THE DISCHARGE COEFFICIENT OF FLARED FILM COOLING HOLES. N Hay and D Lampard Department of Mechanical Engineering The University of Nottingham, UK

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1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St, Now York, N.Y. 117 The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy material for internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of $.3 per page is paid directly to the CCC, 27 Congress Street, Salem MA 197. Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright 1995 by ASME All Rights Reserved Printed in.s.a. g5-gt-15 THE DISCHARGE COEFFICIENT OF FLARED FILM COOLING HOLES N Hay and D Lampard Department of Mechanical Engineering The niversity of Nottingham, K ABSTRACT The coefficient of discharge (C d) of flared film cooling holes is reported for a range of pressure ratios, geometries and flow conditions. The geometry of the holes used was typical of present day designs produced by the method of electrical discharge machining or spark erosion. C d data are given for normal (9 ) holes and for 3 inclined holes. The effects of the following geometrical and flow parameters have been investigated and are reported. Effect of the length of the cylindrical portion of the hole prior to the flare. Effect of the deletion of the layback of the hole flare Effect of the presence of cross flow on the inlet to and on the outlet from the hole. Effect of the orientation of the cross flow relative to the axial direction of the hole. The flare increases C d over that for a cylindrical hole. Eliminating the layback has little effect on C d, but reducing the length of the cylindrical portion has a marked adverse effect when an inlet cross flow is present. As for cylindrical holes, an inlet cross flow reduces C d for normal holes, but flared holes can maintain higher Cd's than cylindrical holes, provided that the cylindrical inlet to the flare is sufficiently long. NOMENCLATRE a - velocity of sound A - Area Cd- Discharge coefficient d, D - Diameter of hole L - Length of hole, or length of cylindrical inlet section of flared hole m - Mass flow rate M - Mach number Ma - Mach number inside the hole p - Static pressure p' - Stagnation pressure R - Gas constant Re d- Reynolds number based on hole diameter T - Stagnation temperature V - Velocity Greek p - Density y - Ratio of specific heats - Angle of inclination of the hole Subscripts h - Inside the test hole c - pstream of test hole (coolant side) - Downstream of test hole (mainstream side) INTRODCTION The use of conically flared holes to inject cooling films on turbine blades was shown by Goldstein et al (1974) to offer two advantages over plain cylindrical holes. The lateral spreading of the jets over the blade surface is enhanced and the slowing down of the jets through diffusion in the flares permits higher injection rates before jet lift-off occurs. The thermal advantages of flare shapes other than purely conical have also been investigated. Snell and Henshaw (1991) compared the performance of fan-shaped holes with a range of cylindrical hole configurations, while Schmidt et al (1994) and Sen et al (1994) used holes with an asymmetric diffusing expansion. Flared holes can be easily produced by the spark erosion method, which is presently the standard method for forming Presented at the International Gas Turbine and Aeroengine Congress and Exposition Houston, Texas - June 5-8, 1995 Downloaded From: on 9/2/218 Terms of se:

2 cooling holes, or by laser drilling. They are now widely used in current gas turbine engines. However, very little data exists in the open literature for the discharge coefficient of flared holes. This information is crucial to the design of the cooling systems of turbine blades as correct hole sizes must be chosen to avoid the coolant over-or under-feed conditions which will give rise to hot spots and hence to reduced blade life. Camci and Arts (199) give some data for conically flared holes, but for only a single geometry and for limited flow conditions. In particular, cross flow at the hole inlet is absent and this has been shown to have a profound effect on the discharge coefficient of cylindrical holes, see, for example Hay et al (1983), Hay et al (1987), McGreehan and Schotsch (1987). This paper describes a test programme on flared holes typical of those used in the cooling of gas turbine blades. The variation of the measured discharge coefficient over a range of geometric and flow conditions is reported and discussed. The discharge coefficient for the flared holes has been based on the 'ideal' flow through a cylindrical hole having the same diameter as the inlet section rather than on the ideal flow through the actual geometry. Comparison of flared hole and cylindrical hole discharge coefficients at a particular pressure ratio will thus yield an immediate indication of the change in the film air flow rate which will arise from the incorporation of the flare. The information in this form is more pertinent for design FLARED HOLE GEOMETRIES TESTED Hole geometries were decided on in liaison with a gas turbine manufacturer. Typical flared hole geometries were supplied and test plates were then designed to incorporate the representative geometries shown in Figure 1. It was decided to use normal holes and 3 inclined holes as is typical in practical applications. The holes generally have a 25 flare as well as a 7.5 layback (Figure 1). It was decided to test holes with and without layback. The blade manufacturing process introduces uncertainties in the thickness of the wall of the blade. It was therefore decided to investigate the effects of variations in blade wall thickness. This was done using the normal hole geometry as this geometry is more sensitive to such a variation because the hole is shorter in length than for 3 inclination. The variation in wall thickness reflects in a variation in the length of the cylindrical section of the hole prior to the flare since the latter is formed as a fixed geometry. In all, five geometries of flared holes were tested (Figure 1), three normal holes with long, medium and short cylindrical lengths, one 3 inclined hole with flare and layback, and one 3 inclined hole with flare but no layback. The nominal hole diameter was 3 mm in each case. The holes were formed by spark erosion. The electrodes used were made initially as cones of 25 included angle with protruding cylindrical spikes sized to give the required hole diameter. For holes with no layback, two parallel flats were machined on the conical portion. The flats were parallel to the electrode axis and spaced symmetrically about this axis one hole diameter apart. For holes with layback, one plane was inclined at 7.5 to the axis. 25 d NL_2 _. d.ti JØ3L s.` Figure 1 Flared hole geometries ^-4 (a) Normal (9 ) holes Dimensions in mm (b) Inclined (3 ) holes / 7.2 TEST RIG AND INSTRMENTATION The test rig used is shown in Figure 2. It is supplied with air from a central compressor plant. It consists essentially of a channel to provide internal and external cross flow for the hole. The test plate into which the hole is formed is mounted on the channel. Depending on whether external or internal cross flow is to be introduced the hole needs to point towards the channel or away from it. Because of the design of the mounting of the plate onto the channel the plate could not be simply turned over to allow both tests to be done. Hence two plates had to be made per geometry; one for use with internal cross flow and one with external cross flow. On the side of the plate away from the channel there is a plenum chamber which supplies the flow of air to the hole or collects it from the hole as the case may be. A system of valves and orifice meters allows the air flowing through the hole to be metered and to flow in the desired direction. The valves also allow the pressure ratio across the hole to be controlled and varied. Air is admitted to the duct carrying the cross flow by valve V 1 and the pressure is controlled by valve V,. For inlet cross flow cases, valves V, and V 8 are closed, while V 3 and V 5 Downloaded From: on 9/2/218 Terms of se:

3 are open. With either V 6 or V 7 open, air can pass from the duct via the test hole into the plenum chamber and hence through the chosen measuring orifice to atmosphere. For outlet cross flow cases, valves V3 and V 5 are closed, and V 8 and V, are open. Air admitted through V8 can pass through a measuring orifice selected by opening V 6 or V 7 and thence to the plenum chamber via V 4. It is then discharged through the test hole into the duct. Ph is the density in the hole given by: Pc1 P6 = X RT c (Pe/P.)'/Y and V h the velocity in the hole is obtained from: Thermocouple and D and DR pressure tappings on each orifice Air supply vs where Vn = an Mh Exhaust Vt Vt l atmosphere Orifice V7 meters V<\ / V5 and M I, is given by: ah = y RTh)^' = Y RTe ^ 1 Y=1 M z 2 h Control valves Plenum chamber Pressure tap and thermocouple I } 1 I Testplate with Air inlet _-^ntrol valve. V,! I.I. holeatmosphere.\p=1 i L Pitot tube Control valve. V. Securing plate Rotatable testplate Skew angle! 75 m x 37 men \ channel fduct static pressure tapping Plan view with plenum chamber removed Figure 2 General arrangement and details of the test rig The instrumentation consisted of orifice meters, mercury and water manometers for pressure measurements and thermocouples for temperature measurements. Pressure differences critical to the calculation of C d were measured directly rather than by subtraction. MhPa, Y1 Y?1 TEST PROGRAMME All of the flared hole geometries were tested over the range of pressure ratio of 1.1 to 1.8. The tests were first done with no cross flow on either side of the hole, then with cross flows at exit of.15 and.3 Mach numbers and finally with cross flows at inlet of.15 and.3 Mach numbers. As explained earlier the design of the rig was such that separate plates had to be used for the tests with internal cross flow and with external cross flow. There were thus 1 plates altogether. The test programme configurations are summarised in Table 1. CALCLATION OF Cd The definition of the discharge coefficient is C _ actual mass flow rate through the flared hole dideal mass flow rate through a cylindrical hole The ideal mass flow is calculated assuming isentropic compressible flow through a cylindrical hole having the same diameter as the actual hole inlet. The pressure ratio is taken as the stagnation pressure upstream to the static pressure downstream: p,/p.. Thus the ideal mass flow rate will be given by: mt = Ph Vn Ah Table 1 Summary of Text Programme Configurations Plate No Hole Inclination Hole Orientation Flaring (25 ) Layback (7.5 ) , , None None 4 Inlet length Lid A,, is the area of the hole = d' 4 Downloaded From: on 9/2/218 Terms of se:

4 RESLTS AND DISCSSION The results are given in graphical form in Figures 3 to 1. Various parameters were tried in plotting the results in an attempt to collapse the data. None of them proved satisfactory. Hence, the results are generally presented as plots against the pressure ratio p +/p to allow comparisons with previous work. The uncertainty in the values of C d was estimated using the method of Kline and McClintock (Kline and McClintock (1953)) and was found to be just below ±3%. This stems from: (a) the uncertainty in the measurement of mass flow rate which, with orifices to BS142, is to ±2%; (b) the uncertainty in the measurement of hole diameter. The spark erosion method used in producing the holes does not give a precisely circular cross section and there can be a variation in cross section along the length of the hole. It is estimated that an uncertainty in cross-sectional area of ±2% can stem from this source; (c) absolute temperature and absolute pressure measurements enter in the calculation of C d. Care was taken to limit the uncertainties in these measurements to less than +.2%. Normal Holes As pointed out earlier the 9 holes had a flare and layback. The length of the flared part was fixed and there were three cylindrical part lengths, L, chosen to give L/d = 4 (long), L/d = 2 (medium) and L/d = 1 (short). The range was chosen so as to accentuate any effects on C d. Diffuser performance is strongly dependent upon inlet conditions. The flow within a diffuser is even more sensitive to upstream flow history than a developing pipe flow. The distortion of the outlet profile increases with that of the inlet profile, with a consequent loss in pressure recovery, see Klein (1981). Lichtarowicz et al (1965) note that the flow within an orifice of L/d = 1 does not fully reattach, while it does so well before the exit for L/d = 4. The range of inlet lengths selected was thus expected to present the flares with inlet profiles varying from separated to as fully developed as is likely to be achievable within the length restrictions imposed in blade cooling. C,, With no Cross Flow The results (Figure 3) show that at high pressure ratio (>1.4) Cd assumes the value of -.83 for all the holes. This indicates that the flow is choked and that the mass flow is determined by the hole diameter and the upstream stagnation conditions. This may be seen clearly in Figure 4, where the nondimensional flow function is plotted against p /p, The value of.83 is in line with the earlier results of Benmansour (1981) for cylindrical holes which are also plotted on Figure 3. For lower pressure ratios, while the cylindrical hole results show a slight decrease in C d, the flared hole results show an increase in C d over the high pressure ratio value. The enhanced Cd levels for the flared holes arise from diffusion within the flare, and the variation with entry length reflects the entry flow behaviour. The increase of C d is highest for the L/d = 2 inlet length hole. Referring to visualisation of similar flows..9 ^ a + ovtoo v o x+ z X x X.7 y.6 o Cl) o s 4 o i( d L_4 Cylindrical Hole Data Ben Vd.2 r(1981); + ud N X11-5 X Lid-6 i.3.2 I = Hole pressure ratio, p /p_ L_1 Figure 3 Discharge coefficient of normal holes -no crossflow.7.6 C-.s.4 E c o}.2 LL.1 CR o o Sb i'o t.6 t.8 2 Hole pressure ratio, p' /p_ Figure 4 Non-dimensional flow function - normal holes, no cross flow (Figure 5), the flow separates at the sharp edge of the hole and reattaches at about L/d = 1.5 to 2.. Thus the flow in this case will enter the diffuser formed by the flare as a diverging streamtube which will help in the diffusing process. For the L/d = 4 hole the increase in C d is not quite so large and this can be explained in that the streamtube is now cylindrical and hence there is no streamline curvature to help in the diffusing process. The L/d = 1 hole shows the least increase, as in this case the diffuser starts at about the position of the vena contracts (see Figure 5) so that little pressure recovery occurs in the flared section of the holes. The flare is a poor diffuser even with the longer inlets. A rough calculation based on one-dimensional flow, and assuming a contraction coefficient of.6 for the entry separation gives a pressure recovery coefficient of between.2 and.3 at low pressure ratios. This indicates that the flow separates close to the flare entry. Such behaviour is expected for diffusers with high wall angles. The decrease in C d with increasing pressure ratio may be due, at least in part, to compressibility effects within the flare. Van d ^ Downloaded From: on 9/2/218 Terms of se: 4

5 Dewoestine and Fox (1966) report a deterioration in pressure recovery with increasing inlet Mach number for short, high area ratio conical diffusers. te.8 a,.7.6 ).5 ) N..3.2 O O 5 _ b Cylindrical Hole Data Benmansour (1981); d =6 Crossflow Inlet Outlet Mach No. (Ma (M_) O.15.3 A I.4 1.6,.8 1 (a) Long inlet, L/d = 4 Hole pressure ratio, p' /p_ Figure 5 Flow visualisation of re-attachement in a long, sharp edged entry (based on JSME (1988)) The performance is in every case better than that for cylindrical holes, giving an increase in C d at low pressure ratio of up to 15%. Effect of Cross flow The effect of cross flow on Cd for the long 9 hole is shown in Figure 6a. The effect of external cross flow up to M. =.3 is small, showing a slight increase in C d at the lower pressure ratios compared with a slight decrease for cylindrical holes. The effect of internal cross flow is, as with cylindrical holes, detrimental, particularly at low pressure ratios, decreasing C d by -13% for M, =.15 and by 16% for M =.3. The reduction in C d caused by the internal cross flow has been observed and reported previously by, among others, Hay et al (1987). It is associated with a distortion of the separated region within the hole entry. The symmetrical separation occurring with zero cross flow becomes a single separation around the upstream edge as the cross flow velocity increases relative to the hole velocity. A potential flow solution by Dewynne et al (1989) shows this effect clearly for a normal slot, while other work at Oxford, see for example Byerley (1989), and Gillespie et al (1984), has used both flow and thermal measurements to reveal the distortion of the hole entry flow and the reduction in C d for cylindrical holes. The medium length 9 hole (Figure 6b) displays the same trends as the long hole.. The external cross flow up to M _.3 has little effect, while the internal cross flow produces a much more marked effect than for the long hole resulting in a very large reduction in C d at low pressure ratios particularly for M =.3. Note that the reduction in Cd for cylindrical holes with L/d = 6 is similarly pronounced over the lower pressure ratio (p /p < 1.3) range. This indicates that the pattern of the flow within the hole is such that the flare is not able to contribute any pressure recovery to improve C d. a) V Cylindrical Hole Data Benmansour (1981) ; L/d =6 Crossilow Inlet Outlet Mach No..3 -'-- -- Crossflow Inlet Outlet Mach No. (M O) (M_) O Medium inlet. L/d = 2 Hole pressure ratio, p' /p_ O O O ' _ b_- - Cylindrical Hole Data p Benmansour (1981) ; d =6 I Crosstlow Inlet Outlet Crossflow Inlet Mach No. Outlet (M,) (M_) Mach No. O A.2,.t 1.6 ;.8 - N.7.6 CD.5 21 Co (b) Ù c.7.v.6.5 CO L.s N.3 4k o O e O 7 I / (c) Short inlet, L/d = 1 Hole pressure ratio, pvp_ Figure 6 Effect of crossflow - 9 holes 4_-_ Downloaded From: on 9/2/218 Terms of se:

6 The performance of the short hole follows the same trend (Figure 6c) except that with external cross flow some improvement in performance is noticed. This is probably the result of the cross flow acting as a "lid" which promotes a certain degree of diffusion in the flare which is not otherwise present, as the flow then emerges as a detached jet as discussed earlier. The detrimental effects of internal cross flow is even more pronounced than for the medium length hole leading to a larger reduction in C d throughout the pressure ratio range, the reduction being greatest at M. =.3 and at the lower pressure ratio range with C d values reducing to half those with no internal cross flow. The general conclusions from the tests is that for 9 holes the flare improves C d over that for the plain hole, particularly at low pressure ratios. The length of the parallel portion of the hole must be at least four times the hole diameter if C d is to remain high at high internal cross flow Mach numbers..9 A D D A AD A. O A: O O O O.5 Cylindrical hole data m Bromley (1994) Mach to Inlet Outlet L Mach No. (Md (M- ) N.. I Crossflow Inlet Outlet Fn Mach No..6.3 O '-.3 A Hole pressure ratio, pvp_ Inclined Holes ( = 3 ) with No Cross Flow The discharge coefficients for 3 inclined holes without cross flow are shown in Figure 7. Note first of all that the results for plates 7 and 8 should be identical. The spread of about 5% reflects the degree of uncertainty in the values of C d ±2.5 to 3%. (3 a) _ ) y.5 21 Ce 2 am.4.3 x O o 8 D m OA AO A x xx xx o G x Plate 8 (with layback) Plate 7 (with layback) Plate 1 (no layback) Cylindrical hole data Bromley (1994) x Figure 8 Discharge coefficient of inclined holes with layback - effect of crossflow Byerley (1989) has suggested that the increase in C d with cross flow for 3 inclined holes arises from the suppression of the separation from the downstream lip of the hole. For small cross flows, the dividing streamline between the hole and cross flow stagnates on the surface downstream of the hole. Some flow therefore enters the hole over its downstream lip and must turn through 15. This results in a massive separation. As the cross flow increases relative to the hole flow, the stagnation point moves upstream to the edge of the hole. As it does so, the amount of flow entering from the downstream side of the hole reduces, the size of the separation is reduced progressively to zero, and the discharge coefficient consequently increases. Cross flow at the outlet has even less effect; for both flared and cylindrical holes the effect is within the measurement uncertainty. Identical conclusions can be drawn for the holes with no layback, see Figure I.8 2 Hole pressure ratio, p7p_ Figure 7 Discharge coefficient of inclined holes with and without layback - no crossflow a^.7 The values of C d are between 15% and 25 % higher than for the cylindrical hole data. They are about the same as for the 9 holes, except that the increase in C d at low pressure ratio noticed for the 9 holes is not apparent here either for the hole with layback or for the one without. C d values stay at the same level D A of -.82 down to very low pressure ratios. ).6 pt.5.4 Crossflow Inlet Outlet Mach No. (M,) (MJ Effect of Cross Flow The effect of internal cross flow up to M =.3 is an increase in C d of -5% for holes with layback, Figure 8. A similarly weak increase has been reported for cylindrical holes by Khaldi (1987) and by Hay et al (1994) and is evident in the data of Bromley (1994) shown for comparison in Figure 8. L7E^ Hole pressure ratio, p' /p_ Figure 9 Discharge coefficient of inclined holes with no layback - effect of crossflow 6 Downloaded From: on 9/2/218 Terms of se:

7 Effect of Skewness (45 to Flow Direction) It is obvious from Figure 1 that 45 of skewness does not affect the level of C d in the absence of cross flow or with external cross flow. For internal cross flow of M. =.3 there is a slight decrease in C d at low pressure ratio. Results with cylindrical holes (Hay et al 1994) showed much the same behaviour. The effect of skewness begins to show only for skew angles in excess of 9 as the form of the separation at the hole entry then becomes significantly changed by the cross flow. The general conclusions from these tests are that flaring of 3 inclined holes increases the discharge coefficient, and leaves its weak dependence on cross flow unchanged. (3 C C) C) C) C) cc Crosstlow Inlet Outlet Mach No. (MJ (M_) rn.4 o A.2 O6 Q' A ` AOa O ^ r rte s A 1.2 I Hole pressure ratio, p'^/p_ Figure 1 Discharge coefficient of 45 skewed inclined holes CONCLSIONS The following conclusions may be drawn from this investigation. The discharge coefficient of flared holes is higher than that for cylindrical holes. Thus flared holes offer the advantage of a smaller pressure drop requirement for a given flow rate, in addition to helping to reduce the momentum of the jet at exit and thereby improving the film cooling performance. The improvement in the discharge coefficient is highest at the lower range of pressure ratio. The cylindrical section of the hole before the flare should be at least two hole diameters in length and preferably four hole diameters. This allows the flow to reattach to the walls of the hole before entering the flare thereby improving the diffusing action of the flare. The inclusion of a layback does not increase the discharge coefficient but the film cooling performance of the hole is likely to benefit from a layback. External cross flow up to M. =.3 does not have much effect on the discharge coefficient of flared holes whether normal or inclined. 5. Internal cross flow leads to a drop in the coefficient of discharge for normal holes, particularly at low pressure ratios (< 1.3). The decrease is most pronounced for the holes with the shortest cylindrical entry length. 6. For 3 inclined holes internal cross flow up to M, =.3 increases the discharge coefficient by about 5%. The effect is much the same for holes with flare and layback and for hole with flare and no layback. 7. Orientation of the hole at 45 to the direction of flow at ini*t does not affect the discharge coefficient measurably for cross flow up to M = Inclination of the hole is obviously advantageous in film cooling as it helps to keep the coolant close to the wall. In so far as the discharge coefficient is concerned, flared 3 inclined holes are less sensitive to pressure ratio and to internal cross flow than flared normal holes, a desirable feature in design. ACKNOWLEDGEMENTS The work described in this paper was done through the award to one of the Authors, N Hay, of a Senior Clayton Fellowship by the Institution of Mechanical Engineers. The experimental facilities used were made available by the Department of Mechanical Engineering at the niversity of Nottingham. The award of the Fellowship, and the use of the experimental facilities are acknowledged with thanks. REFERENCES Benmansour (1981), 'Discharge coefficients of film cooling holes', MPhil Thesis, niversity of Nottingham. Bromley S J (1994), 'Flow in flares', BEng Thesis, Department of Mechanical Engineering, niversity of Nottingham. Byerley, A R, (1989), 'Heat transfer near to a film cooling hole in a gas turbine blade', DPhil Thesis, niversity of Oxford. Camci C and Arts T (199), `An experimental convective heat transfer investigation around a film-cooled gas turbine blade', Trans ASME J of Turbomachinery, 112, pp Dewynne, J N, Howison, S D, Ockendon, J R, Morland, L C and Watson, E J, (1989), 'Slot suction from an inviscid channel flow', J Fluid Mechanics, Vol 22, pp Gillespie, D R H, Byerley, A R, Ireland, P T, Warg, Z and James, T V. (1994), 'Detailed measurements of local heat transfer coefficient in the entrance to normal and inclined film cooling holes', ASME Paper 94-GT-1. Goldstein R J, Eckert E R G and Burggraf F (1974), `Effects of hole geometry and density on three-dimensional film cooling', Int J Heat and Mass Transfer, 17, pp Hay N, Henshall S E and Manning A (1994), `Discharge coefficient of holes angled to the flow direction', Trans ASME Journal of Turbomachinery, Vol 115, pp Downloaded From: on 9/2/218 Terms of se:

8 Hay N, Khaldi A and Lampard (1987), 'Effects of cross flows on the discharge coefficients of film cooling holes with rounded entries and exits', Proc 2nd ASME-JSME Thermal Engineering Joint Conference, Honolulu, Hawaii, Vol 3, pp Hay N, Lampard D and Benmansour S (1983), 'Effects of cross flows on the discharge coefficient of film cooling holes', ASME Journal of Engineering for Power, Vol 15, pp Japan Society of Mechanical Engineers, (1988), 'Visualised flow', Pergamon Press. Khaldi A (1987), 'Discharge coefficient of film cooling holes with rounded entries or exits', PhD Thesis, niversity of Nottingham. Klein A (1981), `Effects of inlet conditions on conical-diffuser performance', ASME Journal of Fluid Engineering, 13, pp Kline, S J and McClintock, F A, (1953), 'Describing uncertainties in single sample experiments', Mechanical Engineering, Vol 75, pp 3-8. Lichtarowicz A, Duggins R K and Markland E (1965), 'Discharge coefficients for incompressible, non-cavitating flow through long orifices', J Mechanical Engineering Science, Vol 7, No 2, pp McGreehan W and Schotsch M (1987), 'Flow characteristics of long orifices with rotation and corner radiusing', ASME Gas Turbine Conferences, Anaheim, California, Paper 87-GT-162. Schmidt D L, Sen B and Bogard D G (1994), 'Film cooling with compound angles: adiabatic effectiveness', ASME Gas Turbine Conference, The Hague, Paper No 94-GT-312. Sen B, Schmidt D L and Bogard D G (1994), 'Film cooling with compound angle holes: heat transfer', ASME Gas Turbine Conf, The Hague, Paper no 94-GT-311. Snell R J and Henshaw D G (1991), 'Measurement and optimisation of film cooling performance at engine representative conditions', IMechE Paper no C432/1, European Conference on Turbomachines, London. Van Dewoestine R V and Fox R W (1966), 'An experimental investigation on the effect of subsonic inlet Mach number on the performance of conical diffusers', Technical Report FMTR-66-1, School of Mechanical Engineering, Purdue niversity. Downloaded From: on 9/2/218 Terms of se: