Fariborz ForghanDepartment of Mechanical and

Industrial Engineering,

Northeastern University,

Boston, MA 02115

Omid AskariDepartment of Mechanical Engineering,

Mississippi State University,

Starkville, MS 39762

Uichiro NarusawaDepartment of Mechanical and

Industrial Engineering,

Northeastern University,

Boston, MA 02115

Hameed MetghalchiDepartment of Mechanical and

Industrial Engineering,

Northeastern University,

Boston, MA 02115

Cooling of Turbine BladesWith Expanded Exit Holes:Computational Analysesof Leading Edge and Pressure-Side of a Turbine BladeTurbine blades are cooled by a jet flow from expanded exit holes (EEH) forming a low-temperature film over the blade surface. Subsequent to our report on the suction-side(low-pressure, high-speed region), computational analyses are performed to examine thecooling effectiveness of the flow from EEH located at the leading edge as well as atthe pressure-side (high-pressure, low-speed region). Unlike the case of the suction-side,the flow through EEH on the pressure-side is either subsonic or transonic with a weakshock front. The cooling effectiveness, g (defined as the temperature difference betweenthe hot gas and the blade surface as a fraction of that between the hot gas and the coolingjet), is higher than the suction-side along the surface near the exit of EEH. However, itsmagnitude declines sharply with an increase in the distance from EEH. Significant effectson the magnitude of g are observed and discussed in detail of (1) the coolant mass flowrate (0.001, 0.002, and 0.004 (kg/s)), (2) EEH configurations at the leading edge (verticalEEH at the stagnation point, 50 deg into the leading-edge suction-side, and 50 deg intothe leading-edge pressure-side), (3) EEH configurations in the midregion of the pressure-side (90 deg (perpendicular to the mainstream flow), 30 deg EEH tilt toward upstream,and 30 deg tilt toward downstream), and (4) the inclination angle of EEH.[DOI: 10.1115/1.4035829]

Keywords: turbine blade, film cooling, expanded exit hole, cooling effectiveness,pressure-side, computational simulation, compressible flow, cooling optimization

1 Introduction

The film cooling of turbine blades has been investigated exten-sively since the pioneering work by Goldstein et al. [1,2]; how-ever, the design parameters have not been discussed in relation tothe film cooling of turbine blades. The blades are cooled by low-temperature air bled from primary stages of the compressor. Thecoolant air, after passing through the serpentine passages withinthe blade, is discharged from EEH onto the blade surface to createa cooling film over the blade, thus protecting the blade surfacesfrom high-temperature gas (combustion product) flow. The cool-ing effectiveness, g, of EEH is defined as the temperature differ-ence between the gas flow over the blade and the blade surface asa fraction of the temperature difference between the gas flow andthe coolant at the inlet to EEH

g ¼ Th � Ts

Th � Tc(1)

with Th is the (static) temperature of mainstream gas flow, Tc isthe (static) temperature of coolant flow at the inlet of EEH, and Ts

is the temperature of turbine blade surface. The magnitude of gvaries along the blade surface through Ts for fixed values of Th

and Tc. The optimization of the film flow is aimed at achieving ahigh cooling effectiveness distribution along the surface of boththe first- and the second-stage blades. Various hydrodynamic andthermal analyses of the film cooling had been reported in the past,

including Refs. [3] (on cooling film development), [4] (flow meas-urements), [5–12] (the heat transfer coefficient and the coolingeffectiveness), and [13–16] effects of mixing between the coolantand the hot gas, vortex, and turbulence. Reports on the geometriceffects of EEH on the film cooling are available in Refs. [17](conical hole), [18] (trapezoidal hole), [9,19–23] (converging slotholes), [24–27] (EEH with compound angles), [28] (laid-backcylindrical holes), and [29] (trenched shaped holes). The above-mentioned studies were mostly experiment-oriented includingwind tunnel tests. Numerical investigations may also be found inRefs. [30–32] (cascade from the suction- to the pressure-side),[33,34] (inclined converging holes), and [35] (heart-shaped EEH).As is the case with any type of flow through a restriction of com-plex geometry, a discharge coefficient is defined for EEH [36–39]as

CD ¼_mact

_misen

(2)

where _mact is the actual mass flow rate through EEH, and _misen isthe mass flow rate through EEH under isentropic flow conditions;the former is measured for a specified EEH, while the latter isevaluated theoretically for given reservoir and geometric condi-tions of EEH. The magnitude of CD should be less than unitybecause such irreversible effects as gas expansion/contraction andviscous shear cause deviations from isentropic conditions. How-ever, various experimental reports in the past maintained that CD

exceeds 1.0 for EEH under certain conditions [40–42]. Startingwith Forghan [43], it has been shown that the flow through EEHmay be choked at the throat (¼the minimum flow cross section),resulting in the presence of a shock front within EEH. A new

Contributed by the Advanced Energy Systems Division of ASME for publicationin the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received December14, 2016; final manuscript received December 26, 2016; published online March 8,2017. Special Editor: Reza Sheikhi.

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definition of the discharge coefficient for EEH is proposed in Ref.[44] to take the choked flow conditions into consideration. Oncethe flow through EEH is choked, the isentropic (ideal) mass flowrate in the denominator of CD becomes independent of the backpressure as well as the combustion gas velocity over turbineblades. The magnitudes of CD under the new definition are signifi-cantly different from the previously reported values which arebased on the isentropic flow analysis when the flow is not chokedat the throat. Its magnitude never exceeds unity as any real (irre-versible) mass flow rate is always less than the choked mass flowrate predicted from the isentropic flow conditions upstream of thethroat. Computational analyses of the film cooling effectivenessare reported in Refs. [45–47] for the suction-side (high-speed,low-pressure) of a blade. The studies showed significant effects ofthe coolant flow pattern (the absence/presence and the location(within or outside EEH) of a shock front)) on the distribution ofthe cooling effectiveness along the blade surface. This report, ascontinuation of our studies on the film cooling technology, dealswith hydrodynamic and thermal effects of EEH placed in thepressure-side (low-speed, high-pressure) of a turbine blade.

2 Computational Analysis

We consider the same case as the suction-side analyses[45–47], in which EEH are placed at 10 mm interval on the bladesurface in the direction normal to the high-temperature gas flowwith the computational domain in the gas flow being taken to bebetween the blade surface and ten times the blade chord line(¼10� 65 mm) above the surface into the pressure-side flow. Theblade material we used in this report is Titanium (k (thermal con-ductivity)¼ 17 (W/m K)). The blade cross section is sketched inFig. 1. Our numerical values (ranges) are

pg (static pressure of gas flow)¼ 300 (kPa),Th (static temperature of gas flow)¼ 1500 (K), andTc (static inlet temperature of coolant flow)¼ 300 (K).

EEH: Cone-shaped

Ae/A* (exit-to-throat cross-sectional area ratio (AR))¼ 3.5,

Dt (minimum diameter)¼ 2 mm, andh (vertex angle (angle between the centerline and theperiphery))¼ 8 deg.

For EEH at the central region of the pressure-side, u (inclina-tion angle (angle between the centerline and the downstream sideof the blade surface))¼ 60 deg or 90 deg or 120 deg. Near thestagnation point of the leading edge, EEH are placed in one of thefollowing three locations:

Location (1): vertical at the stagnation point,Location (2): 50 deg from the center plane of location (1) to theleft (to the suction-side), andLocation (3): 50 deg from the center plane of location (1) to theright (to the pressure-side).

A commercially available computational fluid dynamics (CFD)program, ANSYS CFX FLUENT, is used to solve the governing

equations (conservation of mass, momentum, and energy with j–eturbulent flow solver and temperature-dependent properties, theideal gas equation of state for the flow, and the thermal conduc-tion equation for the blade). The computational mesh size (thenumber of computational elements) of the mainstream flow, theblade, and the EEH has to take into considerations of such effectsas the finer grids in the boundary layers at the blade surfaces andin the EEH surfaces as well as conduction within the body of theblade. The number of elements is �600,000 as a mixture of ele-ments with quadrangle- and triangle-cross section, determinedfrom the convergence of the computed distribution of the bladesurface temperature (as any further increase in the number of ele-ments is confirmed to affect the magnitude of the blade surfacetemperature by much less than 1%).

3 Results and Discussion

Figure 2 shows the computational validity test of g versus S/Dt

(distance from the downstream edge of EEH, normalized withrespect to the EEH minimum diameter Dt) for the blade of Fig. 1(low-conductivity blade material (rubber), u¼ 90 deg, and _m(coolant mass flow rate)¼ 5� 10�4 (kg/s)) [47]. Our computa-tional result (solid curve) shows a good agreement with the datapoints of Liu et al. [22].

Because the pressure-side of the turbine blade is characterizedby high-pressure and low-gas speed compared to the suction-side,our examinations of computed Mach number distribution alongthe passage indicate that the coolant flow through EEH is eithersubsonic or transonic with a weak shock front. Figures 3–5,respectively, present (a) the temperature profile (distribution), (b)the Mach number profile, and (c) g versus S/Dt when EEH are atthe following three different locations near the leading-edge stag-nation point.

A comparison of these temperature profiles clearly indicatesthat EEH placed near the leading-edge stagnation point onlyserves to enhance cooling of the suction-side and a part of thepressure-side upstream of EEH. The effectiveness distributiondoes not show differences of note between EEH at the stagnationpoint (Fig. 3(c)) and EEH at the suction-side of the stagnationpoint (Fig. 4(c)) although EEH at the stagnation point registers aslightly higher effectiveness over the suction-side surface of theblade. A significantly higher effectiveness is achieved by EEHplaced at the pressure-side of the leading-edge stagnation point(Fig. 5(c)). The improvement appears only in the suction-side,where @g/@(S/Dt) (a change of the slope of the effectiveness along

Fig. 1 Blade cross section at the midplane, hole angle of90 deg from the blade surface on the pressure-side

Fig. 2 g (cooling effectiveness) versus S/Dt (distance from theedge of EEH, normalized with respect to EEH throat (minimum)diameter). Filled triangle experiment from Ref. [22] and solidcurve—this study. (Reproduced with permission from Forghanet al. [47]. Copyright 2016 by ASME).

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the blade surface) is low. In the case of Fig. 3, left (right) sidebelongs to the suction (pressure) side of the blade, while, in Fig. 4(5), both left and right sides are part of the suction (pressure) sideof the blade surface. The g distributions over the blade surface

and their change may be related to these conditions of the EEHlocation.

Figures 6–8 are effectiveness distributions for EEH placed atthe central region of the pressure-side of the turbine blade when

Fig. 3 Profiles around EEH at the leading-edge stagnationpoint (EEH axis normal to the blade surface): (a) temperaturewith _m 5 4 3 1023 (kg/s), (b) the Mach number with _m 5 4 3 1023

(kg/s), (c) g versus S/Dt (right dotted—pressure-side, left solid—suction-side, bottom curves for _m 5 1023 (kg/s), middle curvesfor 2 3 1023 (kg/s), and top curves for 4 3 1023 (kg/s))

Fig. 4 Profiles around EEH at the leading-edge suction-side:(a) temperature, _m 5 4 3 1023 (kg/s), (b) the Mach number,_m 5 4 3 1023 (kg/s), and (c) g versus S/Dt (right dotted—

pressure-side, left solid—suction-side, bottom curves for_m 5 1023 (kg/s), middle curves for 2 3 1023 (kg/s), and top

curves for 4 3 1023 (kg/s))

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u¼ 90 deg (Fig. 6), u¼ 120 deg (Fig. 7), and u¼ 60 deg (Fig. 8)with (a) as the temperature distribution, (b) as the Mach numberdistribution over the blade surface, and g versus S/Dt in (c) forthree different _m values of 10�3 (bottom), 2� 10�3 (middle), and4� 10�3 (top) (kg/s). When EEH are directed either straight intothe pressure-side flow (Fig. 6) or upstream (Fig. 7), the cooling jet

may be seen to affect mostly the region upstream of EEH. Also,the cooling effectiveness drops sharply on the right-hand side (theregion downstream of EEH) with increase in S/Dt, implying thatthe jet from EEH creates a cooling film most effectively in theupstream region along the pressure-side. On the other hand, whenthe EEH inclination angle is 60 deg as sketched in Fig. 8 (i.e., the

Fig. 6 Profiles around EEH at pressure-side central region,u 5 90 deg: (a) temperature, _m 5 4 3 1023 (kg/s), (b) the Machnumber, _m 5 4 3 1023 (kg/s), and (c) g versus S/Dt (rightdotted—pressure-side, left solid—suction-side, bottom curvesfor _m 5 1023 (kg/s), middle curves for 2 3 1023 (kg/s), and topcurves for 4 3 1023 (kg/s))

Fig. 5 Profiles around EEH at the leading-edge pressure-side:(a) temperature, _m 5 4 3 1023 (kg/s), (b) the Mach number,_m 5 4 3 1023 (kg/s), and (c) g versus S/Dt (right dotted—

pressure-side, left solid—suction-side, bottom curves for_m 5 1023 (kg/s), middle curves for 2 3 1023 (kg/s), and top

curves for 4 3 1023 (kg/s))

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jet is directed downstream along the blade surface), a cooling filmis formed on the downstream side of the blade surface (Figs. 8(a)and 8(b)), resulting in high effectiveness values in both theupstream and the downstream regions near EEH for _m¼ 4� 10�3

(kg/s).The effectiveness may be seen to deteriorate sharply on the

downstream side than on the upstream side when _m is reduced

from 2� 10�3 (kg/s) to 4� 10�3 (kg/s), implying that the overalleffects of EEH on the pressure-side of the turbine blade mostlyhelp improve cooling of the region upstream of EEH location.Figure 8(c) also clearly demonstrates a shift in the effectivenessdistribution from high effectiveness in the region downstream of

Fig. 7 Profiles around EEH at pressure-side central region,u 5 120 deg: (a) temperature, _m 5 4 3 1023 (kg/s), (b) the Machnumber, _m 5 4 3 1023 (kg/s), and (c) g versus S/Dt (rightdotted—pressure-side, left solid—suction-side, bottom curvesfor _m 5 1023 (kg/s), middle curves for 2 3 1023 (kg/s), and topcurves for 4 3 1023 (kg/s))

Fig. 8 Profiles around EEH at pressure-side central region,u 5 60 deg: (a) temperature, _m 5 4 3 1023 (kg/s), (b) the Machnumber, _m 5 4 3 1023 (kg/s), and (c) g versus S/Dt (rightdotted—pressure-side, left solid—suction-side, bottom curvesfor _m 5 1023 (kg/s), middle curves for 2 3 1023 (kg/s), and topcurves for 4 3 1023 (kg/s))

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EEH at _m¼ 1� 10�3 (kg/s) to high effectiveness in the regionupstream of EEH at _m¼ 4� 10�3 (kg/s).

Figure 9 shows the temperature profile near EEH placed in themiddle region of the pressure-side at the coolant mass flow rate of_m¼ 1� 10�3 (kg/s). The high back pressure coupled with the low

coolant flow rate is shown to cause the penetration of the hot gasinto the region within EEH, which could result in the burnout ofthe EEH wall.

Finally, Figs. 10(a) and 10(b) are presented to show coupledeffects of the parameters on the distribution of the cooling effec-tiveness. In both cases, EEH are tilted 30 deg to the right. Figure10(a) with the coolant mass flow rate of _m¼ 2� 10�3 (kg/s) indi-cates that the blade surface cooling is achieved at the downstreamside, the intended region for cooling effects. However, when thecoolant flow rate is reduced to _m¼ 1� 10�3 (kg/s) as shown inFig. 10(b), the resulting cooling moves to the upstream (left handside) region.

4 Summary and Conclusions

A flow through EEH placed along the suction-side of the tur-bine blade had been shown to be typically choked at its throat[43,44], resulting in a supersonic flow, a shock, and then a sub-sonic flow downstream. The location of the shock relative to thehigh temperature gas flow determines the temperature distributionalong the suction-side of the blade surface, as presented in Refs.[45–47]. On the other hand, the flow through EEH placed on theleading edge as well as on the pressure-side is either subsonic ortransonic with a weak shock front. When EEH are placed near theleading-edge stagnation point where the suction and the pressuresides meet, the cooling effectiveness improves mostly in theregion to the left of EEH (suction-side) over _m range of the pres-ent study, 1� 10�3–4� 10�3 (kg/s). EEH placed at the centralpart of the pressure-side may create cooling film either on theupstream or on the downstream side, depending on the magnitudeof _m and/or u, although greater improvements occur upstreamside of EEH in the magnitude of the cooling effectiveness. Com-putation analyses presented in Refs. [45–47] for the suction-sideand the present report for the pressure-side together are aimed atquantifying the distribution of g around a single row EEH. Ther-mofluid and geometric conditions are varied to find quantitativeeffects of such factors as _m, u, DT, AR, the EEH location, and theblade material on the cooling effectiveness. Evaluations of thefilm cooling technology must be performed on the g-distributionover the entire surface of a turbine blade as the cooling jet fromeach EEH affects the flow- and temperature-field of the entireblade surface. However, our study has shown successfully that thecomputational approach offers an effective way for optimizationof the film cooling technology.

Nomenclature

Ae ¼ EEH exit cross-sectional areaA* ¼ EEH throat cross-sectional areaCD ¼ discharge coefficientDt ¼ EEH minimum diameterK ¼ thermal conductivity of blade material (W/m K)_m ¼ (¼ _mact) jet mass flow rate

_misen ¼ mass flow rate through EEH under isentropic flowconditions

pb ¼ back pressure¼ pressure of hot gas flowpg ¼ pressure of hot gas flowp0 ¼ stagnation pressure of the coolant flowS ¼ distance from the downstream end of EEH along the

blade surfaceTc ¼ static temperature of coolant flow at the inletTh ¼ static temperature of mainstream gas flowTs ¼ temperature of turbine blade surface

DT ¼ Th� Tc

Greek Symbols

g ¼ EEH cooling effectiveness (Eq. (1))h ¼ vertex angle (EEH angle between the centerline and the

periphery)u ¼ inclination angle (EEH angle between the centerline and

the downstream side of the blade surface

Fig. 9 Temperature profile around EEH at the pressure-side,showing the hot mainstream gas penetrating into EEH due tolow coolant flow ( _m 5 1023 (kg/s))

Fig. 10 Temperature profile of the pressure-side EEH 30 deg tothe right: (a) coolant flow rate 5 0.002 (kg/s) and (b) coolantflow rate 5 0.001 (kg/s)

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Acronyms

AR ¼ area ratio (¼Ae/A*)

CFD ¼ computational fluid dynamicsEEH ¼ extended exit hole

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