Applied Thermal Engineering 107 (2016) 271–283

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate /apthermeng

Research Paper

Aerothermal characteristics of a transonic tip flow in a turbinecascade with tip clearance variations

http://dx.doi.org/10.1016/j.applthermaleng.2016.06.1551359-4311/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: yuegq@hrbeu.edu.cn, 421319625@qq.com (G. Yue).

Jie Gao a, Qun Zheng a, Xiying Niu b, Guoqiang Yue a,⇑aCollege of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, ChinabHarbin Marine Boiler & Turbine Research Institute, Harbin 150078, China

h i g h l i g h t s

� New physical insights of transonic blade tip flow mechanisms are proposed.� We examine effects of tip gap height on transonic tip aerothermal characteristics.� Opposite tip aerothermal variations between tip leading and trailing edge regions.� Tip gap effects on tip leading-edge aerothermal performance are relatively small.� Suggested 3D tip-surface contouring concept for enhanced aerothermal performance.

a r t i c l e i n f o

Article history:Received 12 April 2016Revised 21 June 2016Accepted 22 June 2016Available online 25 June 2016

Keywords:Transonic turbineTurbine cascadeTip leakage flowTip clearance heightAerothermal characteristics

a b s t r a c t

A significant portion of flows over a modern high-pressure turbine blade tip is transonic, and the transonictip leakage flows lead to significant aerodynamic losses and high heat loads onto the blade tips. This paperaims to develop a deeper understanding of the transonic tip leakage flow physics and its influence on theloss mechanism and blade-tip heat transfer. Three-dimensional (3D) Reynolds-averaged Navier-Stokes(RANS) calculations were performed using the ANSYS CFX 14.5 numerical prediction code, adopting theSST k-x turbulence model to investigate the sensitivity of aerothermal performance of transonic tip flowsto tip clearances in a RT27a turbine cascade. The transonic tip leakage flow pattern within the tip gap, theflowfield downstream of the cascade, and the blade tip heat transfer distribution are studied. The numer-ical results give a reasonable agreement with the experimental data. The tip aerodynamics and surfaceheat transfer variations with tip clearances are opposite between leading and trailing edge regions of bladetips, and tip clearance effects on the former are relatively small. As the tip clearance increases, the shockwave reflections are delayed but more evident, and it therefore leads to reduced leakage massflow densityand decreased heat loads on the rear part of blade tips. Despite this, since the leakage flow near the leadingedge of blade tips remains subsonic resulting in increased leakage mass flowrate and tip heat transfer, theleakage losses and overtip heat loads are increased with the increasing tip clearance.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Tip leakage flow in modern unshrouded high-pressure turbinescauses large aerodynamic penalties, induces significant heat loadsand gives rise to intense thermal stresses onto the blade tips.Obtaining a good aerothermal performance of the blade tiprepresents a major challenge for turbine designers.

Numerous experimental and numerical studies in the pastseveral decades have been devoted to the understanding of tipleakage flowmechanisms in many different environments, in order

to develop innovative tip designs. Investigations in this area havecontinued from theoretical study, to cascade flow environments,and then to full turbine test rigs, for different tip geometries andtip clearances. Sjolander [1] presented an overview of the tipleakage flow, summarized its effect on the performance of axialturbines, and gave an overview of the investigations on the overtipleakage flows. Later, Bunker [2] presented an extensive researchreview, mainly performed in low-speed environments, on theturbine blade tip aerothermal performance in a high-pressureenvironment.

Having understood the general physics of tip leakage flows,several tip design approaches have been proposed to mitigate tipleakage effects [3] and to improve the thermal performance of

Nomenclature

cps static pressure coefficient [–] cps ¼ p�pexitp0�pexit

h heat transfer coefficient [W/(m2�K)] h ¼ qwT1�Tw

Ma Mach number [–]Nu Nusselt number [–]p pressure [Pa]q heat flux [W/m2]T temperature [K]v velocity [m/s]x, y, z coordinate direction [mm]z/cz relative axial chord length [–]

Greeksb flow angle [deg]q density [kg/m3]s tip clearance [–]

Subscriptsexit cascade exitg gasin cascade inlet

is isentropicref referencetip blade tipw wall0 total1 far field

Superscripts⁄ total

AbbreviationsCFD computational fluid dynamicsEXP experimentIL interference linePS pressure sideRANS Reynolds-averaged Navier-StokesSS suction sideTLV tip leakage vortexTPV tip passage vortex3D three-dimensional

272 J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283

blade tips [4]. Squealer tip designs adopting rims are proved toenhance the blade tip aerothermal performance compared to flattips [5]. In order to further increase the turbine efficiency and toreduce the blade-tip heat loads, winglet tips [6] can be consideredas a suitable alternative.

The steadily increasing demand for higher turbine stage loadingand rotational speeds causes the blade tip leakage flow to exceedthe transonic regime, which drastically modifies the aerothermalstructures within the overtip region. Although the existence ofsupersonic flows was already suggested in 1988 by Moore andTilton [7] and afterwards experimentally identified throughwater-table experiments that consider the effects of Reynoldsnumber [8] and model the shock formation in overexpanded tipleakage flow [9], only recent investigations were capable of reveal-ing the complex shock flow phenomena. Zhang et al. [10] reportedthe detailed experimental evidences of the heat transfer stripe dis-tributions caused by the shock wave structures over the blade tips.Most recently, the overtip choking and shock structures [11] aswell as its effects on tip heat transfer [12] were reported by Zhanget al. and for even a modern winglet-tip design by O‘Dowd et al.[13].

Wheeler et al. [14] showed that, at an engine-realistic Machnumber, the tip leakage flow is predominantly transonic. At highspeeds, the pressure-side separation bubble reattaches through alocal supersonic acceleration that halves the length of the bubble,when the tip-gap exit Mach number is increased from 0.1 to 1.0.Numerical work presented by Wheeler et al. [15] also suggestedthat tip-leakage flows in transonic blade rows differ significantlyfrom those in subsonic blade rows. Arisi et al. [16] numericallystudied the effect of exit Mach number on the blade tip andnear-tip heat transfer characteristics. The overtip heat transfer isfound to generally increase with the increase of the exit Machnumber, because of the high turbulence generation within the tipgap and the flow reattachment. Additionally, O’Dowd et al. [17]showed that an increase in the tip gap height is found to causeincreased leakage flow velocities in the overtip region, resultingin an enhanced tip leakage massflow and a leakage vortex corefurther detached from the blade suction side (SS).

The effect of turbulence on the overtip heat transfer has alsobeen given in open literatures. Using a simplified blade model,Wheeler and Sandberg [18] investigated the effect of turbulenceintensity on the blade tip heat transfer. Their study found that tur-bulence intensities greater than 10% significantly augment theblade tip surface heat transfer. Similarly, Zhang et al. [19] foundthat turbulence intensities below 9% have no noticeable effectson the flat tip heat transfer.

For the effects of casing endwall motion, there are very fewinvestigations about its effects on the transonic tip flow and heattransfer, especially by experimental test. Using numerical meth-ods, Zhang et al. [11] and Zhou [20] indicated that a tangential vis-cous force is imposed by the endwall motion, and it changes theflow physics within the tip gap, thus altering the heat transfer dis-tribution over a transonic flat tip.

Recently, the use of contoured blade tip designs has been pro-posed to force the passage to remain choked while large flow accel-erations are exploited to minimize the heat flux. Shyam et al. [21]suggested a diverging pathway for the tip leakage flow that mayreduce the shock wave strength and consequently lessen the heattransfer fluctuations. Then, Zhang and He [22] proposed to locallyaccelerate the flow in the front part of the blade tip through aconvergent-divergent nozzle to significantly reduce the overallheat transfer. More recently, Maesschalck et al. [23] developedan optimization strategy to produce a set of blade tip profiles withenhanced aerothermal performances for a number of tip gap flowconditions. The results indicated that the tip geometries that per-form superior in subsonic conditions are not optimal for supersonictip gap flows. The prime tip profiles exist depending on the tipclearance flow conditions. Overall, their work gives an insight onthe physics involved in the tip leakage flows, and demonstratesthe potential of tip contouring to control the tip flow aerothermo-dynamics. They [24] also suggested that one can attempt to curtailthe detrimental effects of transonic tip leakage flows by runningtight clearances.

In addition, there are some studies for squealer tips which wereconducted at high-speed conditions. Hofer and Arts [5] conductedan experimental study for a squealer tip in the VKI light piston

Table 2Grid dependency study based on the case with tip gap of 0.6% span and tip average y+details.

Mesh elements/(�106) 3.2 4.2 4.9

Heat transfer coefficient/(W/(m2�K)) 999.3 1017.5 1019.7Tip gap height 0.4% 0.6% 0.8% 1.0%Tip average y+ 0.124 0.126 0.193 0.273

Fig. 1. Three-dimensional computational grid and tip grid details.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

TransonicSS

Ma is

/Ma ex

it

z/cz

EXP CFD

PS

Fig. 2. Comparison of CFD and experiment for midspan isentropic Mach numberdistributions.

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.000.0

0.2

0.4

0.6

0.8

1.0

1.2

SS

Nu/Nu re

f

z/cz

EXP CFD

PS

Transonic

Fig. 3. Comparison of CFD and experiment for midspan Nusselt numberdistributions.

Table 1Details of RT27a cascade and test conditions.

Parameters Values

Maexit 0.98Inlet flow angle 42.75�Exit flow angle 68�Tg/Tw.tip 1.5Pitch-to-chord ratio 0.86Total-to-static pressure ratio 1.95Tip-gap 0.4%, 0.6%, 0.8%, 1.0%Inlet turbulence intensity 5%

J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283 273

compression tube facility. The tip leakage flow was investigatedthrough oil-flow visualizations as well as wall pressure measure-ments. The squealer tip provides a significant reduction in the tipleakage flow velocity, and it is relatively insensitive to changes inthe Reynolds number with respect to the flat tip. Li et al. [25]computationally investigated the overtip leakage flow for a typicalsquealer tip design of a high pressure turbine blade at a transoniccondition. The results indicated that the squealer tip design workswell even in the presence of choked overtip leakage flow. It shouldbe noted that the results of Wheeler’s numerical work [26] showed

that the cooling injection still has the potential to reduce overtipleakage losses. In the meantime, the results of Ma’s experimentalwork [27] indicated that when the cooling injection is introduced,distinctive series of stripes in surface heat transfer coefficient areobserved with an opposite trend in the chordwise variations onthe squealer cavity floor and on the suction surface rim.

As described above, the blade-tip region of a modernhigh-pressure turbine is widely acknowledged to be one of themost difficult regions for gas turbine manufacturers to design. Inservice, the tips of high-pressure turbine blades can be severelyeroded due to the exposure to high-temperature fluids, and it leadsto a gradual increase in the tip clearance and correspondingadverse issues. Although researchers have carried out numerousstudies about transonic tip flows and transonic blade tip design,until now the details of the flow physics within the transonictip-gap region are still poorly understood as compared to theunderstanding of the subsonic tip flows, particularly in relationto the effects of tip gap height.

The objective of this paper is to develop a deeper understandingof the transonic tip leakage flow physics that influences the loss

274 J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283

mechanisms and blade-tip heat transfer. 3D numerical methodshave been employed to investigate the sensitivity of the aerother-mal performance of transonic tip leakage flows to tip gap heights ina RT27a turbine cascade. Four tip gaps of 0.4%, 0.6%, 0.8% and 1.0%of blade span are studied. The transonic tip leakage flow patternwithin the tip gap, the endwall flowfield downstream of thecascade, and the blade transonic-tip heat transfer distribution arepresented and discussed in the paper.

2. Computational method and validation

2.1. Solver description

The ANSYS CFX 14.5 numerical prediction code was employedfor the present numerical predictions. The software core is ageneral finite volume based Navier-Stokes solver, and solutionsare obtained by solving the compressible RANS equations using afinite volume method to discretize the equations. The overall com-putational accuracy is of the second order. In this paper, the SSTtwo-equation model based onWilcox k-xmodel [28] was adopted,and in order to accurately capture the small flow features in the tipclearance region, no ‘‘wall function” is employed in this study. TheCFX ‘‘Gamma-Theta” transition model [29] was also used here topredict the transition over the blade suction surface. Accordingto Wheeler et al. [14], the transonic tip leakage flow is not as sen-sitive to the turbulence modeling as in low-speed tip flows.

(a) Tip leakage flow streamlines on a contour of tip surface pressure distribution

0.0 0.2 0.4 0.6 0.8 1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

SSPS

c ps

Normalized y

S1 S2

(b) Static pressure coefficient plots on two lines across the blade tip

Fig. 4. Contours of static pressure coefficient on the blade tip and tip leakagestreamlines.

2.2. Geometry, grid and boundary conditions

A typical modern high-pressure turbine blade profile wasadopted in this investigation. The blade profile is largely close tothat employed by Wheeler et al. [14] and Nicholson et al. [30],and their experimental data provide excellent validation for theCFD tool. The tip gap height is varied from 0.4% (0.4 mm) to 1.0%(1.0 mm) of the blade span (100 mm), and there are four tipclearances investigated here.

Fig. 1 shows the computational domain, a section of the tip andtip grid details. Commercial structured grid generation packageAutogrid5, preprocessor to NUMECA was used to build the multi-block structured grids. The channel is discretized into H-type grids,while the regions around the blade surface and the tip gap are dis-cretized into O-type grids to ensure high grid quality. The turbinecascade has about 4.2 million elements in total. Inside the tip gap,there are 70 grid layers in the spanwise direction, and 47 cells areemployed across the blade tip from the pressure side (PS) to the SS.The y+ values near the tip are kept at about 0.18 at different tipgaps, by setting the near-wall grid to satisfy the computationalrequirement in a transonic condition. All these ensure that the flowaround the blade tip region is effectively resolved.

In order to minimize computational costs, only one bladepassage was modeled with periodic boundary conditions in thepitch-wise direction. The inlet boundary is placed at one axial-chord length of the blade upstream of the leading edge. At the inlet,total temperature, total pressure and inlet flow angle are specifiedalong with the turbulence intensity level. There is no boundarylayer applied at the cascade inlet, and the boundary layer developsas the flow enters the cascade test-section. The exit boundary islocated at two axial-chord lengths of the blade downstream ofthe trailing edge, and the static pressure is specified at the exit.In order to mimic the heat transfer characteristics in a true turbineenvironment, the gas-to-tip-wall temperature ratio is set to 1.5(the inlet total temperature is 374 K). The remainder of the domainwalls is designated as adiabatic walls. Besides, the no-slip condi-tion is applied. Further details of the cascade and blade propertiesare summarized in Table 1.

Convergence criteria for these numerical computations arebased on the reduction of RMS (Root Mean Square) residuals below1 � 10�4. However, for cases with strong shock waves, the conver-gence level becomes worse, but still better than 1 � 10�3. All theresults have been checked for convergence by using blade tip sur-face average heat transfer coefficient monitoring, and the solutionis said to be converged when the average heat transfer coefficientis not changed more than 0.05% during 100 successive iterations.

2.3. Experimental validation

In the current research, ANSYS CFX tool was first validated andthen used to study more cases. In order to make a fair comparison,a transonic cascade calculation with tip gap was performed andcompared with the experiment at an exit Mach number of 0.96.Note that the exit Mach number is 0.98 for all the following cases.Fig. 2 compares the predicted and measured midspan isentropicMach number distributions. The measured data are taken fromNicholson et al. [30], and note that no uncertainty data for exper-imental test are available here. It can be seen that the flow overthe SS from the location of 30% surface length to the trailing edgeis transonic. Due to the fact that the experimental condition is not

J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283 275

available directly, and the two blade profiles are not exactly thesame as well, although there are some discrepancies between thetwo results, the agreement between the prediction and themeasurements can be considered to be quite reasonable.

The prediction of the midspan Nusselt number distribution isshown in Fig. 3. As the flow develops downstream, the Nusseltnumber reduces significantly on the blade suction side from theleading edge location to about 5% axial chord, since the flow is lam-inar in this region. After the flow transition occurs, the Nusseltnumber increases gradually as the flow accelerates downstreamuntil about 30% axial chord. Then, the Nusselt number has fewvariations from about 30% axial chord to trailing edge, since theshock waves have formed. However, on the blade pressure side,the Nusselt number first reduces significantly, keeps nearlyunchanged, and then increases gradually. As a whole, thecomputational fluid dynamics (CFD) tool produces a good qualita-tive prediction of the Nusselt number distribution over the bladepressure surface and late suction surface. It is found that itunder-predicts the stagnation-point heat transfer, which is gener-ally common with eddy-viscosity turbulence models. In addition,the present prediction and Wheeler et al.’s [14] prediction by k-eturbulence model differ significantly with the experimental data

Series of oblique shocks

Region of strong shock/boundary layer

interaction

(a) Contours of tip heat tra

plane

0.0 0.2 0.40

500

1000

1500

2000

2500

h /(W

/(m2

K))

Norma

PS

(b) Tip heat transfer coefficient pl

-component of densi

Fig. 5. Contours of tip surface heat transfer coefficient and z-c

over the early suction surface. The present prediction produces amuch better agreement over the early suction surface with thedata, since the transition prediction is activated in current CFDcalculations.

It should be noted that, for the transonic turbine cascade,because the experimental results of the loss coefficient are notavailable, the predicted loss coefficients are not validated in thecurrent investigation.

2.4. Grid-dependency study

In order to preclude the effects of grid resolution on the numer-ical loss and heat transfer results, a grid-dependency studywas alsoconducted. The grid is refined until further refinement results inless than 0.5% variation in the tip surface heat transfer coefficientwith no changes in the local heat transfer coefficient distribution.In this way, the numerical results obtained are independent ofthe grid resolution. A summary of the grid-dependency studyresults is outlined in Table 2. It clearly shows that the tip y+ valuesof the tip grids used later is 0.124, 0.126, 0.193 and 0.273 withdifferent tip gaps, which satisfies the computational requirementof the local turbulence model used in the paper.

nsfer coefficient and z

0.6 0.8 1.0

SS

lizedy

S1 S2

ots on two lines across the blade tip

ty gradient on a cut

omponent of density gradient on a cut plane of blade tip.

(a) =0.4% (b) =0.6%

(c) =0.8% (d) =1.0%

Fig. 6. Local Mach number contours in the middle of tip gap for different tip gaps.

276 J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283

3. Results and discussion

In order to better understand the transonic tip leakage flowphysics, and to provide guidance on the blade tip aerothermaldesign, numerical calculations have been performed to explorethe effects of tip clearance variations on the turbine blade tip flowfield and its associated loss and heat transfer. The results are dis-cussed in this section, which can be divided into four major parts.

3.1. Identification of a transonic overtip flow topology

Since the overtip leakage flow is driven by the lateralpressure gradient across the tip gap, the plots of static pressurecoefficient on the blade tip and tip leakage streamlines areshown in Fig. 4, which can reveal the overtip leakage flow andheat transfer characteristics. The static pressure coefficient isdefined as follows:

30

45

60

75

90

105

120

135

150

exit-

tip /d

eg

0.0 0.2 0.4 0.6 0.8 1.0z/cz

0.4% 0.6% 0.8% 1.0%

Onset of shockwave flow

Fig. 7. Distributions of deviation of flow angle between outflow and tip leakageflow along the mean camberline of the blade tip.

J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283 277

cps ¼ pressure� cascade exit pressurecascade inlet total pressure� cascade exit pressure

ð1Þ

It is seen that high static pressure coefficient distributions are foundthroughout the leading edge region, which is mainly affected byflow separation, reattachment and diffusion. In the rear part ofthe blade tip, the stripe distribution of the static pressure coefficientis due to the effects of shock wave reflection within the tip gap.More details about the flow pattern within the tip gap can be foundin lots of published literatures and are not repeated here for the

(a) =0.4%

(c) =0.8%

Fig. 8. Tip Mach number contours on tw

sake of brevity. Overall, the static pressure coefficient is higher nearthe leading edge region of the tip surface and relatively low in themiddle and rear parts of the blade tip.

Gao et al. [3] showed that in subsonic flows, the tip leakage flowmechanisms can be further defined as ‘‘direct tip leakage” in thefront part of the blade tip and ‘‘indirect tip leakage” in the rear partof the blade tip, dependent on the different tip leakage flow pat-terns. Therefore, in order to investigate the transonic tip leakageflow mechanisms in depth, a comparative analysis between thetransonic tip flow physics over the front and rear parts of the bladetip will be implemented in the following. Typically, two planes(or lines), which are oriented in the local leakage-flow directionsand labeled ‘‘S1” and ‘‘S2”, were chosen at locations that clearlyshow different physics within the tip gap as shown in Fig. 4(a).

Fig. 4(b) shows static pressure coefficient plots on two linesacross the blade tip. The abscissa is the circumferential coordinatey over the local profile width. The ‘‘0” value of the abscissa corre-sponds to PS, and ‘‘1” to SS. As the leakage flow crosses the bladetip from PS to SS, the static pressure coefficient reduces slowlyand smoothly in the front part of the blade tip. However, thereare several peaks and valleys presented in the rear part of the bladetip, and the pressure near the blade tip SS is increased as comparedto that near the blade tip PS.

The thermal performance of the blade tip is determined by theflow physics within the tip gap. Here, the blade tip-wall heattransfer coefficient is defined using

h ¼ qw

T1 � Twð2Þ

where qw is the wall heat flux, T1 is the inlet total temperature, andTw is the tip wall temperature.

(b) =0.6%

(d) =1.0%

o cut planes for different tip gaps.

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6 0.8% 1.0%

c ps

Normalizedy

0.4% 0.6%

(a) Static pressure coefficient plots on the S1 line across the blade tip

0.0 0.2 0.4 0.6 0.8 1.0

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

0.8% 1.0%

c ps

Normalizedy

0.4% 0.6%

(b) Static pressure coefficient plots on the S2 line across the blade tip

Fig. 9. Comparisons of static pressure coefficient distributions on two lines acrossthe blade tip for different tip gaps.

0.0 0.2 0.4 0.6 0.8 1.0150

200

250

300

350

400

450

0.8% 1.0%

v)tip

/(kg/

(m2

s))

z/cz

0.4% 0.6%

Fig. 10. Distributions of tip-leakage massflow density along the mean camberlineof the blade tip.

278 J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283

Fig. 5 presents contours of tip surface heat transfer coefficient.In this figure, Mach number is shown on the S1 plane by colorscales, and z-component of density gradient distributions arepresented on the S2 plane in gray scales. It can be seen fromFig. 5 that the tip surface heat transfer shows similar distributionsas the static pressure as shown in Fig. 4. High heat transfer coeffi-cients are observed near the leading-edge PS region and PS edgeregion, because of the cross-flow diffusion and the separated flowreattachment. Two stripes with low heat transfer coefficients areclearly observed around the middle position of the tip surface.Combined with the density gradient contours, the stripes in theheat flux contour are linked to shock waves reflected within thetip gaps. It should be noted that strong variations of the heattransfer levels can give rise to high thermal stresses onto the bladetips. It can also be seen that the flow near the leading edge of theblade tip is subsonic, and the majority of the blade tip experiencestransonic flows. This phenomenon also proves the feasibility of theanalytic method as mentioned above.

In a similar study on blade tip heat transfer by Zhang et al. [10],the authors reported higher heat transfer distribution throughoutthe leading edge region. This result does not exactly compare withthe present results, where a low heat transfer region exists near theleading-edge SS region. This difference may be due to thedissimilarity of the blade geometry used in both studies.

The above analyses can be proved by the tip surface heat transfercoefficient plots on two lines across the blade tip in Fig. 5(b). Simi-larly, as the tip leakage flow crosses the blade tip, in the front part ofthe blade tip, the heat transfer coefficient first increases quickly,and then reduces slowly and smoothly. However, there are severalpeaks and valleys presented in the rear part of the blade tip.

In summary, in transonic tip flows, there are still two typicalflow patterns over the entire blade tip, which leads to differingcharacteristic tip aerothermal performances. The differences ofeffects of tip clearance variations on transonic tip flow and tip heattransfer will be discussed in the following.

3.2. Tip clearance effects on tip flow fields and losses

Fig. 6 shows local Mach number contours in the middle of thetip gap for different tip gaps as well as velocity vectors in the over-tip region. Mach 1 isolines are drawn to highlight the supersonicregions. The distributions of the deviation of the flow anglebetween outflow and tip leakage flow along the mean camberlineof the blade tip are also given in Fig. 7. The overtip leakage flowshows a conventional flow pattern in the subsonic flows withstreamlines crossing the blade tip region from PS to SS, driven bythe lateral pressure differences across the tip gap. The interferenceline ‘‘IL” where the overtip leakage flow and the main passage flowmeet can be clearly seen closer to the blade SS.

With the tip clearance variations in Fig. 6, the overtip flowpattern has no noticeable changes, but the local distribution issignificantly varied. For all tip gaps, in the front part of the bladetip from leading edge to about 20% axial chord, the leakage flowremains subsonic, and the local Mach number generally increaseswith the tip gap. Besides, when the leakage flow crosses the bladetip, it turns more towards the tip SS as shown in Fig. 7, and the flowdirection appears to be offset by about 12 degrees in the front partof the blade tip. In the middle and rear parts of the blade tip, thetransonic flow region is increased, and the peak Mach number islarger as the tip gap increases. It is found from Fig. 7 that thedeviation of the flow angle between outflow and tip leakage flowhas a sudden increase when the leakage flow becomes supersonic.However, the flow direction exhibits only very small anglevariations in the supersonic region.

The above analyses can be further proved by Fig. 8 that showstip Mach number contours on two cut planes (also see Fig. 4(a)

for the position of cut planes) for different tip gaps. For the 0.4%tip gap case, a separation zone indicated by low Mach numbersis formed near the PS corner as the leakage flow enters the tip

(a) =0.4% (b) =0.6%

(c) =0.8% (d) =1.0%

Fig. 11. Entropy-increase contours at three axial chords for different tip gaps.

J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283 279

gap. The Mach numbers within the supersonic flow region aresmall. The resulting shock wave is also very weak. No evidentshock wave reflection appears. As the tip gap increases, theseparation zone increases with an increasing tip gap on the S2cut plane, and the shock wave reflections are more evident in therear part of the blade tip. Similar trends are observed for the bladetip leading edge region, that is, the Mach number becomes larger,but remains subsonic.

Quantitative comparisons of the static pressure coefficientdistribution on two lines across the blade tip for different tip gapsare shown in Fig. 9. Different trends are observed for the blade tipleading and trailing edge regions. For the tip leading edge region,when the leakage flow crosses the blade tip, the static pressurecoefficient reduces slowly and smoothly. It reduces overall as thetip gap increases due to the effects of accelerated leakage flows.However, for the tip trailing edge region, the static pressure

0.4% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0%0.8

1.6

2.4

3.2

4.0

4.8

Val

ue /%

Leakage Entropy-loss Entropy-loss per unit leakage

Fig. 12. Effects of tip gap height on tip leakage flowrate and blade exit entropy-loss.

280 J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283

distributions across the blade tip are more complicated. It can beseen from Fig. 9(b) that there are several peaks and valleys presentexcept in the 0.4% tip gap case, that is because the shock wave isvery weak with a small tip clearance. As the tip clearance increases,the leakage flow is greatly affected by the presence of shock waves.It is found that the first valley moves towards the tip SS, becausethe increased separation zone tends to shift the shock patterntowards the tip SS. Since a normal shock wave is generated imme-diately afterwards as the leakage flow comes out of the tip gap nearthe SS tip-edge as shown in Fig. 5(a), the static pressure near thetip SS becomes large accordingly.

The different tip leakage flow patterns between tip leading andtrailing edge regions therefore have significant effects on the tipleakage mass flowrate and associated losses. First, the distributionsof tip-leakage massflow density (mass flowrate per unit area) alongthe mean camberline of the blade tip are shown in Fig. 10. As seen,for the 0.4% tip gap case, the overtip-leakage massflow densityincreases gradually from leading edge to about 45% axial chordof the blade tip, and then keeps unchanged from about 45% axialchord to the trailing edge where the shock wave is very weak. Asthe tip gap increases, the tip-leakage massflow density in the frontpart of the blade tip increases generally. However, in the rear partof the blade tip, there is an evident reduction in the tip-leakagemassflow density as the tip gap increases. That is because, withthe larger tip clearance, the shock wave reflections are moreevident, and then the overtip leakage flow is effectively choked,setting a limiter on the leakage mass flowrate.

Similarly as the subsonic tip leakage flows, after the leakageflow exits the tip gap, it interacts with the passage flow and rollsup, forming a tip leakage vortex, and then the leakage and passagevortices interact with each other. The associated effects of tip clear-ance on the transonic blade exit flow fields and loss generation canbe seen in Fig. 11, which shows entropy-increase contours at threeaxial locations (labeled ‘‘A”, ‘‘B” and ‘‘C”) along the blade chord fordifferent tip gaps. The black isoline represents the constantentropy-increase value. As shown, downstream of the transoniccascade, the shape, the size and the position of the leakage vortexare significantly changed with tip clearance variations. At axiallocations ‘‘A” and ‘‘C”, the shape of the leakage vortex has few vari-ations with the tip clearances. However, at axial location ‘‘B”, as thetip gap increases, the leakage vortex shape deforms from ‘‘circular”to ‘‘elliptical”, which reduces the spanwise impact-region, and it isnot conducive to the full mixing between tip leakage flow andmain flow. In addition, at three axial locations, the center of thepeak loss locates further away from the blade SS, as the tip gapincreases. And, the scale of the passage vortex is also increasedwith the increasing tip gap. All in all, although the tip leakage lossis increased with the tip gap as expected, the leakage vortex corehas caused decreasing losses. It means that the tip leakage lossper unit leakage flowrate is reduced as the tip gap increases. Itcan be further concluded that the tip leakage flowrate is the maincause that leads to the increase in the tip leakage loss for thesecases presented.

It should be noted that the turbine blade should be rotating inoperation, but the present simulations assume the blade to bestationary. Since the work of Zhou [20] indicated that a tangentialviscous fore is imposed by endwall motion, and a scrapping vortexis formed in the main flow passage, it can be concluded that theleakage vortex shape may be altered due to the interactionbetween leakage vortex and scraping vortex, and then it affectsthe leakage loss characteristics.

The effects of tip gap height on the overall performance of tran-sonic tip cascades are shown in Fig. 12. The blade exit entropy-lossis defined as the ratio of the entropy-increase to the exit dynamichead. It can be seen that, as the tip gap height increases, both theleakage mass flowrate and the blade exit entropy-loss are almost

increased linearly. However, the exit entropy-loss per unit leakageflowrate is reduced with the increasing tip gap gradually, becauseof the effects of reduced tip mixings near the blade tip SS region.

3.3. Effect of tip clearance on turbine blade tip heat transfer

The transonic tip leakage flow pattern has a significant effect onthe thermal performance of the blade tip. Since an isothermal wallcondition is employed on the blade tip, the near-tip contours of thelocal temperature to inlet total temperature ratio for different tipgaps can be used to straight analysis the thermal fields as shownin Fig. 13. For all tip gaps investigated, the near-tip fluid tempera-ture is higher near the leading edge region of the tip surface andrelatively low in the middle and rear parts of the blade tip. As seen,there are no evident changes with the increasing tip gap in thefront part of the blade tip. However, a low-temperature zone canbe found in the middle and rear parts of the blade tip. An increasedtip gap seems to reduce the temperature and then the heat transfernear the midchord region. More details about the effect of theovertip transonic flow pattern on the blade tip heat transfer canbe found in [10] and are not repeated here.

Quantitative comparisons of the heat transfer coefficientdistributions on two lines across the blade tip for different tip gapsare shown in Fig. 14, and similarly the different trends areobserved for the blade tip leading and trailing edge regions. Forthe tip leading edge region, high transfer rates are observedtowards the tip PS, with a smoothly falling trend up to the tip SS.However, for the tip trailing edge region, the heat transfer variationis more complicated and it is broadly consistent with the staticpressure plot as shown in Fig. 9(b). As the tip clearance increases,the heat transfer is strengthened slightly in the front part of theblade tip. On the contrary, the heat transfer is weakened near thetip trailing edge region. The combined results can be seen inFig. 15, which shows the effects of tip gap height on the heattransfer coefficient on the blade tips. As shown, an increase inthe tip gap height results in an overall increase in the heat transfercoefficient. Specifically, the averaged blade overtip heat transfercoefficient is increased by 5.6% for an increased tip gap from 0.4%to 1.0% based on the blade span.

It should be noted that, in operation, the turbine blades areworking at a high temperature, and therefore the real temperatureeffects should be considered in future simulations; so do thephysical properties.

(a) =0.4% (b) =0.6%

(c) =0.8% (d) =1.0%

Fig. 13. Near-tip contours of local temperature to inlet total temperature ratio for different tip gaps.

J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283 281

3.4. Discussions about proposed 3D tip-surface contouring concept

As described above, there are evident differences patterns of tipaerodynamics and heat transfer between blade tip leading and trail-ing edge regions. The heat transfer is higher near the leading edgeregion of the tip surface. Although the heat transfer is relativelylow in the middle and rear parts of the blade tip, there are strong

variations of heat transfer levels, which gives rise to severe thermalstresses onto the blade tips. Based on these issues, the besttransonic blade tip design should have lower aerodynamic losses,lower heat fluxes near the tip leading edge region, and a more flatheat flux distribution near the tip trailing edge region.

For aerodynamic issues, the researchers, for example, Zhangand Wheeler, have shown that the transonic tip leakage loss

0.0 0.2 0.4 0.6 0.8 1.0400

800

1200

1600

2000

2400

2800

3200

0.8% 1.0%

h /(W

/(m2

K))

Normalized y

0.4% 0.6%

(a) Heat transfer coefficient plots on the S1 line across the blade tip

-2000

200400600800

100012001400160018002000220024002600

0.8% 1.0%

0.4% 0.6%

h /(W

/(m2

K))

0.0 0.2 0.4 0.6 0.8 1.0Normalized y

(b) Heat transfer coefficient plots on the S2 line across the blade tip

Fig. 14. Comparisons of heat transfer coefficient distributions on two lines acrossthe blade tip for different tip gaps.

0.4% 0.6% 0.8% 1.0%950

975

1000

1025

1050

1075

1100

h /(W

/(m2

K))

Fig. 15. Effects of tip gap height on heat transfer coefficient on the blade tips.

282 J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283

generation is decoupled from the driving pressures. Therefore, ahigh-loaded blade design with aft-loaded profiles (the lateralpressure difference is maximum in the rear part of the blade) couldmaintain similar performances.

For heat transfer issues near the tip leading edge regions, asdescribed above, the heat transfer is reduced in the front part ofthe blade tip as the tip clearance decreases. Gao et al. [31]proposed an axially non-uniform tip clearance concept. The resultindicated that an optimal axially non-uniform tip clearance cancontrol the interaction between tip leakage and passage flows,and then to reduce the total losses in turbines. Based on this, theaxially non-uniform tip clearance concept could be applied to thetransonic blade tip to reduce the tip leading-edge heat transfer,for example, the expanding tip clearance.

For heat transfer issues near the tip trailing edge regions, theshock wave structure is very sensitive to the blade tip surface,and therefore the heat transfer fluctuations could be lessened bythe tip surface contouring from PS to SS.

Based on the above analyses, a novel 3D tip-surface contouringconcept, which are optimal combinations of a high-loaded bladedesign with aft-loaded profiles, axially non-uniform tip clearanceconcept near the tip leading edge region, and tip surfacecontouring from PS to SS near the tip trailing edge region, couldbe proposed with the aim of obtaining the best transonic bladetip aerothermal performance. And yet, it needs to be furtherinvestigated by researchers.

4. Conclusions

To better understand the transonic tip leakage flow physics, andto provide the necessary knowledge to optimize the blade tipaerothermal design, 3D RANS calculations were performed usingthe ANSYS CFX 14.5 numerical prediction code, adopting the SSTk-x turbulence model to investigate the sensitivity of the aerother-mal performance of transonic tip flows to tip clearances in a RT27aturbine cascade. Four tip gaps of 0.4%, 0.6%, 0.8% and 1.0% of bladespan are studied. The numerical results give a reasonableagreement with the experimental data. Some of the importantconclusions are summarized as follows:

(1) The heat transfer is higher near the leading edge region of thetip surface. Although the heat transfer is relatively low in themiddle and rear parts of the blade tip, there are strong varia-tions of heat transfer levels,which causes severe thermal stres-ses onto the blade tip. Overall, the tip aerodynamics andsurface heat transfer variations with tip clearances are oppo-site between leading and trailing edge regions of blade tips,and the tip clearance effects on the former are relatively small.

(2) Downstream of the transonic cascade, the shape, the sizeand the position of the leakage vortex are significantlyaltered with tip clearance variations. As the tip gapincreases, the shape of the leakage vortex deforms from‘‘circular” to ‘‘elliptical", and the center of the peak losslocates further away from the blade SS. Although the tipleakage loss is increased with the tip gap as expected, theleakage vortex core has caused decreasing losses as the tipgap increases. It means that the tip leakage loss per unitleakage flowrate is reduced as the tip gap increases.

(3) The overtip flow pattern has no noticeable changes with tipclearances, but the local distribution is significantly varied.As the tip clearance increases, the shock wave reflectionsare delayed but more evident, and it therefore leads toreduced leakage massflow density and decreased heat loadsin the rear part of blade tips. Despite this, since the leakageflow near the leading edge of blade tips remains subsonicresulting in increased leakage flowrate and heat transfer,the leakage losses and overtip heat loads are increased withthe increasing tip gap. The averaged blade tip heat transfercoefficient is increased by 5.6% for an increased tip gap from0.4% to 1.0% based on the blade span.

J. Gao et al. / Applied Thermal Engineering 107 (2016) 271–283 283

The results presented in the paper indicates that the besttransonic blade tip design should have lower aerodynamic losses,lower heat fluxes near the tip leading edge region, and a more flatheat flux distribution near the tip trailing edge region. Correspond-ingly, a novel 3D tip-surface contouring concept could be proposedwith the aim of obtaining the best blade transonic tip aerothermalperformance. The present results yields new physical insights ofblade transonic tip leakage flows, and provides guidelines forfuture blade transonic tip designs with enhanced aerothermalperformances.

Acknowledgments

This work has been supported by the National Natural ScienceFoundation of China (Grant No. 51406039) and the Natural ScienceFoundation of Heilongjiang Province of China (No. QC2016059),which are gratefully acknowledged.

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