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Applied Thermal Engineering 27 (2007) 692–698

Advances in effusive cooling techniques of gas turbines

Giovanni Cerri a, Ambra Giovannelli a, Lorenzo Battisti a,*, Roberto Fedrizzi b

a University of Rome3, via della Vasca Navale, 79, 00146 Rome, Italyb University of Trento – DIMS, via Mesiano, 77, 38050 Trento, Italy

Abstract

Gas turbine combustion chambers and turbine blades require better cooling techniques to cope with the increase in operating tem-peratures with each new engine model. Current gas turbine inlet temperatures are approaching 2000 K. Transpiration-cooled compo-nents have proved an effective way to achieve high temperatures and erosion resistance for gas turbines operating in aggressiveenvironments, though there is a shortage of durable and proven technical solutions. Effusion cooling, on the other hand, is a relativelysimple and more reliable technique offering a continuous coverage of cooling air over the component’s hot surfaces. This paper presents anumerical model suitable to design the geometric features of effusive cooling systems of gas turbine hot components, and to evaluate theirthermo-fluid-dynamic characteristics. The model has been developed specifically with the aim to show the potential advantages derivingfrom the adoption of the new Poroform� technology. According to this technology the design of the distributions of the diameter anddensity of holes on the cooled surface allows complete freedom for the thermo-mechanical optimization of the cooled component, with aview to reducing the metal’s working temperature and achieving isothermal conditions for large blade areas.

In this paper the diameter, density and spacing of the holes, the adiabatic film efficiency and the coolant air consumption of a firststage gas turbine effusion cooled blade are extensively discussed to highlight the system cooling capacity.

The results of two cooling solutions for a first-stage gas turbine blade are presented, i.e. the thermo-fluid-dynamic optimized designand one possible manufacturing-oriented optimized design of the cooled component.� 2006 Published by Elsevier Ltd.

Keywords: Effusive cooling; Gas turbines; Blades; Combustion chambers

1. Introduction

Numerous experimental and numerical studies haveshown the potential deriving from the adoption of transpi-ration cooling for advanced cooling problems [1–11]. Withregard to combustor liners cooling for instance, the maindrawback of pure film cooling is actually that the heat sinkpotential of the cooling air is not effectively utilized, andcooling air flows represent a significant portion of the totalflow entering the combustor. Consequently attention isfocused on wall cooling schemes that make more efficientuse of cooling air, allowing the designer more latitude inoverall secondary flow management.

1359-4311/$ - see front matter � 2006 Published by Elsevier Ltd.

doi:10.1016/j.applthermaleng.2006.10.012

* Corresponding author. Tel.: +39 0461 882515; fax: +39 0461 882599.E-mail address: lorenzo.battisti@ing.unitn.it (L. Battisti).

The transpiration cooling, for example, is obtained bymeans of porous walls; they combine two heat exchangeeffects: the convective one at the cooler surface and throughthe wall, and the ‘‘film’’ one at the warmer surface wherehot and cold gases mix. The mixing produces both anincrease of the heat exchange coefficient by convection,dependent on the fluids’ flow features, and a drop of thegas temperature at the surface (see Metzger et al. [12]).The net effect is however a decrease of the heat flux fromthe hot gas to the component’s surface.

Transpiration cooling is obtained, for instance, throughsintered stainless steel walls (Porosint� [13]), which usuallyhave a pore diameter ranging between 10 and 50 lm and awall thickness of about 1 mm. Although they have beenextensively used to demonstrate the suitability of porousmaterials and evaluate their thermodynamic efficiencies,problems occurring when the component has to cope with

Nomenclature

BR Blowing Ratioc chordDh hole hydraulic diameter_me;o effused cooling air mass flowNh holes’ densityr radiusrh blade hub radiuss curvilinear coordinateTwall wall temperatureTrec hot gas recovery temperature

Tfilm hot gas film temperatureTg,r hot gas total temperature at the rotor blade inletTe,o coolant effusive temperatureve,o coolant effusive speedvg hot gas speedx chordwise holes’ pitchgfilm adiabatic film efficiencyqe,o coolant effusive temperatureqg hot gas density

Hot gas stream

Coolant

Film coolingFilm

Coolant

FilmHot gas stream

Impingementcooling

Hot gas streamFilm

Effusion cooling

Coolant

Porous wallFilm

Transpiration

Coolant

Hot gas stream

Coolant

Hot gas stream

TransplyFilm

Convection

Impingement

Coolant

Hot gas stream

Lamilloy

Film

Hot gas stream

Coolant

Poroform

Film

Fig. 1. Main cooling technologies using intermediate fluids. (a) Coolingschemes; (b) wall manufacturing technologies suitable for cooling by aireffusion.

G. Cerri et al. / Applied Thermal Engineering 27 (2007) 692–698 693

both thermal and mechanical stress have limited the appli-cation of this technology to the turbomachinery field.

Meanwhile, manufacturing solutions have been deve-loped to reproduce the cooling features of porous walls insystems with a better behavior in terms of thermo-mechan-ical resistance. They are called effusive systems and adoptstructural solutions consisting of metallic nets and wallswith discrete holes. In the Seventies, Curtiss Wright [14]conducted tests on gas turbines using metallic nets shapedonto supports, obtaining good results in terms of bothTIT (turbine inlet temperature) and surface fouling. In theeighties two new technologies came onto the scene: theTransply� from [15] and the Lamilloy� from Detroit Diesel(G.M. Corporation) [16,17]. About the latter, an industrialuse is forecast for the combustion chamber of the F136 air-craft engine [18]. Transply� (see Fig. 1) is produced by braz-ing together two or more laminates of a high temperaturealloy containing an interrelated pattern of holes and chan-nels, produced by electro-chemical machining. Lamilloy�

(see Fig. 1) is a multi-laminate porous structure fabricatedfrom several diffusion-bonded, photoetched thin (0.254 to0.635 mm) metal sheets (usually three or five) (see Fig. 1).Typical holes diameter to spacing ratio could be around4. This solution allows freedom in holes size and spacing,laminate thickness, number of laminates, grid depth, griddiameter, and grid spacing. Serious thermal gradients arenevertheless an intrinsic drawback of such architecture.

Lamilloy� and Transply� were developed to maximizethe inner convective heat transfer, while much of the liter-ature on film cooling focuses on improving the heat shield-ing processes. When film cooling is used, the strategies forimproving the inner convection are impingement coolingand reducing the diameter of the holes (increasing theirnumber accordingly).

If the number of holes increases considerably, the filmcooling system is called an effusion cooling system. A num-ber of studies [19–27] analyze the performance of such sys-tems: walls have been investigated with hole diametersranging between 640 and 8820 lm, hole densities between4305 and 26910 m�2, and a spacing parameter x/Dh

between 1.9 and 10.7. No data are available on themechanical features of the slabs used. Regarding the fluid

dynamic behavior, permeability (or pressure difference)does not affect the hot–cold gas mixing process in the caseof porous media, but discrete holes strongly influence themixing process due to their larger diameter. In the lattercase, the injection velocities of the coolant are higher, thusreducing the stability of the boundary layer at the externalblade’s surface. The coolant injection speed can be moder-ated by reducing the diameter of the holes and increasingtheir number to maintain the same coolant mass flow. This

Fig. 2. Scheme of the control volumes.

694 G. Cerri et al. / Applied Thermal Engineering 27 (2007) 692–698

means that the boundary layer’s features can be influencedto a minor extent, as they are by a porous wall.

In effusion cooling systems, the inner convective heattransfer and the heat shielding process are strongly relatedin that an intense heat extraction by convection throughthe holes reduces the ability of the cooling air to lessenthe heat transfer between the hot gas and the blade’s wall,due to its higher temperature when it is injected into themain flow. Recently, a new technology called Poroform�

[28] (see Fig. 1) has been presented. It allows manufactur-ing components having walls equipped with micro holes,obtained by galvanic electroforming techniques. The fabri-cation process allows the fabrication of effusive systemswith the required distribution of hole diameter and densityon the cooled surface, to achieve isothermal conditions forlarge component areas. According to this technology, thecomponent is replicated onto a matrix serving as a cathodefor the galvanic bath. On the matrix, dielectric prefabri-cated areas prevent the metallic growth during the deposi-tion process, thus ending as holes on the electroformedwall.

While the mechanical strength is still under test, thethermo-fluid-dynamic behavior exhibited excellent poten-tial. In a former work [27], by the use of a dedicated 2Dmodel, the authors showed that a very effective cooling sys-tem performance can be obtained only by varying thediameter and distribution of the holes, without the needfor using pressure control systems within the blade.

The analysis indicated that for the selected test case, theblade could withstand temperatures up to 1200 K with TITequal to 2000 K, using the effusive cooling system describedherein, by providing at the same time an uniform tempera-ture distribution over the blade’s wall.

From the manufacturing point of view, a regular arrayof holes, instead of the one freely determined as a conse-quence of the thermo-fluid-dynamic optimization leads toa simpler fabrication of the matrix for the galvanic bath.Therefore, using the 2D code, a set of simulations were per-formed for a 3 mm thick gas turbine blade wall, which wallfeatures large areas having a single hole spacing. The effectof this technological choice on the cooling effectiveness,wall isotherms, blowing ratio is here presented anddiscussed.

2. 2D Numerical model

Taking the turbine’s cycle data as a starting point, thecode computes a 1D thermo-fluid-dynamic analysis at themid span, followed by a NISRE (non isentropic radialequilibrium) analysis, to assess gas temperature, pressureand velocity at the rotor inlet annulus. The 2D pressureand gas speed distributions on the rotor blade are thencomputed using a panel method [30]. The static gas temper-ature around the blade is calculated assuming a uniformtotal temperature along the rotor channel. Such anassumption is justified by the consideration that the totalamount of effused cooling air is minimal in current gas tur-

bine practice, and even less cooling air has been shown tobe necessary for the Poroform� technology [29]. The fea-tures of the effusing cooling air at the blade surface areobtained from said thermo-fluid-dynamic conditions byapplying the energy and mass conservation equations toappropriate control volumes. Fig. 2 shows the projectionsof the three control volumes considered (the length orthog-onal to the plane of the figure is unitary), i.e. volume (a)encloses the inner surface of the shell, volume (b) includesthe single hole through the blade wall and a proper volumeadjacent to the inner surface of the blade, and volume (c),with a generic surface area A, encloses a section of theblade wall and again a proper volume at the inner surfaceof the blade, like volume (b). A full discussion of the equa-tions applied to the three control volumes can be find in[29].

2.1. Choosing the geometric features of the wall

The code allows computing the hole diameter and sur-face distribution once the flow field conditions on the outersurface of the blade’s wall, the cooling air conditions at theblade’s hub and the wall temperature are known. Wallthickness and temperature depend on the materials usedand the maximum allowable stress on the blade, in bothtransient and stationary turbine working conditions. A firstevaluation suggested a suitable wall thickness between 0.5and 2.5 mm at a blade’s working temperature of 1200 K;this is typical of turbine components made out of single-crystal nickel-based alloys, like GTD 111, for example.Even though the mentioned wall thickness is adequate forblades manufactured with current techniques, a wall thick-ness of 3 mm was conservatively chosen for this analysis.

The choice of the optimal hole diameter is based on theassumption that both external and internal flow parameters(internal pressure, external pressure, main stream speed,temperature, etc.) are set as constraints. The geometricalfeatures of the cooling system (i.e. external hole diameterand distribution) are thus used as free variables to designa cooling system that minimizes the cooling air mass flow,once a maximum working temperature (Twall = 1200 K)and a maximum blowing ratio ðBR ¼ qe;ove;o=qgvg ¼ 0:4Þare set (this last constraint enables the disturbance on theboundary layer due to air injection from the blade wall

Table 1Blade’s geometrical parameters and flow features at the mid span

Cycle parameters

Cycle pressure ratio 9.1TIT (K) 2000Mass flow (kg/s) 23.4

Rotor parameters

Blade working temperature (K) 1200Peripheral velocity (m/s) 386Relative frame inlet angle (�) 42Relative frame inlet Mach number 0.59Relative frame total temperature (K) 1747Blade hub coolant pressure (bar) 6.3

Rotor blade geometrical features

Chord (mm) 42.7Height (mm) 38Pitch/chord 0.86

Fig. 4. Surface distribution of hole diameters.

G. Cerri et al. / Applied Thermal Engineering 27 (2007) 692–698 695

to be controlled). Thus the procedure allows a thermo-fluid-dynamic optimization of the hole diameter and spac-ing by setting an objective function written as

F obðx;DhÞ ¼ min _me;ojBR� 0:4 < 0; T wall � 1200 ¼ 0f g:ð1Þ

Since the holes are arranged in hexagonal arrays as inFig. 3 (this distribution assures the best surface coverageby the cooling air), holes’ spacing and diameter are con-nected to each other and to the hole density (holes persquare meter):

xDh

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3p

2NhD2h

s: ð2Þ

A manufacturing-oriented optimization, aimed at a simplerfabrication of the matrix used in the galvanic bath, is car-ried out with a similar procedure. According to such astrategy, wall temperature and effused-air blowing ratioare still set as constraints; however, the hole spacing isset uniform within large areas on the blade surface, allow-ing the hole diameter to be only free variable. It followsthat, the minimization of the effused-air flow rate is pre-cluded, if this design approach is pursued.

3. Results

A typical first-stage rotor blade in a heavy-duty gas tur-bine was chosen for the present analysis. Fig. 2 representsthe mid span section and Table 1 gives the turbine’s cycle,stage and geometrical data chosen for the numericalsimulations.

Figs. 3–7 show the results of the simulation where thehole diameters, hole density and spacing are obtained bysolving the objective function (Eq. (1)). Figs. 8 and 9 showthe blowing ratio and on hole diameter distribution conse-quent to fixing uniform hole spacing for large blade areas.

3.1. Thermo-fluid-dynamic optimization

Fig. 4 shows the external diameter of the holes versusthe normalized curvilinear coordinate s/c and the normal-

Fig. 3. Surface distribution of holes. The arrow shows the flow (chordwise)direction.

Fig. 5. Surface distribution of hole density.

ized blade length. Said diameter ranges between about 10and 90 lm on the blade’s outer surface, the minimum valuebeing prompted by the need to prevent fouling in the holes.The chordwise distribution of the hole diameters is stronglyaffected by the pressure gradient between the outer andinner sides of the blade’s wall. Where the external pressureis lower (along the red segments), the diameter of the holes

Fig. 6. Surface distribution of adiabatic film efficiency.

Fig. 7. Surface distribution of spacing parameter.

Fig. 8. Surface distribution of specific mass flow of coolant.

Fig. 9. Blowing ratio surface distribution.

696 G. Cerri et al. / Applied Thermal Engineering 27 (2007) 692–698

is smaller, while it becomes larger, the lower the pressuregradient. This parameter is also generally lower at theblade’s tip than at the hub because the cooling air pressureon the inner surface of the blade increases from hub to tipdue to the centrifugal force.

The distribution of the hole diameters depends on thelimitation imposed on the blowing ratio: where the pressuregradients are higher, the holes have to be narrower to pro-duce pressure losses intense enough to contain the cooling

air ignition speed. The constraint on the effusion speed lim-its the maximum diameter too, which in this case is about90 lm. The holes at the leading edge have a small diameteras well, for much the same reason: though minor pressuregradients are encountered at the leading edge between theinner and outer surfaces of the blade, the hot gas speed isnear zero, so the cooling air effusion velocity needs toapproach the same value.

The density of holes per unit area is shown in Fig. 5. Themaximum hole density is confined to the area with thesmallest hole diameters. I.E., the red area features hole den-sities higher than 3000 holes/cm2 with a peak at about9000 holes/cm2 at the very leading edge. A greater densityof holes in the areas where they have smaller diametersensures that the necessary cooling air mass flow is still pro-vided on the blade’s outer surface. The adiabatic film effi-ciency defined as:

gfilm ¼T rec � T film

T g;r � T e;o

ð3Þ

is plotted in Fig. 6. In the areas with narrower holes, theadiabatic film efficiency reaches its maximum values andthe film temperature drop (see Eq. (3)), giving rise to thebest heat shielding effect.

The plot in Fig. 7 comes from the one in Fig. 6, since theadiabatic film efficiency is more or less inversely propor-tional to the spacing parameter x/Dh. The adiabatic filmefficiency is in the range of 0.23–0.35, while the spacingparameter x/Dh varies from 3 to 10, which is typical of effu-sive cooling systems (see Andrews et al. [20]).

The distribution of the cooling air mass flow per unitarea is shown in Fig. 8: it follows the hole diameter andadiabatic film efficiency distributions, showing that a lowercoolant mass flow is needed in the areas where there is abetter heat removal from the wall (through narrower holes)and a better heat shielding at the blade’s outer surface. Thegeometrical configuration of the holes discussed aboveenables a total coolant mass flow of about 0.0057 kg/s tobe obtained for the whole blade. In the case of a turbinerotor built with 60 blades, the coolant mass flow is about1.2% of the hot gas mass flow.

G. Cerri et al. / Applied Thermal Engineering 27 (2007) 692–698 697

3.2. Manufacturing-oriented optimization

Figs. 3–7 show that a continuous variation of hole diam-eter and distributions guarantees an isothermal blade sur-face and minimum cooling mass flow consumption.

Since a great simplification in the fabrication of thematrix could be obtained if large areas on the blade’s sur-face are fabricated with uniform hole distribution, a newsolution of the cooling problem was investigated movingfrom the results of the former simulations oriented to athermo-fluid-dynamic optimization. In particular suchareas were tentatively identified moving from that ofalmost constant hole spacing (see) in Figs. 9 and 10 thoseareas are highlighted with rectangles named with lettersfrom ‘‘A’’ to ‘‘H’’. For each area, the hole spacing in chord-wise direction was established (see also Table 2). In partic-ular, it was decided to maintain the blowing ratio lowerthan 0.4 everywhere on the blade’s surface, while keepingan isothermal surface temperature of 1200 K.

Compared to what emerges from the simulations carriedout for the thermo-fluid-dynamic optimized case, the blow-ing ratio distribution presents a large variability on the sur-face ranging from 0.1 to 0.4 (see Fig. 9). For the samereason, the hole diameter distribution changes with respectto the one presented in Fig. 4. Fig. 10 shows that the aver-age hole diameter decreases significantly, even though thehole diameter still ranges from 10 to 90 lm.

The hole configuration discussed allows roughly thesame coolant mass flow to be effused through the blade sur-face compared to the thermo-fluid-dynamic optimized case,since this parameter is essentially proportional to the bladetemperature and working conditions. The matrix manufac-turing-oriented optimization brings an increase of theholes’ number by a factor of about 2.5, i.e. 14,000 holes

Table 2Spacing between rows of holes

A B C D E F G H

x hole spacing (lm) 450 250 120 60 200 300 500 600

Fig. 10. Temperature surface distribution.

in the thermo-fluid-dynamic optimized case – 33,000 holesin the present case, where the hole spacing is smaller thanthe optimum value for large portions of the blade’s surface.This increase is easily managed during the matrix fabrica-tion stage and does not determines additional fabricationcosts for the component, since this technology is cost insen-sitive to the number of holes required on the surface.

A further improvement with respect to the manufactur-ing process could be obtained if the hole diameter would beset constant within sub-areas that are included in the onespresented in Figs. 9 and 10. However, since in this case thehole diameter is set (i.e. it is not computed as in previouscases), a certain temperature variability has to be acceptedwithin each of the sub-areas. It follows that, the extent ofthe sub-areas as to be setup as a function of the maximumtemperature gradients that are acceptable on the blade’swall. This extra step is not presented in this paper forbrevity.

4. Conclusions

The paper presents a discussion of some consequences ofthe flexibility offered by the Poroform� technology on thedesign and performance of the effusive cooling systems.The 2D model, developed for designing and analyzing thegeometrical parameters of effusive cooling systems, provesthat a very effective cooling system performance can beobtained either by varying both the diameter and distribu-tion of the holes, or by fixing the hole spacing, with minoreffects on cooling effectiveness and cooling air consump-tion. The latter solution copes quite well with a simplifica-tion in the design and fabrication matrix for theelectroforming process. The analysis showed that for bothcases the blade can withstand temperatures up to 1200 Kusing the effusive cooling system described herein, and thatthe coolant mass flow for the manufacturing-optimizedcase resulted to be about unchanged compared to thethermo-fluid-dynamic optimized one.

References

[1] F.J. Bayley, J.W. Carnforth, A.B. Turner, Experiments on transpi-ration cooled combustion chamber, Proc. I. Mech 187 (1973) 187.

[2] F.J. Bayley, Performance and design of transpiration cooled turbineblading, AGARD Conference Proceedings No. 229. High Tempera-ture Problems in Gas Turbine Engines, Paper 10, 1978.

[3] I.E. Smith, M.J. Watts, Radiation heat transfer to a porous surfacecooled by transpiring flowCombustion and Heat Transfer in GasTurbine Systems, Pergamon Press, 1971, 207–228.

[4] G.E. Andrews, A.A. Asere, M.C. Mkpadi, Transpiration and fullcoverage discrete hole film cooling, I, in: E. Chem (Ed.), 11th AnnualResearch Meeting Proceedings, 1984, pp. 92–96.

[5] G.E. Andrews, A.A. Asere, Transpiration cooling of gas turbinecombustion chamber walls, in: Proceedings of the First U.K.National Heat Transfer Conference, Leeds, I. Chem. E. SymposiumSeries No. 86, 2, pp. 1047–1056.

[6] F.J. Bayley, A.B. Turner, Transpiration cooled turbines, AGARDCP-73-71, High Temperature Turbines, Paper 12, 1970.

[7] P. Grootenhuis, The mechanism and application of effusion cooling,J. Royal Aero. Soc. 63 (1959) 73–89.

698 G. Cerri et al. / Applied Thermal Engineering 27 (2007) 692–698

[8] M. Torii, N. Nishiwaki, M. Hinta, Heat Transfer and skin friction inturbulent boundary layer with mass injection, in: Proceedings of theThird Int. Heat Transfer Conference, 1966, pp. 34–48.

[9] G. Cerri, C. Marra, A. Sorrenti, S. Spinosa, Iniezione di vapore nelleturbine a gas e raffreddamento delle palette: considerazioni teoriche.IV Convegno Nazionale Gruppi Combinati Prospettive Tecniche edEconomiche, Firenze, 31 maggio 1990.

[10] G. Cerri, C. Marra, A. Sorrenti, S. Spinosa, Iniezione di vapore nelleturbine a gas e raffreddamento delle palette: analisi di un’applicaz-ione. IV Convegno Nazionale Gruppi Combinati Prospettive Tecni-che ed Economiche, Firenze, 31 maggio 1990.

[11] J.C. Wolf, S. Moskowitz, G.R. Manning, Development of a HighTemperature Turbine Operation on Coal Derived Fuel, ASME Paper80-GT-188, 1980.

[12] D.E. Metzger, H.J. Carper, L.R. Swank, Heat Transfer with filmcooling near non-tangential slots. Trans. ASME J. Eng. Power (1) 1968.

[13] Technical pages, Available from: www.gkn.com.[14] Curtiss-Wright topical Report, low pressure rig engine test Program,

FE-2291-75, 1981.[15] D.A. Nealy, S.B. Reider, Evaluation of laminated porous wall

materials for Combustor linear cooling, ASME Paper 79-GT-100,1979.

[16] D.A. Nealy, S.B. Reider, H.C. Mongia, Alternate cooling configura-tion for gas turbine combustion systems, AGARD-CPP-390, HeatTransfer and Cooling in Gas Turbines, Paper 25, Bergen, May 1985.

[17] A.B. Wassel, J.K. Bhangu, The development and application ofimproved combustor wall cooling techniques, ASME Paper 80-GT-79and Trans. ASME J. Eng. Power (106) 1984, pp. 183–192.

[18] Technical pages GE Transportation – Aircraft Engines: F136, http://www.geae.com.

[19] G.E. Andrews, M.C. Mkpadi, Full Coverage Discrete hole WallCooling – Discharge Coefficients, ASME Paper 83-GT-79 and Trans.ASME J. Eng. Power (106) 1985, pp. 183–192.

[20] G.E. Andrews, M.K. Gupta, M.C. Mkpadi, Full Coverage DiscreteHole Wall Cooling: Cooling Effectiveness, ASME Paper 84-GT-212,1984.

[21] G.E. Andrews, M.L. Gupta, M.C. Mkpadi, Combined radiative andconvective heat transfer in an enclosure, in: Proceedings of the FirstU.K. National Heat Transfer Conference, Leeds, I. Chem. E.Symposium Series No. 86, 2, 1984, pp. 929–988.

[22] G.E. Andrews, A.A. Asere, M.C. Mkpadi, A. Tirmahi, Transpirationcooling: contribution of film cooling to the overall cooling effective-ness, Int. J. Turbo Jet Engine 3 (1986) 245–256.

[23] G.E. Andrews, A.A. Asere, C.L. Hussain, M.C. Mkpadi, 1985,Transpiration and full coverage discrete hole impingement/effusionfilm cooling, in: Proceedings of the Seventh International Conferenceon Air Breathing Engines, Peking, AIAA, p. 12.

[24] G.E. Andrews, A.A. Asere, M.L. Gupta, M.C. Mkpadi, FullCoverage Discrete Hole Film Cooling: The Influence of Hole Size,ASME Paper 85-GT-47, 1985.

[25] G.E. Andrews, I.M. Khalifa, A.A. Asere, F. Bazdidi-Tehrani, FullCoverage Effusion Film Cooling with Inclined Holes, ASME Paper95-GT-274, 1995.

[26] J.J. Scrittore, K.A. Thole, S.W. Burd, Investigation of VelocityProfiles for Effusion Cooling of a Combustor liner, ASME PaperGT2006-90532, 2006.

[27] L. Arcangeli, M. Surace, L. Tarchi, D. Coutandin, S. Zecchi,Correlative Analysis of Effusion Cooling Systems, ASME PaperGT2006-90405, 2006.

[28] L. Battisti, US PATENT 6,488,238 – Boundary Layer Control ofAerodynamic Airfoils, 2002.

[29] L. Battisti, G. Cerri, R. Fedrizzi, Novel Technology for Gas TurbineBlade Effusion Cooling, in: Proceedings of ASME Turbo Expo 2006 –GT2006-90516, Barcelona, Spain, May 8–11, 2006.

[30] R.I. Lewis, Turbomachinery Performance Analysis, Butterworth-Heinemann, 1971.