Effect of purge flow on endwall flow and heat transfer characteristics of a gas turbine blade

Applied Thermal Engineering 110 (2017) 504–520

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Research Paper

Effect of purge flow on endwall flow and heat transfer characteristics of a gas turbine blade Liming Song, Peiyuan Zhu, Jun Li ⇑, Zhenping Feng Institute of Turbomachinery, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China

h i g h l i g h t s
We numerically investigate the endwall with upstream slot for a gas turbine blade.
The influences of mass flow ratio of purge flow and ejection angle of slot have been studied.
The flow structure near the endwall with purge flow is further discussed and presented.
The effects of the purge flow on the endwall film cooling, heat transfer characteristics and aerodynamic losses are studied.

a r t i c l e

i n f o

Article history: Received 26 May 2016 Revised 27 August 2016 Accepted 27 August 2016 Available online 28 August 2016 Keywords: Purge flow Film cooling Endwall heat transfer Gas turbine blade Secondary vortexes Numerical simulation

a b s t r a c t This paper presents a numerical investigation on the influence of purge flow on endwall flow and heat transfer characteristics of a gas turbine blade. Upon the numerical validation with experiment data, the Reynolds-averaged Navier-Stokes equations coupled with standard k  x turbulence model are utilized in this study. Five mass flow ratios (MFR) of the purge flow (MFR = 0.5%, 0.75%, 1.0%, 1.25%, 1.5%) and four ejection angles a of the upstream slot (a = 30°, 45°, 60°, 90°) are selected to investigate the effects of purge flow on endwall flow structure and their thermal behaviors. The results indicate that the purge flow provides some cooling effectiveness and increases the heat transfer on the endwall. The reduction of the ejection angle a improves the film cooling effectiveness and increases the heat transfer coefficient of the endwall. The averaged film cooling effectiveness of the endwall is reduced by 53.4% and the heat transfer coefficient at the leading edge is increased by 18.89% when the ejection angle a is increased from 30° to 90° at MFR = 1.5%. Comparing to another case without purge flow, the purge flow increases the aerodynamic losses, and as the increasing of MFR, the aerodynamic losses is increased first and reduced afterwards, obtaining the largest aerodynamic losses at MFR = 1.0% for the ejection angle a ¼ 30 . Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Gas turbines are widely applied to aero-propulsion, ship power and industrial power generation [1]. For the enhancement of thermal efficiency and power output of gas turbines, the inlet temperature of gas turbines has been ever increasing. The inlet temperature of modern gas turbines is in excess of 2000 K, which is far beyond the melting point of the component material. Therefore, internal cooling and film cooling techniques are employed to protect gas turbine blades. However, temperature profiles in modern gas turbines are much more flat, resulting in a much higher thermal load on the endwall [2]. Hence the cooling requirements for endwall are improved to approach those for blades, great ⇑ Corresponding author. E-mail address: [email protected] (J. Li). http://dx.doi.org/10.1016/j.applthermaleng.2016.08.172 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

efforts are also devoted to provide a better cooling protection for the endwall region in recent years. The complex secondary flow structure in the blade passage has significant influences on the heat transfer and film cooling performance of the endwall, which also makes it more difficult to be cooled than the blade surface. The formation and development of the secondary flows in the passage are summarized by Goldstein and Spores [3], Wang et al. [4] and Langston [5]. The dominant secondary flow structures such as horseshoe vortex, passage vortex and endwall cross flow are presented in these studies. Yamada et al. [6] claimed that due to a significant development of the boundary layer on the endwall, much larger passage vortex was produced close to the endwall. Maclsaac et al. [7] measured experimentally the secondary flow downstream of a turbine cascade. The results indicated that the fluid is forced up by the passage vortex at the junction between the endwall and the blade suction sur-

L. Song et al. / Applied Thermal Engineering 110 (2017) 504–520

505

Nomenclature C Cax P S D W L Reoutlet qw h MFR M T1 Tc T aw Tw Nu m pt U

chord length of blade, mm axial chord of blade, mm blade pitch, mm blade span, mm distance between slot and blade, mm slot width, mm slot length, mm outlet Reynolds number based on blade passage outlet velocity and blade chord wall heat flux, W/m2 heat transfer coefficient, W/(m2 K) mass flow ration of purge flow to mainstream flow blowing ratio of purge flow, (qc U c =q1 U 1 ) inlet temperature of mainstream, K inlet temperature of purge flow, K adiabatic wall temperature, K wall temperature, K Nusselt number mass flow rate, kg/s total pressure, Pa velocity

face to collect and funnel high loss fluid to low loss regions. The experiment results of Knezevici et al. [8] indicated that the pitchwise cross-flow rolls up the boundary layer near the endwall, and the reduction of pitchwise cross-flow near the endwall can lead to the reduction of the passage vortex. Many studies have analyzed the influences of the above mentioned secondary flows in the aspect of heat transfer characteristic on the endwall. Radomsky and Thole [9] experimentally investigated the influence of the high free-stream turbulence on the endwall heat transfer. The results indicate that high free-stream turbulence and secondary flows can significantly increase the heat transfer on the endwall. While low increase of the endwall heat transfer caused by the high free-stream turbulence is found in the regions where horseshoe vortex and passage vortex have dominated effects. Papa et al. [10] experimentally and numerically studied the effects of secondary flows in the aspect of heat transfer on the gas turbine blade and endwall. The results show that the horseshoe vortex enhances the heat transfer of the blade leading edge region, and the vortex shedding increases the heat transfer of the trailing edge region on the endwall. In modern gas turbines, to prevent hot mainstream gas ingesting into the disk cavity, the cooling air bled from the compressor is ejected from the gap between stator and rotor. The mechanisms of the rim seal ingestion have been extensively studied [11,12]. Besides, the purge flow can also provide a cooling effect on the endwall. Related studies are performed recently. Burd et al. [13,14] studied the effects of the upstream purge flow on the secondary flow structure as well as film cooling. The results indicate that higher purge flow rate both prevents the coolant being entrained to the secondary flow and provides good cooling for the endwall. Thole and Knost [15] showed that the purge flow from the interface between combustor and turbine can provide film cooling in local areas of the vane endwall and change the inlet boundary condition. The experiment conducted by Cardwell et al. [16] indicates that the increase of the mass flow rate of the purge flow from the combustor-turbine gap improves the local film cooling effectiveness, and the increase of the momentum flux of the purge flow improves the coverage area of the coolant.

Greek letter ejection angle of slot, deg film cooling effectiveness k fluid thermal conductivity, W=ðm KÞ q fluid density, kg/m2 / non-dimensional temperature, ðT 1  T aw Þ=ðT 1  T c Þ lT turbulent viscosity, kg=ðm sÞ lL laminar viscosity, kg=ðm sÞ
np;t total pressure loss coefficient local total pressure loss coefficient nlocal X streamwise vorticity, s1

a g

Subscripts aw adiabatic wall w wall c coolant 1 freestream out blade passage outlet

The purge flow also has significant influences on the secondary flow structure, which will then alter the heat transfer characteristics on the endwall. Schüpbach et al. [17] investigated the effect of the purge flow on the flow structure and the performance of an endwall-profiled turbine. They found that the purge flow can alter the secondary flow structure to change anticipated effects of the design for the endwall. Ong et al. [18] found that the purge flow is entrained into the secondary flow and the negative incidence of the purge flow can strengthen the secondary flow. Rehder and Dannhauer [19] demonstrated in their experiment that the local heat transfer on the endwall, in particular between gap and vane leading edge, can be increased by using perpendicular coolant ejection to enhance the horseshoe vortex intensity. Lynch and Thole [20,21] experimentally and numerically investigated the effect of the leakage flow from combustor-turbine slot and midpassage gap on vane endwall heat transfer. The results indicate that more leakage flow from the upstream slot increases the heat transfer downstream of the slot, and the leakage flow from the midpassage gap causes an increase of the heat transfer in the throat region. Aydın Durmusß et al. [22] investigated the mechanism of augment of heat transfer rates by applying the snail type swirl generators. It was found that the Nusselt numbers may be increased from 85% to 200% for 15–75° swirl flow angles. Among previous studies, only a few papers have studied the effect of the purge flow from the upstream slot on the endwall flow and heat transfer for high performance turbine blades with high turning angle [2,23–26]. The details of the secondary flow structure directly depend on the profile of blades [2]. The strong transverse pressure gradient in the blade passage with high turning angle has an important influence on the secondary flows. Papa et al. [2] experimentally investigated the effect of the purge flow on the flow and heat transfer of the blade endwall with different blowing ratios. For higher blowing ratio, coolant can penetrate to the blade pressure side on the endwall. Gao et al. [23] performed film cooling effectiveness measurement with the purge flow in the linear blade cascade for different purge flow rate. Barigozzi et al. [24] investigated the effect of the swirl purge flow on the film cooling and aerodynamic behavior of a blade cascade. Li et al.

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[25,26] studied the mainstream turbulence intensity and swirl ratio in regard to the cooling performance of turbine blade endwall with the purge flow from the upstream slot. They found that the best cooling performance is obtained at a high main turbulence intensity of 13%. Most of these studies are focused on the effects of the flow conditions on the flow and the heat transfer performance on the blade endwall with an upstream slot. While both the flow condition of the purge flow and the geometry parameter of the upstream slot are considered in this paper. A detailed analysis with the influences of the mass flow rate of the purge flow and the ejection angle of the slot on the cooling performance, heat transfer characteristics and aerodynamic losses is performed in this paper to enhance the understanding of the effect mechanisms of the upstream purge flow to the flow and thermal behavior of the blade endwall. 2. Numerical method

Table 1 Blade and slot geometric parameters. Parameters

Value

Chord length of blade, C (mm) Axial chord of blade, C ax (mm) Pitch, P (mm) Span, S (mm) Inlet angle (deg) Outlet angle (deg) Slot position, D (mm) Slot width, W (mm) Slot length, L (mm) Slot orientation, a (deg)

184.15 129.64 0.75 2.48 35 72.5 12.96 4.00 25.50 30, 45, 60, 90

To be noted, the experimental study was only conducted with 45 slot orientation. In current study, 4 different slot orientations are studied as shown in Fig. 2.

2.1. Geometrical model

2.2. Boundary conditions

In this study, a high-pressure gas turbine blade referring to the experimental model of Papa et al. [2] is numerically investigated. Fig. 1 shows the schematic of the rotor blade with the upstream slot, and detailed geometrical parameters are shown in Table 1.

Profiles of velocity, total temperature, turbulent kinetic energy and turbulent eddy dissipation are given at the mainstream inlet. These profiles are obtained from a two-dimensional (2D) simulation that can provide the same boundary layer and momentum

(a) Computational model

(b) Upstream slot geometry Fig. 1. The schematic diagram of the rotor blade with upstream slot.

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2.2 million, 3.2 million, 4.2 million, 5.2 million and 6.2 million are used to validate the grid independence based on the standard k  x turbulence model. The first grid layer of all the grids near the wall are in the same thickness, with the yþ remained less than 1. Fig. 3 shows the average film cooling effectiveness on the endwall of a ¼ 45 and MFR = 1.5% for different grid sizes. It is shown that the grid number has no significant influence on the computational results when the grid number is >4.2 million. Therefore, the grid of 5.2 million is finally adopted in the current study by taking the computational cost into account. 2.4. Turbulence model and validation

Fig. 2. Computational mesh.

thickness (d and h) as those measured in the experiment of Papa et al. [2]. The total temperature and mass flow rate are specified at the chamber inlet. The static pressure condition is assigned at the outlet. According to symmetry and periodicity, a symmetric condition is specified at the blade midspan, and periodic conditions are specified in the pitchwise direction. For the study of endwall film cooling effectiveness, an adiabatic no-slip wall condition is used at all walls, while a no-slip wall with a constant heat flux qw ¼ 1000 W=m2 is used at the endwall for the study of endwall heat transfer coefficient. Other wall conditions are the same with that in the study of endwall film cooling effectiveness. Detailed boundary conditions are shown in Table 2. The film cooling effectiveness g, heat transfer coefficient h, mass flow ratio (MFR) and Nusselt number (Nu) used in this study are defined as:

g ¼ ðT 1  T aw Þ=ðT 1  T c Þ

ð1Þ

h ¼ qw =ðT aw  T w Þ

ð2Þ

MFR ¼ mc =mg

ð3Þ

Nu ¼ hC=k

ð4Þ

where mc is the mass flow rate of the purge flow; mg is the mass flow rate of the mainstream flow; T 1 and T c respectively denotes the static temperature in the mainstream flow inlet and in the slot inlet; T aw refers to the adiabatic wall temperature; T w is the wall temperature with constant heat flux boundary condition; qw is regard as the wall heat flux; k is the thermal conductivity.

The experiment data of the endwall cooling effectiveness obtained by Papa et al. [2] for a ¼ 45 are utilized to validate the numerical methods with 4 different turbulence models, including standard k  e, standard k  x, RNG k  e and SST k  x. The ANSYS CFX is used to conduct simulating calculation. When all the root mean square residuals of continuity, momentum energy and turbulent kinetic energy equations are less than 105 , the computation is considered convergent. The experiment of Papa et al. [2] is focused on the effect of blowing ratio, thus the validation of the numerical method is conducted at flow conditions which is the same as that in the experiment. Figs. 4 and 5 respectively presents the comparisons of the laterally averaged film effectiveness and contours of film effectiveness on the endwall between the four turbulence models and the experiment data for blowing ratio M ¼ 0:5 and M ¼ 1:0. In Fig. 4, when M ¼ 0:5, the standard k  x model has the best prediction accuracy for all the regions. When M ¼ 1:0, the standard k  x model presents slightly higher values of film effectiveness at X=C ax < 0:5, while the other three turbulence models have a better prediction accuracy in this region, but the prediction accuracy of standard k  x model at X=C ax > 0:5 is better than the others. In addition, the distributions of the film effectiveness on the endwall are well predicted by the standard k  x model for both blowing ratios as shown in Fig. 5. Therefore, the standard k  x is finally employed in the current study. 3. Results and discussion For numerical validation, the blowing ratio is used as the nondimensional flow parameter of the purge flow that is consistent

2.3. Mesh generation Fig. 2 shows the computational mesh generated by the software ICEM-CFD. A structured grid is used in this numerical calculation and O-type grids are employed around the blade. Grids near the wall boundaries are sufficiently refined to ensure the near-wall yþ less than 1. The first refined grid layer thickness near the wall is 5  106 m and the growth ratio of the refined grid is 1.2. A grid sensitivity analysis is conducted to ensure that the computational results are independent on the mesh size. Five mesh sizes of

Table 2 Boundary condition. Parameters

Value

d (mm) h (mm) Reoutlet MFR T c;total (K)

22 2.2 600,000 0.5%, 0.75%, 1.0%, 1.25%, 1.5% 298.15

Fig. 3. Grid independence.

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0.7 Experiment k-ε k-ω RNG k-ε SST

0.6 0.5

ηf

0.4 0.3 0.2 0.1 0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

X/Cax

(b) M = 1.0

(a) M = 0.5

Fig. 4. Comparison of the laterally averaged film cooling effectiveness on the endwall between the numerical results and experimental data.

k −ε

RNG k − ε

k −ω

SST k − ω

Experiment result[2]

η (a) M = 0.5

k −ε

RNG k − ε

Experiment result[2]

k −ω

SST k − ω

(b) M = 1.0 Fig. 5. Comparison of film cooling effectiveness contours between the numerical results and experimental data.

L. Song et al. / Applied Thermal Engineering 110 (2017) 504–520

with the experiment. Meanwhile, for numerical analysis in this paper, the MFR is adopted as the non-dimensional flow parameter of the purge flow. The specific study is carried out in the conditions of a ¼ 30 , 45 , 60 , 90 and MFR = 0:5%, 0:75%, 1:0%, 1:25%, 1:5%. 3.1. Effect of MFR and a on the film cooling effectiveness Fig. 6 presents the axial distributions of laterally averaged film cooling effectiveness on the endwall at different MFR and a. It is indicated that purge flow from the upstream slot can provide better film cooling effectiveness on the endwall for X=C ax < 0:5. With

the increasing of MFR, the film cooling effectiveness shall be enhanced. However, the film cooling effectiveness on the endwall for X=C ax > 0:5 is limited, especially when MFR < 1.0%, the purge flow hardly provides any cooling effect on the endwall for X=C ax > 0:5. The influence of a is not that significant when MFR < 1.0%, especially when a ¼ 30 ; 45 ; 60 , there is just a small difference in the distributions of laterally averaged film cooling effectiveness on the endwall when MFR < 1.0%. The effect of a arises as the increase of MFR, and the ejection angle a increasing decreases the film cooling effectiveness on the endwall. The reduction of endwall averaged film cooling effectiveness is as high as

1

MFR=1.5%

0.9

30deg 45deg 60deg 90deg

0.8 0.7

η

0.6 0.5 0.4 0.3 0.2 0.1 0

0

509

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

X/C ax Fig. 6. Axial distribution of laterally averaged film cooling effectiveness on the endwall.

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53.4% when the ejection angle a is increased from 30° to 90° at the point when MFR = 1.5%. Fig. 7 shows the contours of film cooling effectiveness on the endwall. For all cases, the high film cooling effectiveness region is restricted to the fore part of the passage near the suction side. It is because the coolant ejection from the slot is swept to the suction side due to the effect of secondary vortexes near the endwall. Consequently, the pressure side is hardly covered by any coolant flow. Besides, the horseshoe vortex can roll down the mainstream flow to enhance the mixing between the mainstream flow and

α = 30

α = 45

coolant, so the film cooling effectiveness of the region near the leading edge is reduced. As the increase of MFR, the purge flow provides a better cooling effect on the endwall as shown in Fig. 7. Ejecting more coolant from the slot will not only enlarge the area of the region covered by coolant, but also improve the film cooling effectiveness on the endwall, because higher MFR of coolant has larger momentum to overcome the effect of the secondary vortexes. In addition, when MFR is less than 1%, the distribution of coolant at the slot outlet is significantly nonuniform, especially when MFR = 0.5%, there is

α = 60

α = 90

(a) MFR = 0.5% η

α = 30

α = 45

α = 60

α = 90

(b) MFR = 0.75%

α = 30

α = 45

α = 60

α = 90

(c) MFR = 1.0%

α = 30

α = 45

α = 60

α = 90

(d) MFR = 1.25%

α = 30

α = 45

α = 60

α = 90

(e) MFR = 1.5% Fig. 7. Film cooling effectiveness contours on the endwall.

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no coolant ejecting from the slot at the region directly facing the stagnation point as shown in Fig. 7(a). Fig. 8 presents the distributions of non-dimensional temperature / and streamlines on three

different sections. At the point when MFR = 0.5%, significant differences can be found among the flow conditions of the three sections. The reason is that the existence of blade can result in the

φ A B C

A B C

Horseshoe vortex

(a) MFR = 0.5%

A-A

α = 30

B-B

C-C

(b) MFR = 0.5%

α = 60

A-A

B-B

C-C

A-A

B-B

C-C

A-A

B-B

C-C

A-A

B-B

C-C

(c) MFR = 0.5%

α = 90

(d) MFR = 1.0%

α = 30

(e) MFR = 1.0%

α = 60

(f) MFR = 1.0%

α = 90

A-A

B-B

C-C

(g) MFR = 1.5%

A-A

α = 30

B-B

C-C

(h) MFR = 1.5%

α = 60

A-A

B-B

C-C

A-A

B-B

C-C

(i) MFR = 1.5%

α = 90

Fig. 8. Non-dimensional temperature and streamline distributions on three sections.

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slot, the horseshoe vortex is weakened due to the ingestion of the mainstream flow at MFR = 0.5%. As the increase of MFR, more coolant ejection can avoid the ingestion of the mainstream flow, the horseshoe vortex intensity will also be strengthened. Meanwhile, the ejection angle a increasing will enhance the interaction between coolant ejection and horseshoe vortex so as to further enhance the strength of horseshoe vortex. In addition, coolant ejection from the upstream slot results in the separation of the incoming boundary layer to form separation vortex. Higher MFR and larger a are subjected to a stronger separation vortex, especially when MFR = 1.5% and a ¼ 90 , complicated vortex system is induced by stronger separation vortex. The change of the secondary flow structure caused by the coolant ejection from the slot dramatically affects the heat transfer performance on the endwall. Fig. 10 presents the distributions of Nusselt number Nu on the endwall. In Fig. 10, the coolant ejection significantly influences Nu distributions on the fore part of endwall, while it has no significant effect on the trend of the Nu distributions on the rear part of endwall. The high Nu regions on the fore part of endwall are caused by horseshoe vortex and separation vortex systems. The suction side leg of the horseshoe vortex moves along the blade surface to enhance the local heat transfer

non-uniform distribution of the mainstream flow pressure, and the pressure near the stagnation point is higher than that of other regions, thus the flow conditions at the slot outlet are different along the pitchwise. In Fig. 8, the ingestion of the mainstream flow occurs at the section directly facing the stagnation point (B-B section) when MFR = 0.5%, which is responsible for no coolant ejection region of the slot outlet shown in Fig. 7(a). When the MFR increases to 1.0%, the phenomenon of mainstream flow ingestion is vanished. More uniform distribution of the film cooling effectiveness is formed by more coolant ejection, and this phenomenon is particularly significant at a = 30° and 45° as shown in Fig. 7. Besides, comparing flow conditions in B-B section in Fig. 8, it is clear that interaction between coolant ejection and horseshoe vortex is also enhanced with the growth of MFR. 3.2. Effect of MFR and a on the endwall heat transfer The purge flow from upstream slot has a significant effect on the secondary flow structure near the endwall, which can change the heat transfer performance of the endwall. Fig. 9 shows the non-dimensional vorticity contours and streamlines at X=C ax ¼ 0 for different MFR and a. Compared with the case with no upstream

-30 -27 -24 -21 -18 -15 -12 -9 -6 -3

Pressure side

0

3

6

9 12 15 18 21 24 27 30

Ω ⋅ C U∞

Suction side

Horseshoe vortex Separation

vortex

(a) No upstream slot α = 30

α = 45

α = 60

α = 90

α = 60

α = 90

α = 60

α = 90

(b) MFR = 0.5% α = 90

α = 45

(c) MFR = 0.75% α = 90

α = 45

(d) MFR = 1.0% α = 90

α = 45

α = 60

α = 90

α = 60

α = 90

(e) MFR = 1.25% α = 90

α = 45

(f) MFR = 1.5% Fig. 9. Non-dimensional vorticity and streamline distributions at plane X=C ax ¼ 0.

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Nu

(a) No upstream slot

α = 30

α = 45

α = 60

α = 90

(b) MFR = 0.5%

α = 30

α = 45

α = 60

α = 90

(c) MFR = 0.75%

α = 30

α = 45

α = 60

α = 90

(d) MFR = 1.0%

α = 30

α = 45

α = 60

α = 90

(e) MFR = 1.25%

α = 30

α = 45

α = 60

α = 90

(f) MFR = 1.5% Fig. 10. Nu contours on the endwall.

coefficient. When MFR > 1.0%, the trajectory of the movement of the pressure side leg of the horseshoe vortex from leading edge to the suction side resulting in the high heat transfer coefficient

region is very obvious. In addition, the high and low Nu regions occur alternately on the fore part of endwall, which is resulted by separation vortex. The flow separation of the separation vortex

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results in the low local heat transfer coefficient. And the high local heat transfer coefficient is caused by the flow reattachment of the separation vortex shown in Fig. 11. The increase of ejection angle a enhances the strength of the separation vortex, so when a ¼ 90 the horseshoe vortex is tend to be entrained by the separation vortex, the high heat transfer regions caused by the separation vortex and horseshoe vortex are tend to be combined as shown in Fig. 11 (d). In Fig. 10, a low heat transfer region appears in the middle of the endwall when MFR > 1.0% and a < 60°. Especially when MFR = 1.5% and a ¼ 30 ; 45 , this phenomenon is dramatically visible. The coolant ejection can increase the momentum of the boundary layer, in which the fluid will be accelerated, and this flow acceleration tends to be stronger as the increase of MFR and the reduction of ejection angle a. Fig. 12 shows the turbulent to laminar viscosity ratio lT =lL distributions near the endwall. The high turbulence regions caused by the horseshoe vortex and separation vortex are extremely obvious in Fig. 12. An evident flow turbulence reduction region appears at MFR ¼ 1:5% and a ¼ 30 ; 45 due to the strong flow acceleration of the coolant ejection. This flow turbulence reduction can reduce the turbulence thermal diffusion which is responsible for the lower heat transfer intensity region appearing at the middle part of the endwall when MFR ¼ 1:5% and a ¼ 30 ; 45 in Fig. 10. When MFR < 1.0% or a > 60°, this flow turbulence reduction region disappears because the flow acceleration of the purge flow is limited under this condition. Fig. 13 presents the laterally averaged heat transfer coefficient ratio h=h0 distributions on the endwall. In this figure, h denotes

Nu

the heat transfer coefficient on the endwall with the upstream slot, h0 denotes the heat transfer coefficient on the endwall without the upstream slot. In Fig. 13, the heat transfer coefficient at X=C ax < 0:2 is enhanced as the increase of MFR. The heat transfer coefficient at 0:2 < X=C ax < 0:6 is increased as the increase of the MFR when the MFR is less than 1.0%, while the heat transfer coefficient at 0:2 < X=C ax < 0:6 is reduced when the MFR is >1.0%, a = 30° and 45° due to flow turbulence reduction caused by flow acceleration of coolant ejection. Especially for the ejection angle a = 30°, the heat transfer coefficient is reduced by 16.77% at X=C ax ¼ 0:4 when the MFR is increased from 1.0 to 1.5%. In addition, when MFR < 1.0%, the purge flow has no significant influence on the heat transfer coefficient at X=C ax > 0:6. When MFR > 1.0%, the purge flow can slightly increase the heat transfer coefficient at X=C ax > 0:6 because the coolant has more momentum to overcome the secondary flow near the endwall at a higher MFR. As the increase of ejection angle a, the heat transfer coefficient of the endwall at X=C ax < 0:5 is significantly enhanced as shown in Fig. 13, which is caused by the enhancement of the strength of the horseshoe vortex and separation vortex. Particularly, the heat transfer coefficient at the leading edge is increased by 18.89% when the ejection angle a is increased from 30° to 90° at MFR = 1.5%. However, when MFR > 1.0%, as the increase of a, the heat transfer coefficient of the endwall at X=C ax > 0:5 is reduced. The reason is that the more horizontal momentum of the coolant will overcome the secondary flow near the endwall at smaller a, so the purge flow will have a greater influence on the heat transfer coefficient on the rear part of the endwall. The above analyses indicate that the purge flow from the upstream slot can provide a certain film cooling effectiveness. Meanwhile, it increases the heat transfer on the endwall, which is not beneficial to cooling protection of the endwall. Therefore, taking both of the effects into account, a net heat flux reduction (NHFR) is adopted to quantify the thermal load on the endwall. The NHFR is defined as

NHFR ¼

(a) α = 30 X Cax = 0

X Cax = 0.13

(b) α = 45

qw;0  qw qw;0

ð5Þ

where qw;0 denotes the wall heat flux without upstream slot, qw denotes the wall heat flux with upstream slot.

qw;0 ¼ h0 ðT 1  T w Þ

ð6Þ

qw ¼ hðT aw  T w Þ

ð7Þ

Combining (5)–(7), NHFR can be written as

X Cax = 0

X Cax = 0.13

NHFR ¼ 1 

  hðT aw  T w Þ h T1  Tc 1g ¼1 h0 ðT 1  T w Þ h0 T1  Tw

ð8Þ

T c In Ref. [27], TT11T ¼ 1:6 is typically used for a typical film-cooled w

(c) α = 60 X Cax = 0

X Cax = 0.13

X Cax = 0

X Cax = 0.13

(d) α = 90

Fig. 11. Streamline distributions on the planes X=C ax ¼ 0 and X=C ax ¼ 0:13 for MFR ¼ 1:0%.

turbine engine conditions. It is noted that if NHFR < 0, it will mean that the heat flux on the endwall is increased by the film cooling. Fig. 14 shows the laterally averaged NHFR distributions on the endwall. The purge flow can effectively reduce the heat flux to the endwall at X=C ax < 0:2, it also has few influences on the heat flux to the endwall at X=C ax > 0:6. When MFR < 1.0%, the NHFR is less than zero near the throat region of the passage, which indicates that the film cooling causes the increase of local heat flux on this region when compared with the case without film cooling. It is because that the throat region of the passage is not well protected by the coolant, at the same time, the coolant ejection increases the heat transfer coefficient on this region. Higher MFR can provide a better cooling protection for the endwall. On one hand, as the increase of MFR, the NHFR on the endwall is reduced. On the other hand, the heat flux reduction region becomes larger at

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μT μ L

α = 30

α = 45

α = 60

α = 90

(a) MFR = 1.0% Flow turbulence reduction region

α = 30

α = 45

α = 60

α = 90

(b) MFR = 1.5% Fig. 12.

lT =lL distributions on the endwall.

higher MFR. As the increase of a, the NHFR is reduced, which indicates that the larger a has a negative influence on the cooling protection for the endwall. In addition, when MFR < 1.0%, the a has no significant influence on the area of heat flux reduction region. When MFR > 1.0%, as the increase of a, the region under well cooling protection by purge flow is decreased. 3.3. Effect of MFR and a on the aerodynamic performance The effect of the purge flow ejection on the aerodynamic losses is discussed in this section. The total pressure loss coefficient
np;t proposed in Ref. [28] is used to indicate aerodynamic losses. The total pressure loss coefficient
np;t is defined as follows m1


np;t ¼ m1 þmc

c pt;1 þ m1mþm pt;c  pt;out c

q1 U 21 =2

ð9Þ

where m1 is the mass flow rate at main flow inlet; mc is the mass flow rate at purge flow inlet; pt;1 is the total pressure at main flow inlet and pt;c is the total pressure at purge flow inlet; pt;out is the total pressure at the turbine blade outlet. Fig. 15 shows the total pressure coefficient based on various MFR conditions and ejection angles. The total pressure coefficient under the condition without upstream slot purge flow is 0.5502 as the reference. The aerodynamic losses are promoted by the purge flow ejection for all conditions comparing with the reference. When MFR < 0.75%, the a has little influence on the aerodynamic losses. As the increase of MFR, the effect of a on the aerodynamic losses tends to be more significant, the increase of a improves the aerodynamic losses as well. When a > 45°, the increase of the purge flow rate enhances the aerodynamic losses. However, when a < 45° and MFR > 1.0%, the increase rate of the aerodynamic losses is reduced. Especially at the point when a ¼ 30 , the maximum value of aerodynamic losses is reached at MFR = 1.0%, and the aerodynamic losses is decreased with the

growth of MFR when MFR > 1.0%. The effect of the purge flow on the secondary flow is responsible for this phenomenon. Fig. 16 shows the local total pressure loss coefficient distributions at X=C ax ¼ 1:2 section when a ¼ 30 and 90 . The passage vortex is presented by the aerodynamic loss core and the wake is responsible for the high loss strip region. It is clear that the variation of the passage vortex with the MFR at a ¼ 30 is different with that at a ¼ 90 . When a ¼ 90 , the increase of the purge flow rate enhances the passage vortex intensity and causes more aerodynamic losses. When a ¼ 30 and MFR < 1.0%, the passage vortex intensity is enhanced as the increase of MFR, and the maximum intensity of the passage vortex is reached at MFR = 1.0%. With further increase of MFR, the passage vortex intensity is reduced to lead to the reduction of the aerodynamic losses. The purge flow has two main effects on the passage vortex. On one hand, the coolant ejection can enhance the horseshoe vortex. The pressure side leg of the horseshoe vortex moves from the pressure side to the suction side and is merged with the passage vortex to strengthen the passage vortex intensity. Hence, the increase of the horseshoe vortex intensity by the purge flow can enhance the passage vortex intensity. On the other hand, the purge flow can increase the momentum of the boundary layer. The enhancement of the momentum of the boundary layer caused by the purge flow is greater at lower a since the purge flow has more horizontal momentum. Greater momentum of the boundary layer can improve the ability of the fluid in the boundary layer to resist the transverse pressure difference between the pressure side and the suction side, so the passage vortex strength is decreased. Fig. 17 shows the limiting streamlines on the endwall surface. Comparing with the case without the purge flow, the triangular region between the separation line and the suction side denoting the extent of the passage vortex is reduced because of the reduction of the passage vortex resulted by the purge flow. To sum up, the purge flow has two opposite effects on the passage vortex. When a > 45°, the enhancement of the momentum of the boundary

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Fig. 13. Axial distributions of laterally averaged h=h0 on the endwall.

layer by the purge flow is not significant, and the purge flow can increase the horseshoe vortex strength so as to enhance the passage vortex intensity, thus the increase effect of the purge flow on the passage vortex turns to be the domination and results in the enhancement of the aerodynamic losses as the increase of the MFR. When a < 45°, especially when a ¼ 30 , the influence of the purge flow on the momentum of the boundary layer is limited when the MFR is less than 1.0%, so the increase effect of the purge flow on the passage vortex is still in domination. But as soon as purge flow rate is >1.0%, the purge flow can significantly enhance the momentum of the boundary layer to reduce the passage vortex

intensity, so the strong reduction effect of the purge flow on the passage vortex takes place. This is responsible for the reduction of the aerodynamic losses when MFR > 1.0% and a ¼ 30 . The influences of the a on the passage vortex vary with different MFR. Fig. 18 shows local total pressure loss coefficient distributions at X=C ax ¼ 1:2 section for MFR = 0.5% and MFR = 1.5%. The ingestion of the main flow takes place at MFR = 0.5%, resulting in the reduction of the horseshoe vortex strength, and this phenomenon is aggravated at larger a. The passage vortex intensity is reduced accordingly due to the reduction of the horseshoe vortex strength as mentioned above. Hence, when MFR = 0.5% the passage

L. Song et al. / Applied Thermal Engineering 110 (2017) 504–520

517

1.8

MFR=1.5%

1.6

30deg 45deg 60deg 90deg

1.4

NHFR

1.2 1 0.8 0.6 0.4 0.2 0 -0.2

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

X/Cax Fig. 14. NHFR distributions on the endwall.

vortex intensity is reduced as the increase of a. However, with the increase of MFR, the purge flow can enhance the horseshoe vortex intensity, and the enhancement of which is greater at larger a. Consequently, when MFR = 1.5%, the passage vortex intensity is enhanced as the increase of a shown in Fig. 18(e)–(h). 3.4. Comparison with previous studies In this section, results acquired from this study are compared with other typical studies. Fig. 19 presents the axial distributions of laterally averaged film cooling effectiveness on the endwall from

present study and other typical studies. In Fig. 19, it is presented according to the results of present study that high film cooling effectiveness region is restricted to the fore part of the passage, which is similar to the results of other typical studies. For these blades with the high turning angle, the strong transverse pressure gradient makes it difficult for the coolant to penetrate into the secondary flows to cover the entire endwall. Papa et al. [2] considered the effect of blowing ratio of the purge flow, Barigozzi et al. [24] investigated the influence of swirling of purge flow and the experiment of Li et al. [26] was focused on the turbulence intensity. Most of these studies were focused on the influence of flow conditions.

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4. Conclusions

Fig. 15. Aerodynamic losses for different MFR and a.

In the present study, both the flow condition and the geometry of the upstream slot were investigated, and in Fig. 19 it is obvious that the film cooling effectiveness of endwall can be improved by geometry optimization of upstream slot such as the ejection angle of slot.

In this paper, the effect of the purge flow on film cooling, heat transfer and aerodynamic characteristics of the endwall is numerically investigated by using three-dimensional Reynolds-averaged Navier-Stokes equations coupled with the k  x turbulence model. The validation of numerical method shows that the numerical results are in well agreement with the experimental data. The majority of the coolant ejection is restricted to the suction side of the endwall to provide local cooling effectiveness due to the effect of the secondary flow near the endwall. Systematically increasing the ejection angle a is presented to reduce film cooling effectiveness and distribution uniformity. The reduction of endwall averaged film cooling effectiveness is as high as 53.4% when the ejection angle a is increased from 30° to 90° at MFR = 1.5%. The purge flow can increase the horseshoe vortex intensity and cause separation vortex to enhance the local heat transfer coefficient of the endwall at X=C ax < 0:2. Meanwhile, as the increase of either the ejection angle a or MFR, the heat transfer coefficient near the leading edge is increased. However, when the MFR is >1.0%, as the increase of the MFR, the heat transfer coefficient of the endwall at 0:2 < X=C ax < 0:6 is reduced for the ejection angle a = 30° and 45° due to the flow turbulence reduction caused by the strong flow acceleration of the purge flow. Especially for the ejection angle a = 30°, the heat transfer coefficient is reduced by 16.77% at X=C ax ¼ 0:4 when the MFR is increased from 1.0 to 1.5%. The purge flow can reduce the net heat flux to the endwall for the fore part of the blade passage. The reduction of the ejection

ξlocal

MFR = 0.5%

MFR = 0.75%

MFR = 1.0%

MFR = 1.25%

MFR = 1.5%

MFR = 0.75%

MFR = 1.0%

MFR = 1.25%

MFR = 1.5%

(a) α = 30

MFR = 0.5%

(b) α = 90

Fig. 16. nlocal distributions at X=C ax ¼ 1:2 section for a ¼ 30 and 90 .

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(b) MFR = 1.5%, α = 30

(a) No upstream slot

Fig. 17. Limiting streamlines on the endwall.

ξlocal

α = 30

α = 45

α = 60

α = 90

α = 60

α = 90

(a) MFR = 0.5%

α = 30

α = 45 (b) MFR = 1.5%

Fig. 18. nlocal distributions at X=C ax ¼ 1:2 section for MFR ¼ 0:5% and MFR ¼ 1:5%.

the MFR is less than 1.0% for all ejection angles. Only when the MFR increases to 1.5%, can the ejection coolant reduce the net heat flux near the throat region for all ejection angles. Comparing with the case without purge flow, the purge flow increases the aerodynamic losses. The aerodynamic losses is increased with the growth of the MFR when the ejection angle a > 45 . When the ejection angle a < 45 , as the increase of the MFR, the aerodynamic losses is first increased and then reduced. The largest aerodynamic losses are obtained at MFR = 1.0%. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant No. 51676149). References

Fig. 19. Axial distribution of laterally averaged film cooling effectiveness on the endwall in present study and other typical studies.

angle a can improve the reduction of the net heat flux to the endwall. However, the net heat flux to the endwall near the throat region is increased (NHFR < 0) by the ejection of coolant, when

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