SS-rib layout (see Fig.3(b)), the perforated rib is installed at the SS squealer.In what is referred to as Case 3 or the CL-rib layout (see Fig.3(c)), the perforated rib is installed along the CL,similar to the triple squealer configuration used by El-Ghandour et al.44; in the present case, the tip cavity is divided into two parts.In what is referred to as Case 4 or the PS-rib layout (see Fig.3(d)), the perforated rib is installed at the PS squealer.In all of the perforated-rib layouts,the inner width of the rib cavity (Wr) is 1.5 mm, and the total width of the perforated rib is 2.9 mm.

2.2.Flow-similarity treatment in boundary conditions

Fig.3 Squealer-tip coolant injection patterns.

Table 1 Flow-similarity treatment of boundary conditions.

Fig.5 Computational grids.

Fig.4 Distributions of local static pressure coefficient.

Table 2 Results of grid-independence test.

Periodic boundary conditions were imposed on the two sides of the cascade passage.The coolant was introduced directly into the injection holes from a coolant plenum, and the coolant-to-mainstream Mass flow Ratio(MR)was selected as 0.50%, 0.75%, or 1.00%.In determining the mass flow ratio, we used a full-span blade cascade inlet, although a half-span zone was used in the numerical simulation.Referring to works by Zhou and Hodson29and others (e.g., Lee and Kim,51Cheng et al.52),TLF is susceptible mainly to the nearby flow in the vicinity of the blade tip, so only a half-span zone was used to evaluate the perforated-rib effects on the leakage-flow performance using a symmetry boundary condition at the hub of the computational domain,as used by Zhou and Hodson.29

2.3.Computational grid and scheme

Fig.6 Distribution of static pressure coefficient on casing surface with different numbers of grid points.

Computational grids were generated by the GAMBIT commercial software.As seen in Fig.5, the volume grids of the computational domain were created by stretching the twodimensional face grids along the blade-span direction.Therefore, except in the boundary-layer regions, computational meshes were dominated by tri-prism grids; in the boundarylayer regions, the heights of the first-layer grids were 0.001 mm, which met the requirements of enhanced wall treatment(Y+<1)in most areas.In order to ensure that iteration results were grid-independent, a grid-independence test was conducted,as reported in Table 2 and Fig.6.Fig.6 shows the distribution of the local static pressure coefficient on the casing surface for Case 1; the differences are mainly at the SS and trailing edge of the casing surface.With more than 4.5 million grid cells, the difference in the area-averaged Cpon the casing surface is only 0.1%,and therefore the computational domain was finally divided into approximately 4.5 million grid cells for Case 1.When the perforated-rib configuration was considered, approximately 6 million grid cells were used in the computational domain after the same grid-independence test.

Fig.8 Comparison of axial velocity at rotor exit.

Fig.7 Comparison of static pressure distribution on casing surface.

The Moving-Reference-Frame (MRF) method was used to treat the cascade flow as a steady flow.According to the research of Acharya and Moreaux,53the rotating force has less effect on the blade-tip flow and heat transfer relative to the relative motion,and it does not alter the flow pattern of the TLF.Therefore, the rotor blade was treated with translational motion based on the tangential velocity of the blade tip.Regarding the iterative process, the ANSYS-Fluent software was used to conduct numerical simulations, and the working fluid was regarded as a compressible ideal gas.To obtain an appropriate turbulence model, we selected three models (i.e.,(A) the Standard k-ε model (SKE), (B) the Spalart-Allmaras model (SA), and (C) the Shear Stress Transport k-ω model(SST)) for comparison with the results obtained by Behr.50These three turbulence models are all well-known from previous research on numerical prediction of the aerodynamic performance of turbine blade-tip flow,i.e.,the SA model by Zhou and Hodson,29the SST model by Zou,31Niu,37and Gao54et al., and the SKE model by Acharya55and Wang56et al.Fig.7 shows the static pressure distributions on the casing surface from the present numerical simulations and Behr’s experiment.In general,the three sets of numerical results agree well with Behr’s experimental data, although there are some local differences.From the pressure drop near the blade-tip PS,the flow contraction at the entrance of the tip clearance was under-predicted with the SKE model but over-predicted with the SA and SST models.However, the pressure contour lines(as indicated by the red arrows)show that the SKE model outperformed the SA and SST ones in predicting the TLF.Fig.8 shows the distributions of the axial velocity (Va) at the rotor exit.It is found from numerical modeling that the velocityrise and velocity-drop regions induced by the blade-tip secondary flow and wake vortices are in good agreement with experimental findings.Moreover,Cheng et al.57also illustrated the prediction accuracy of the SKE model for a squealer-tip flow with coolant injection.Results showed that the computed blade-tip cooling effectiveness agreed well with the experimental result, indicating that the numerical simulation reasonably predicted the mutual interaction between the coolant jet and the squealer-tip flow.Referring to the current validation and some previous numerical studies,55,56we finally chose the SKE turbulence model for the present study.

2.4.Parameter definitions

To evaluate the aerodynamic performance of the present perforated-rib layouts, we use two main characteristic parameters.Firstly, the total pressure loss coefficient (Ψ) is given by

where p, p*, and m are the static pressure, total pressure, and mass flow rate,respectively,and subscripts‘‘∞”,‘‘o”,and‘‘c”represent the cascade inlet,cascade outlet,and coolant plenum inlet, respectively.In this manner, the influence of the cooling jet is considered by a correction of the total pressure at the cascade inlet.

The other characteristic parameter is the thermodynamic isentropic efficiency of the rotor cascade with tip injection,defined in the same manner as by Behr et al.,18i.e.,

3.Results and discussion

3.1.Flow-field features

Fig.9 Flow patterns near blade tip with different injection schemes.

For the typical squealer-cavity case (Case 1), as shown in Fig.9(a), the primary flow is driven by the pressure difference between the PS and SS of the blade to enter the shallow tip gap and form a TLF.In the presence of the tip cavity, part of the TLF is sucked into the cavity, and the flow therein is highly energy-dissipating, thereby decelerating the TLF.Moreover,coolant jets with large blade-spanwise momentum build up discrete-jet columns to block the TLF.In this common injection scheme, because the distances between the injection holes and the turbine casing are relatively long, the coolant jets are affected more evidently by the mixing with the oncoming TLF, so their blocking effect on suppressing the TLF is limited.The mixing flow leaves the tip clearance from the SS squealer rim to form a TLV,beneath which is the Tip Passage Vortex (TPV) that originates from the separation of the oncoming casing boundary-layer flow and grows gradually along the blade SS.

In the SS-rib case (Case 2), because the distances between the injection holes and turbine casing are shorter than those in Case 1, coolant jets issuing from the injection holes penetrate deeper into the tip clearance.These discrete coolant jets are rarely mixed by the oncoming TLF, so the latter is obviously split into many branches, as shown in Fig.9(b).Compared to Case 1, the size of the TLV is reduced effectively,but because the coolant jets are positioned at the SS,they leave the tip gap quickly without diffusing adequately in the holepitch areas, so that between adjacent coolant jets, the TLF is not well blocked by the air injection.Therefore, we conjecture that the TLF will be aggravated in Case 2 compared to Case 1.

For the CL-rib case (Case 3), where the perforated rib is installed along the CL, as shown in Fig.9(c), the diffusion of the coolant jets is improved compared to Case 2.A similar situation is also identified for the PS-rib case(Case 4),where the perforated rib is installed at the PS squealer,as shown in Fig.9(d).In these two cases, the mixing between the TLF and coolant jets inside the tip cavity plays nearly the same role as that in Case 1.Moreover, the stronger coolant penetration plays a more prominent role in blocking the TLF,so the latter is suppressed more effectively and the TLV affects less fluid.

Fig.10 Distribution of dimensionless streamwise vorticity on blade crossing planes and limiting streamlines on blade suction side.

Fig.10 shows the streamwise vorticity (ωs)on five crossing planes (SP1-SP5), nondimensionalized by the axial chord (Ca)and primary flow inlet velocity(u∞).Additionally,the limiting streamlines (colored by the blade spanwise wall shear stress(τw,Z)) on the blade SS surface are shown to distinguish the influence areas of the TLV and TPV.Obviously, the streamwise vorticity of the TLV is generally stronger than that of the TPV, although it seems that the TPV affects a broader zone than that of the TLV.In Case 1,a large TLV is generated at the blade SS, this being because the TLF is affected less by the injection flow.When the injection holes are uplifted by applying the rib cavity, as seen in Figs.10(b)-(d), the sizes of the TLV and TPV are clearly diminished.Meanwhile,the limiting streamlines on the blade SS show that two main regions(Region A —TLV-affected area, and Region B —TPVaffected area) are generated by three characteristic lines (Line A —TLV separation line, Line B —TLV reattachment line,and Line C —TPV separation line).Comparing Cases 1–4 shows that Case 2 produces the widest TLV-affected area(Region A) and TPV-affected area (Region B) on the blade SS surface, whereas Case 4 is at the opposite extreme, this being related strongly to the leakage mass flow rate.

Fig.11 Local relative streamlines and dimensionless temperature contours on SP1.

Fig.12 Local static pressure coefficient on blade tip and SS surface.

Fig.11 shows the local relative streamlines and dimensionless temperature contours on the SP1 plane.It is found that the vortex dissipation and the obstructing effect of injection are the main flow mechanisms in the baseline case for suppressing the tip leakage.However, as the Scraping Vortex (SV) inside the tip cavity is destroyed by coolant injection from the cavity-floor injection holes, its labyrinth-seal role is also eliminated.In addition, because the tip cavity has a larger space than that of the gap entrance, the obstructing effect of the injection on the tip leakage flow will be less.For the SS-rib and PS-rib cases (Cases 2 and 4), since the injection does not directly impact the cavity vortices, the labyrinth-seal role of the SV is reasonably retained.It should be noted that the jet-obstructing impact of the SS-rib case is much smaller than that of the PS-rib case due to the insufficient diffusion of the SS-rib injection.For the CL-rib case (Case 3), its flow mechanisms in controlling the tip leakage flow differ from those of the PS-rib and SS-rib cases.As seen in Fig.11(c),the insertion of the CL-rib has a strong obstructing impact on the TLF.In the meantime, the CL-rib also inevitably eliminates the scraping vortex, which is similar to the baseline case.According to the above analysis, the flow mechanics of the four injection schemes for controlling the tip leakage can be summarized as follows:(A)baseline case—vortex dissipation and jet obstruction; (B) SS-rib case —vortex dissipation, SV-labyrinth seal,and jet obstruction; (C) CL-rib case —vortex dissipation,rib obstruction, and jet obstruction; (D) PS-rib case —jet obstruction, vortex dissipation, and SV-labyrinth seal.

Fig.12 shows the distribution of Cpon the blade tip and SS surface.In Case 1, a significant low-pressure zone is produced very close to the blade tip at the blade SS because of the separation of the TLF as it is ejected into the primary cascade flow.When the perforated-rib coolant injection schemes are used(Cases 2–4),it is found that the low-pressure zone is a little smaller than that in Case 1, which accords with the aforementioned flow-field features.Note also that the static pressure on the cavity floor in Case 4 is reduced dramatically relative to that in Case 1, which indicates that the scraping effect of the TLF on the blade tip surface is suppressed correspondingly.

Fig.13 Contours of turbulent kinetic energy on five slice planes.

Fig.13 shows the contours of the turbulent kinetic energy(k) on five slice planes.It is found that zones with high turbulent kinetic energy are located mainly outside the TLV, where the TLV intensively shears and mixes with the primary flow.In Case 1, as shown in Fig.13(a), a high-k zone forms in the squealer cavity, which is attributed to the intense mixing between the coolant jets and the oncoming TLF.Regarding the perforated-rib injection schemes, as seen in Figs.13(b)-(d),the turbulent kinetic energy inside the tip cavity is reduced significantly relative to Case 1,especially for the SS-rib case.In Case 2, because the SS coolant injection blocks the TLF the worst, the high-k zones caused by the TLV expand.However,when the injection holes are placed at the PS of the squealer rim, as seen in Fig.13(d), the production of turbulent kinetic energy is suppressed significantly because of the reduced leakage mass flow rate.

To evaluate further the aerodynamic performances of the present cases,we introduce the dissipation term(φ)of the fluid kinetic energy, which is defined as

where μ is the dynamic viscosity of fluid, and uirepresents velocity component.

The dissipation term is associated strongly with the fluid strain rate, which reflects the work done by the viscous force in resisting fluid deformation; fluid kinetic energy is converted irreversibly into heat energy, and this is one of the main reasons for an entropy increase.Fig.14 shows the distribution of the natural logarithm of the dissipation term (based on Yu et al.’s research23) on the 0.98H plane.Apparently, there are four main zones near (A) the blade leading edge, (B) the upper part of the SS cascade passage, (C) the blade tailing edge, and (D) the TLV-dominated region near the blade SS,in which high kinetic energy dissipation occurs.Compared to the baseline case, the perforated-rib coolant injection schemes mainly alter the kinetic energy dissipation in the TLVdominated zone near the blade SS.In particular, the kinetic energy dissipation in this zone is extremely high because of the strong interaction between the TLF and the primary flow.In Case 1,this strip-shaped zone of high kinetic energy dissipation,featuring high kinetic energy loss,starts at approximately 0.20Caand departs gradually from the blade SS when Ca> 0.5.With the perforated-rib coolant injection schemes,the strip-shaped zone is deflected a little toward the blade SS surface compared to Case 1,which is attributed to the reduced size and intensity of the TLV.

Fig.15 shows the local total pressure loss coefficient(Ψlocal)on the plane at 0.2Cadownstream from the blade trailing edge,where Ψlocalis calculated by using the local total pressure according to Eq.(3), and the abscissa axis ‘‘Pitch”represents the dimensionless distance within one cascade pitch.From this figure, the influence of the blade-tip secondary flow on the local pressure loss can be clearly identified.The primary factors contributing to the total pressure loss are the Tip Leakage Vortex (TLV), the Tip Passage Vortex (TPV), and the Wake Vortex(WV).Generally,the WV-induced total pressure losses in the four cases are comparable, and the TPV-induced total pressure losses in the baseline and SS-rib cases are somewhat greater than those in the other two cases.The biggest difference between the four cases is reflected in the TLV-affected region.In Case 1, due to the severe blade-tip leakage flow,its high-Ψlocalregion induced by the TLV is broader and closer to the right side (outside) than those in the other cases.Using the perforated-rib injection schemes can effectively minimize the TLV-induced total pressure loss, which is attributed to a reduction of the TLV strength.

Fig.14 Contours of turbulent kinetic energy dissipation on 0.98H plane.

3.2.Leakage flow performance

In this section,the effects of the injection scheme and injection mass flow rate on the aerodynamic performance of the TLF are analyzed in detail.Fig.16 shows the influence of the injection Mass flow Ratio (MR) on the tip leakage mass flow rate(mL) for the four injection schemes, where mLis measured from the entrance of the tip clearance.Generally, with an increasing MR, the blocking effect of the discrete-jet columns on the TLF is enhanced, so mLdecreases monotonically with an increasing MR.Regarding the efficacy of the perforatedrib coolant injection layouts in controlling the tip leakage, it is confirmed that Case 2 aggravates mLa little compared to that in the baseline case, in accordance with the aforementioned flow-field features.Under MR = 1.00%, Case 2 increases mLby ～4.5% compared to that in Case 1.When the perforated-rib coolant injection is located at the blade tip CL or PS, its role in suppressing the leakage flow is very pronounced.Meanwhile,the varying slopes of the mL-MR curves show that mLin the CL-rib and PS-rib cases reduce more rapidly with an increasing MR.Under MR = 1.00%, Case 3 reduces mLby ～16%, and Case 4 reduces mLby ～27%compared to that in the baseline case.

Fig.15 Local total pressure loss coefficient on X = 1.2Ca plane.

Fig.16 Effect of coolant injection scheme on tip leakage mass flow rate.

Fig.17 Effect of coolant injection scheme on total pressure loss coefficient.

In general, the overall total pressure loss includes the aeroprofile loss, secondary flow loss, and tip flow loss.Regarding how the tip injection scheme affects the total pressure loss,the differences among the present coolant injection schemes come mainly from the tip flow, such as the losses (A) inside the tip clearance and cavity and(B)from the shearing and mixing between the blade tip vortices(TLV and TPV)and the cascade passage flow.It is tough to quantify the losses produced in each fluid element inside the tip clearance and cavity.Since the tip leakage flow will eventually merge into the cascade flow, the total pressure loss at the cascade outlet is used to assess the aerodynamic loss,as seen in Fig.17.It is found that the variation of the total pressure loss coefficient agrees well with its distribution(Fig.15).When the coolant is ejected from the bottom of the tip cavity (Case 1), the coolant jets mix strongly with the oncoming leakage flow and form a large TLV, which causes great flow loss; therefore, Case 1 performs the worst in terms of total pressure loss.In addition, because both the TLV-induced and TPV-induced losses are reduced by the successful control of tip leakage, Case 4 produces the lowest total pressure loss coefficient among the four cases.Note that the total pressure loss in Case 2 is also reduced relative to that in Case 1, even though it produces the highest leakage flow rate; the main reason for this is that Case 2 produces the smallest TLV.Regarding the influence of MR, it is found that the total pressure loss coefficient increases with an increasing MR in all cases.However, the sensitivity of Ψ with a varying MR is quite different among the different coolant injection schemes:MR affects Ψ strongly in Cases 1 and 3 but weakly in Cases 2 and 4.Under MR = 1.00%, Case 4 reduces the total pressure loss by 0.74%, Case 2 reduces it by 0.60%, and Case 3 reduces it by 0.32% compared to that of the baseline case.Fig.18 shows the effect of the coolant injection scheme on the isentropic efficiency of an axial turbine blade.In all cases,the isentropic efficiency decreases gradually with an increasing MR.Moreover,all the perforated-rib coolant injection layouts (Cases 2–4) improve the isentropic efficiency of the axial turbine blade.Under MR = 1.00%, the perforated-rib layout increases the isentropic efficiency by 1.25% in Case 4, 0.43% in Case 2, and 0.88% in Case 3.

Fig.18 Effect of coolant injection scheme on isentropic efficiency of a turbine blade.

3.3.Effects of blade rotation and high-pressure condition

In this part, the impacts of the blade-motion type (translational motion and rotation) and the boundary condition(High-Pressure (HP) and High-Temperature (HT)) on the aerodynamic performances of the current injection schemes are also illustrated by the numerical method.

Fig.19 Effect of blade rotation on aerodynamic performance.

Fig.20 Effect of HP-HT condition on aerodynamic performance.

Fig.21 Contours of dimensionless temperature on casing surface.

Fig.22 Contours of dimensionless temperature on blade-tip surface.

Fig.19 shows the tip leakage mass flow rate and the isentropic efficiency under situations with blade translational motion and rotation, respectively.It is found that the blade rotation slightly increases(～5%)the tip leakage mass flow rate compared to that of the blade translational motion due to an increase of the pressure difference across the blade tip.Therefore, the isentropic efficiency is reduced (～0.5%) by the blade rotation.It should be noticed that the variation trends of mLand η do not change with the blade motion type, indicating that the flow mechanisms of the coolant injection in tip leakage control are similar between the translational and rotational blade motions.Fig.20 shows the tip leakage mass flow rate and the isentropic efficiency under the situation with HP-HT condition,where the total pressure and temperature of the turbine inlet are 1.8 MPa and 2100 K, respectively, and the total temperature of the injection is 900 K.It is also found that the variation trends of mLand η under the HP-HT condition are comparable to those in Fig.19, despite the fact that the tip leakage mass flow rate is approximately eight times of that in Fig.19.

3.4.Thermal performance

In this part,we also illustrate the thermal performances of the four injection schemes.Fig.21 shows the local dimensionless temperature contours on the casing surface with different injection schemes.In Case 1, because the injection holes are located at the bottom of the tip cavity, the coolant jets must travel far to reach the casing surface; thus, the impingement of the coolant on the casing surface is weakened,causing poor coverage of coolant there.Regarding the perforated-rib injection schemes, because the coolant injection holes are uplifted,the impingement distance between them and the casing surface is reduced, so the cooling protection near where the jets stagnate on the casing surface is improved.Of the three perforated-rib layouts,it is found that Case 2 shows the poorest coolant coverage on the casing surface, the main reason being that the coolant retention in the blade tip clearance is weakened because the cooling jets are entrained immediately into the TLV.When the perforated-rib injection holes are moved toward the PS (Cases 3 and 4), the coolant coverage on the casing surface is improved significantly.Fig.22 presents the local dimensionless temperature contours on the blade-tip surface.It is found that the film coverage areas of Cases 2 and 3 are smaller than that of Case 1, which is related to the locations of injection holes.While for the PS-rib case,since it produces the lowest tip leakage mass flow rate and its injection holes are situated near the gap entrance, the coolant injection can greatly lower the temperature of the TLF inside the tip cavity.Therefore,it is seen that Case 4 provides the best cooling protection to the cavity floor.It should be noted that Case 4 also has a disadvantage in cooling the pressure-side squealer rim, but this situation would be improved in an actual blade due to the presence of blade-surface injection holes near the blade tip and the inherent heat conduction effect of the blade material.

3.5.Effects of tip clearance

Tip clearance is an important factor in the aerodynamic performance of the rotor cascade.To verify further the effectiveness of the PS-rib configuration under different tip clearances,here for comparison, we use two other gap heights (t/H = 0.5% and t/H = 1.5%) as well as the corresponding baseline cases.

Figs.23(a)and(b)and the previous Fig.10(a)confirm that increasing the tip clearance increases the size of the TLV but decreases that of the TPV.Because the TLV- and TPVaffected areas are associated strongly with the corresponding vortex scales, it is found that the variation trends of Regions A and B are consistent with those of the TLV and TPV,respectively.Careful comparison between the PS-rib(Figs.23(c)and(d)) and baseline cases also shows that the PS-rib configurations produce a smaller TLV compared to that with the conventional squealer-cavity configuration, for either a small clearance (t/H = 0.5%) or a large one (t/H = 1.5%), which further demonstrates the effectiveness of the PS-rib design in restraining the TLF.

Fig.24 shows the development of the TLF and coolant injection near the blade tip for the baseline and PS-rib cases.Under a small tip clearance(t/H=0.5%),the TLF is weak,so the coolant injection can impinge on the casing surface easily in both configurations,which facilitates the cooling protection of the casing surface.Moreover, under this tip clearance, the TLFs of the two configurations can smoothly enter the tip cavity for kinetic energy dissipation.Noting that the SV is strengthened under a small tip clearance, thus the SV will also serve as a labyrinth seal to suppress the TLF in Case 1.Under a large tip clearance(t/H=1.5%),the cooling jet in the baseline case can no longer impact the casing surface directly, and part of the TLF exits the tip clearance without entering the squealer cavity, which results in significantly reduced blocking and cooling effects of the coolant injection.However,the situation is different for the PS-rib configurations: even under a large tip clearance (t/H = 1.5%), the tip injection can still reach the casing surface, and because of the suppressed TLF,the mixed flow of the TLF and cooling air subsequently enters the tip cavity for kinetic energy dissipation, which reduces the aerodynamic loss of the TLV compared to that of the corresponding baseline case.In this situation, the PS-rib configurations produce a better temperature distribution near the casing and blade tip surface than that of the squealer-cavity configuration.

Fig.24 Local relative streamlines and contours of dimensionless temperature on SP1 (MR = 0.75%).

Fig.25 show the effects of the tip clearance on the tip leakage mass flow rate, total pressure loss coefficient, and isentropic efficiency, respectively.Generally, increasing the tip clearance aggravates the tip leakage and total pressure loss,thereby reducing the isentropic efficiency of the rotor cascade.Under all tip clearances, the PS-rib configurations produce a lower mLand Ψ but a higher η compared to those of the baseline cases, especially under a high injection mass flow rate.At MR=1.00%and under t/H=0.5%,1.0%,1.5%,the PS-rib configurations increase the isentropic efficiency by approximately 0.95%, 1.25%, and 1.23%, respectively, compared to that of the baseline configuration.

Generally,the PS-rib layout is the most promising configuration for improving the aerodynamic performance of an axial turbine blade, followed by the CL-rib layout.However,because the present study has focused mainly on how a perforated rib and its layout affect the aerodynamic performance of the TLF, further investigations are needed to show how the perforated rib affects the thermal performance.

4.Conclusions

Herein, a novel perforated-rib configuration was proposed for controlling the TLF of an axial turbine blade.Three perforated-rib layouts were considered, with a perforated rib installed at (A) the SS squealer (SS-rib), (B) the PS squealer(PS-rib), and (C) the additional squealer along the blade CL(CL-rib).Numerical simulations showed the effects of the novel rib and its layout on the aerodynamic performance of the TLF, and main conclusions are as follows.

(1) With the use of a perforated rib, the distances between the injection holes and the turbine casing are reduced compared to those in the baseline squealer-tip case, so coolant jets issuing from the injection holes show stronger penetration into the tip clearance.How the perforated-rib coolant injection affects the TLF depends strongly on its layout.

Fig.25 Effect of tip clearance on tip leakage mass flow rate,total pressure loss coefficient and isentropic efficiency.

(2) In the SS-rib case,because the discrete coolant jets leave the tip gap quickly without diffusing adequately in the hole-pitch areas, the TLF is not blocked well by the coolant injection, and the leakage mass flow rate is increased slightly compared to that in the baseline squealer-tip case.However, because the SS-rib coolant injection scheme is effective at reducing the size of the TLV, it somewhat improves the total pressure loss and isentropic efficiency of the turbine blade.

(3) The CL- and PS-rib layouts are suggested as promising configurations for TLF control, and their flow mechanisms are identified as:(A)CL-rib scheme—vortex dissipation,rib obstruction,and jet obstruction; (B)PS-rib scheme —jet obstruction, vortex dissipation, and SVlabyrinth seal.In particular, the PS-rib layout reduces the leakage mass flow rate by 27% and increases the isentropic efficiency by 1.25% compared to those in the baseline squealer-tip case, under an injection mass flow ratio of 1% and a tip clearance of 1% blade span.

(4) The advantages of the PS-rib configuration in suppressing the TLF are also confirmed under a small tip clearance of t/H = 0.5% and a large clearance of t/H = 1.5%, improving the isentropic efficiency by approximately 0.95% and 1.23%, respectively, compared to those in the baseline cases.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Science and Technology Major Project, China (No.2017-III-0001-0025) and the Interdisciplinary Innovation Foundation for Graduates at Nanjing University of Aeronautics and Astronautics in China (No.KXKCXJJ202002).