Characteristics of Partial Length Circular Pin Fins as Heat Transfer Augmentors for Airfoil Internal Cooling Passages

Transcription

1 E s THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47 St., Now York. N.Y The Society Shall not be responsible for statements or opinions advanced in papers or in discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. M Discussion is printed only if the paper is published in an ASME Journal. Papers are available ^^( from ASME for fifteen months after the meeting. Printed in USA. Copyright 1989 by ASME 89-GT-87 Characteristics of Partial Length Circular Pin Fins as Heat Transfer Augmentors for Airfoil Internal Cooling Passages S. C. ARORA and W. ABDEL-MESSEH Structures Analysis, Turbine Pratt & Whitney Canada Inc. Longueuil, Quebec, Canada ABSTRACT Pin fins are commonly used as heat transfer augmentors for internal cooling of turbine airfoils. These pins may extend from one wall to the other or may be segmented to meet specific requirements of removing the airfoil's varying heat load. Three configurations of the partial pins were tested in a 5:1 aspect ratio channel and the results are compared with those for the full pins. The array average heat transfer rate decreases linearly with increasing gap and is bounded by the value for full pins at one end and that for the smooth channel at the other. However, the local distribution of the sselt number and the average for each of the two walls depends on the configuration of the partial pins. The friction factor was lower for partial pins than for the full pins and also decreased with increasing gap. For the configuration with all partial pins on one wall, the friction factor was found to be the lowest with no change in the corresponding heat transfer rate from a wall with pins. NOMENCLATURE A Heat transfer surface area Ac Channel cross sectional area Cp Specific heat of air D Pin diameter Dh Hydraulic diameter of the smooth channel fr Friction factor; fr = dp D dx p Vmax G Gap (clearance) between the endwall and the partial length pins H Channel height h Heat transfer coefficient K Thermal conductivity of air m Mass flow rate sselt number; = hd or hdh K K P Pressure Pr Prandtl number of air q Heat flow rate ynolds number; = p VmaxD ; Dh = m Dh p Ac p S Pin spacing in the spanwise direction T Temperature Amax Average streamwise velocity at the minimum flow area X Pin spacing in the streamwise direction x Axial coordinate p Fluid dynamic viscosity p Fluid density Indicates average quantity Subscripts b Bulk average; base case with full pins f Film m Mixing chamber P Pin s Surface t Total INTRODUCTION Modern gas turbine airfoils make extensive use of internal cooling passages augmented with pin fins to remove the excess heat load and maintain them at desired metal temperatures. These pin fins may extend from one wall to the other specially in the trailing edge of the airfoil or may be segmented (Figure 1) to meet specific requirements of varying heat load. The complete pins provide structural strength, may add additional heat transfer surface area while augmenting the heat transfer rates over those achieved with smooth channel flows. The internally cooled stator airfoils (Figure 1) usually have an insert which provides the coolant for impingement at the airfoil leading edge. The flow splits thereafter into the two channels around the insert. These channels are augmented with pin fins. Since the pins are normally cast in place and the insert is fitted during assembly, the manufacturing tolerances necessitate that there be some clearance between the pins and the insert wall. This clearance is usually of the order of 15% of the total channel height. This, however, is likely to alter the structure of flow in the channel by forcing the flow in to the gap, thereby affecting the associated heat transfer rates and Presented at the Gas Turbine and Aeroengine Congress and Exposition June 4-8, 1989 Toronto, Ontario, Canada This paper has been accepted for publication in the Transactions of the ASME Discussion of it will be accepted at ASME Headquarters until September 30, 1989

2 I the pressure gradient. a. Stator airfoil cross section b. Rotor airfoil cross section IGURE 1: PIN FIN AUGMENTED EUULING SCHEME FOR TYPICAL HIGH PRESSURE TURBINE AIRFOILS maintained at.83 and.4 respectively. The H/D ratio was The gap ratio (G/H) for the single sided pins (Figure a) was 15% of the channel height. For comparison, the same gap was maintained for other additional configurations (Figures b & c). To evaluate the relative effect of the partial pin lengths, the corresponding full pin data were taken from the previous work reported by the authors (Arora and Abdel-Messeh, 1983). The overall performance of the array may also be influenced by the ratio of the pin to the total heat transfer surface area. Therefore it was decided to test 3 additional geometries of partial pins with G/H =.47 having total surface area equal to the case for the full pins. The heat transfer surface area equality with the full pins was achieved by varying the height of the partial length pins. Thus heat transfer and pressure drop data for 6 partial length and one full length pins are reported in the paper. These geometries are considered to be practical from the design point of view and the resulting data attempt to fill in the void in the existing literature. X Due to the varying external heat load the cooling requirements of the pressure and suction surfaces could be significantly different. In such applications, the designer must resort to a cooling scheme with discriminating rates of heat pick up to achieve metal temperature uniformity. This is feasible by employing partial length pin fins on the surface where high rates of heat transfer are desired. However, sufficient design information is necessary to properly optimize the cooling scheme. The available information on the pressure drop/heat transfer characteristics of such pin fin geometries is meagre in comparison to that for the full pins. Peng (1983) has published some data for geometries with gaps of 0, 50 and 67% of the channel height at the centre of the pins. Only the array average data for 8, 11 and 16 rows of pins with H/D of 4 and 6 were reported. The results showed that both the array average heat transfer and the pressure drop decreased with increasing gap size. Because of the averaged nature of the data and the large H/D ratio of the pins, these results have only limited use from the design point of view. Steuber and Metzger (1986) have also reported the heat transfer data on partial length pins epoxied to one wall and the other wall being smooth. The gap between the pins and the opposite smooth wall was maintained equal to 1/3, 1/ and /3 of the channel height. In a typical gas turbine airfoil this gap is usually of the order of 15%. Also, the axial pitch of the pins was 1.5D. However, the manufacturing constraints impose a minimum pitch of the order of D. The double sided partial pins with the gap equal to /3 the height of the channel at the centre of the pins were also tested. Although this geometry, with no full pins, is not practical, nevertheless the results do provide additional information to the designer. sults showed that from the heat transfer point of view alone, partial length pins were judged to be inferior to the full length pins. The present study was guided by the requirements for the design optimization of airfoil cooling. The axial (X/D) and lateral (S/D) pitches were -- S D s- G ^ n n n T a n LJ b n C y H FIGURE : PIN FIN ARRAY NOMENCLATURE In the present study, the local row-by-row heat transfer data were obtained for 10 rows of pins mounted in a 5:1 aspect ratio channel (Figure 3). Because of the staggered arrangement of pins, the even numbered rows had one less pin than the odd numbered rows. EXPERIMENTAL DETAILS A schematic layout of the test rig used for this study is shown in Figure 4. The details of the apparatus and the test procedure have previously been described by Arora and Abdel-Messeh (1985) and therefore only a brief review is given here for completeness. Compressed air is fed to the test section through a plenum chamber (10.16 cm x cm) to settle the flow and an entrance duct of over 50 hydraulic diameters length to provide a fully developed velocity profile at inlet to the test section. After the test section air passes through a smooth channel of over 16 hydraulic diameters

3 L cm 0 cm H 0 H '-1k 038 c,io Tenon sw ion Copper pins (D=.476cm) were epoxied to the endwall slabs at desired locations using the technique first proposed by Arora and Abdel-Messeh (1983). rithe technique involves the use of a thin layer of silver based high conductive epoxy to bond the pins to the endwall. Ten units of copper slabs were mounted with pins to provide 10 rows of pin fins. A smooth (blank) slab was provided in between two successive rows of pins to achieve the desired axialitch. p' Also, no pins were mounted on the first 3 and the last 7 slabs to avoid any end effects. al l0 sows of wo ms- FIGURE 3 : TEST SECTION GEOMETRIC SET UP length to avoid any "exit effects", followed by a mixing chamber where its bulk average temperature is measured. Smooth Mixincl - - SOH c^^ -4-0 cm.i G6.6,^_.^9^c ch,,, cress section 51 cm. 17 cm The heat transfer tests were carried out at steady state by maintaining endwalls at a constant surface temperature ( 71 C). This was achieved by varying the power input to the heaters. The isothermal condition of endwall segments 1 to 9 was generally maintained to within ±.3 C, however, the temperature of two adjoining slabs was maintained to within ±.14 C. The variation in the two thermocouples in each slab was also within this range (±.14 C). The heat transfer coefficient, h, for top and bottom copper slabs with or without pin was obtained from the power supplied (q) to the respective heater corrected for conduction losses from the back ends of the segments and for inter segment conduction across the teflon insulation. The inter-segment losses were calculated for each test run and were generally small. The back losses for each slab were measured experimentally with no flow through the test section. These losses varied from about to 10 percent of the power input depending on the ynolds number. Then using the temperature difference between the segment surface, Ts, and the air flowing over as the driving potential, the heat transfer coefficients were calculated as: q h = (1) A(T s - Tb) FIGURE 4 : SCHEMATIC LAYOUT OF THE TEST RIG The top and bottom walls of the test section consisted of 30 copper slabs (Figure 3) of which only 9 were fully instrumented. Each copper slab had copper constantan thermocouples to monitor its temperature during testing. A.318 cm square cartridge heater located at the back of each slab was used as a heat source. The top and bottom walls were maintained at a constant channel height of.51 cm by two units of spacers (one for each side), which also formed the side walls of the test section. Thirty static pressure holes of.1 cm diameter were drilled through both spacer side wall units. In addition 8 pressure taps were mounted in the entrance duct to measure the pressure distribution. The heater and thermocouple leads passed through the spacers and were then connected to multi-pin connectors for quick assembly and disassembly of the test section. The heat transfer area, A, for all experiments was the actual copper surface area (pin + endwall) exposed to the flow. The local bulk average temperature Tb, as a function of streamwise endwall segment position, was determined in the present experiment from an energy balance. The air temperature measured in the mixing chamber (Tbm) was taken as the bulk average temperature at the end of slab no. 9. Working towards the upstream end of the test section, the bulk temperature for use with the ith segment is calculated as: Tbi = Tbm - 9 qj/m Cp for j < 9 q lj=i+1 m Cp L () =0 The qi and the qj include the total heat input to both the top and bottom slabs up to the ith and jth location respectively. The calculated air temperature at the inlet to the rig using this procedure differed from the measured temperature by less than 1.5%. The friction factor for the pin arrays was I

4 estimated as dp D fr = (3) dx p Vmax 100 Full pins = 1309 Partial pins = where dp/dx is the pressure gradient through the pin fin array. Pressure drop across the array normalized by the number of pin rows has been used by other researchers to compute the friction factors. However, such a definition does not take into consideration the length of the test section over which the given number of pin rows are located (i.e. the axial pitch of the array) Smooth upper surface y Rough lower surface 0 G/H =.15 All relevant properties (k, p, p, Cp) were evaluated at the film temperature (Tf), defined as: Row number Ts + T b Tf = (4) FIGURE 5: DISTRIBUTION OF LOCAL NIJSSELT NUMBERS WITH ALL FINS ON ONE WALL The experimental uncertainty was estimated, using the method of Kline and McClintock (1953), to be ± 4.5% on friction factor and ± 5% on the heat transfer coefficients. RESULTS AND DISCUSSION The local row-by-row distribution of the heat transfer coefficients in terms of the sselt number () for the configuration with all pins epoxied to one wall and the other wall being smooth are shown in Figure 5. The data are plotted for only one value of clearance gap (G/H =.15) and for a ynolds number () of The data for different ynolds numbers and for the other values of the gap showed a similar pattern and therefore are not reported here. The row-by-row distribution of the sselt number for both walls is generally similar to that for the case with full pins, however the magnitude for the smooth wall is lower. Except for the first row, the sselt number for the wall with partial length pins is comparable to that for the full pins, however for the smooth wall, it is much lower. Though the local sselt numbers for the partial pins is slightly higher than the full pins, about 4% of this difference is due to the variations in the respective ynolds numbers. The rest could be attributed to the experimental uncertainties in the two data sets. Thus, the local sselt numbers for the wall with the partial pins can be taken to be equal to that for the channel with full pins. Sparrow and Ramsey (1978) reported that the heat transfer coefficients from the surface of partial length pin increases with increasing pin height. No data on the heat transfer from the endwall with pins or the opposite smooth wall were reported. The results of the present study show that the heat transfer rate from the endwall with pins (pins + endwalls) remains independent of the pin height. This implies that the contribution of the endwall to the heat transfer must be decreasing with the increasing pin height. Steuber and Metzger (1986) also obtained the row-by-row local heat transfer data for a similar pin fin geometry with X/D = 1.5 and S/D =.5 and for clearances of 33, 50 and 66% of the channel height. The distribution of the local sselt number was presented for only two values of clearance (33 and 50%) and for = 10,000. Their heat transfer data for the wall with the partial pins (epoxied to the upper wall) did not show any increase over the first 3-5 rows. In contrast the sselt number on the opposite wall (with no pins) decreased like the entry flow in a smooth duct. After the 3rd row, the heat transfer rate on the smooth wall starts to increase as the effect of the turbulence generated by the pins on the opposite wall propagates to the wall with no pins. The turbulence generated by the pin fins should, however first affect the rate of heat transfer from the pins and the wall to which the pins are epoxied. Its effect should eventually propagate to the opposite wall. The results of Steuber and Metzger (1986) show a trend contrary to this hypothesis, however, the present study shows a physically consistent behaviour. This particular array geometry has a specific application in estimating the rate of the heat transferred to the coolant from the hot gas through the wall with pins. A part of this heat is transferred to the incoming coolant through the smooth wall of the insert. Because of such a design application, the array average data were obtained separately for both walls. These array averaged sselt numbers are shown in Figure 6. sults show that the heat transfer rate from the wall with the pins is not affected by the height of the partial pins (for the range investigated here) and can be taken to be equal to the case for the full pins. However, the heat transfer rate from the smooth wall is dependent on the height of the partial pins on the opposite wall and decreases with increasing gap size. The total heat transfer surface area (A t ) of the array with the clearance of 47% of the total channel height is the same as for the full pin array. However the ratio of the pin surface area (Ap ) to the total area (A t ) is different. The array with a clearance of only 15% has the same A to A t ratio as the full pin but the total heat transfer area is about 7% greater than for the full pin geometry. These differences do not appear to be significant from the heat transfer point of

5 U G/H Smooth wall Wall with pins Ap/At ' ,000 H 00Smooth wall 80 y r r H o^ 60 0 o Wall with pins 0 D 30 o 0 0 NaS/X) Present story 8.83, S Steuber & Metzger x.1986, 8 1.5, S D.5 Dh 13,83 Full S'. dins _.han11 in FIGURE 6 : VS FOR THE GEOMETRY WITH ALL PINS ON ONE WALL view. The normalized clearance (G/H) on the other hand seems to be a more dominant factor. To establish the effect of the clearance on the overall heat transfer for the channel (including both the walls and the pin surface), the averaged sselt numbers were computed. These are shown in Figure 7 for one value of the ynolds number ( = 10,000). The data from the work of Steuber and Metzger (1986) are also shown in the figure. The value of G/H = 0 indicates the case of full pins and that of G/H = 1.0 is for the smooth channel. The smooth channel sselt number was estimated from the relationship: =.03 Dh 8 Pr 4 (5) This equation utilizes the ynolds number based on the channel cross-section and the hydraulic diameter. Therefore, the ynolds number of 10,000 for the pin array was corrected to 13,83 (Dh) for the present study and to 1151 for the work of Steuber and Metzger for the same mass flow rate as for the full pin fins. The data obtained in the present study are for a pin array configuration different to that reported by Steuber and Metzger. Therefore, to facilitate the comparison of the two data sets, the array averaged sselt numbers were multiplied by a factor (S/X) -. This is based on the correlation proposed by Zukauskas (197) for arrays of large cylinders, i.e. u =.35 (S/X).6 Pr.36 (6) The sselt numbers for the smooth channels were also multiplied by the respective (S/X) - values of the two configurations. It is assumed that the S/X dependence of large cylinders will also be applicable to the pin fins of length to diameter ratio of unity. The function (S/X) - FIGURE 7 : EFFECT OF THE CLEARANCE ON NUSSELT NUERS 1.1B FOR ALL PINS ON ONE WALL decreases linearly with the increasing clearance. The rate of decrease is much higher for the array configuration with S/D = 1.5 than for the array with S/D =.4. Since the two curves shown in figure 8 for two different array configurations have different slopes, the function (S/X) - proposed by Zukauskas (197) may not be truly applicable to the configurations considered here. The data from the present study show a linearly decreasing effect with increasing clearance right up to the smooth channel, whereas the data reported by Steuber and Metzger (1986) show that the average heat transfer rate from the partial pins of length equal to the 33% of the channel height yield the same sselt number as the smooth channel. Since the pins with 33% of the channel height are definitely longer than the viscous sublayer thickness, the presence of these partial length pins would be expected to result in some augmentation in the heat transfer. Data of Steuber & Metzger tend to, however, contradict this reasoning. The distribution of the array average sselt numbers for the configuration with rows of partial pins epoxied alternatively to the bottom and top walls are shown in Figure 8. The partial length pin fins of the first row are all epoxied to the bottom wall whereas those of the nd row are epoxied to the top wall. This is repeated for all subsequent rows of pin fins. The data in Figure 8 are plotted separately for the top and the bottom walls. The results show that the average sselt number for each wall decreased with the decreasing pin fin height (i.e. with increasing G/H). However, the bottom wall which has the first row of pin fins and one more pin per row than the top wall experiences higher rate of heat transfer than the opposite wall. This difference was of the order of 10 to 15%. Furthermore, the heat transfer coefficients for the bottom wall (with the first row of partial length pins) with G/H =.15 were comparable to the case with G/H = 0. The row-byrow distribution of the sselt number at = 15,745 and G/H =.15 is shown in Figure 9. The data at the other values of G/H and ynolds numbers were similar in nature. The experimental data points are connected by lines for visual simplicity. The local sselt number oscillates as 5

6 the flow moves through the row of partial length pins epoxied alternatively to the two walls. function (S/X) -. may not fully account for the effect of the array configuration for these pin fins. The full pin array with higher density of pins (S/D = 1.5) having high sselt number shows higher rate of decrease with the increasing clearance (G/H) than the array with lower density of pins (S/D =.4). G/H Upper wall Lower wall A y G4- n H 0 90 eo I S; X) z '^. 50 ^^^- " Dh 13, Present slay XD.83, S Steuber & Metzger (1986) X D 15, S r^5 0 t Ins G Hchannel 10 t , ' FIGURE 8: No US FOR STAGGERED PARTIAL LENGTH PINS The distribution of the overall array average sselt numbers (for both the walls) as Au (S/X) - for this geometry is shown in Figure 10 as a function of the clearance (G/H). Also shown are the data taken from the work reported by Steuber and Metzger (1986). Both the data sets show that the (S/X) - decreases linearly with the increasing clearance and is bounded by the value for full pins at one end and the smooth channel flow at the other. This suggests that the array average sselt number for any clearance can then be interpolated from the value for the full pin fins and that for the smooth channel. The slope of the two curves for different array geometry are however different implying that the A Lower surface = 79.7 o Upper surface = 73.3 y^^a r GI N =.15 i 1 = 15, Pin row number FIGURE 9: ROW--BY- RHW DISTRIBUTION OF FOR STAGGERED PARTIAL LENGTH PINS FIGURE 10 : AVERAGED NUSSELT NUMBERS AS A FUNCTION OF CLEARANCE FOR STAGGERED PINS Figure 11 shows the array average sselt number for the geometry where the pin fins in every second row were cut at the centre. Unlike the other cases of partial pin fins, this geometry is symmetric. Therefore, the average data for the two walls were equal. Similarly the row-by-row variations of the local data were also equal for both walls and are similar to that for the full pin fins. However, the magnitude of the sselt number decreases with the increasing clearance. This decrease in the sselt number is about 5% for G/H =.15 and 10% for G/H =.47. The Au (S/X) -. function for this geometry also showed a linear dependence on the G/H ratio. The bounding values being, like the other geometries, the full pin array and the smooth channel. No data were available for comparison in the literature for this particular geometry of the partial length pins. 00 G/H 1..O /1 z.95 N3/1 z L FIGU.F. 11 : AVERAGE NUSSELT NUMBERS FOR ALTERNATE ROWS SEGMENTED AT THE CENTRE 6

7 Li These data show that the average sselt number decreases linearly with increasing clearance and the rate of decrease is dependent on the full pin array geometry. This slope can be established by drawing a straight line between the Fu for the full pin array to the smooth channel value. The resulting FIu for any clearance can then be interpolated. This suggests that the reduction in the Au due to the clearance is not affected by the geometry of partial pins, at least for the 3 geometries tested in this study. However, the gap not only reduces the average sselt number, but it also changes the distribution of heat transfer from the two walls except for the 3rd geometry. Therefore, for design applications the relative heat transfer behaviour of the two walls must be taken into consideration. ^ ^ 8 Y r 6 G/H T H fr ^ ^ The friction factor results for the channel with pin fins are shown in Figure 1 for all three geometries corresponding to G/H = 0,.15 and.47. These friction factors are based on the pressure gradient in the channel with pin fins. It is evident that for all 3 geometries, the friction factor decreases with the increasing clearance. This is consistent with the observed distribution of the averaged sselt numbers. A similar conclusion was also reported by Sparrow and Ramsey (1978). Figure 13 compares the friction factors of full and partial length pin fins for a constant gap ratio of G/H =.47. As expected, the full pins have the highest friction factor followed by the geometry with every second row having gap at the centre. Third is the geometry with the rows of pins bonded alternatively to the bottom and the top walls. The geometry with all pins bonded to one wall and the other wall being smooth has the lowest friction factor. This ranking of the partial length pin fins on the basis of friction factor appears to be consistent with the structure of the flow that could possibly exist in the array..47_^ n n n --' HII n 4 fl Configuration fr 10 G/H ~ n_ H n 0 -. A.15 ^^`` ^ ^ -^ ^.47 `^^^^^ A AAA G/H.47 3.^ 10' ' 3 4 FIGURE 13 : COMPARISON OF FRICTION FACTORS FOR DIFFERENT GEOMETRIES fr G/H H G H o..15 AA r FIGURE 1 : FRICTION FACTOR CHARACTERISTICS OF PARTIAL LENGTH PIN FINS To evaluate the relative performance of different pin fin geometries, the respective sselt number and the friction factor for each clearance normalized by the corresponding full pin fin data (the base case) at = 0,000 are plotted in Figure 14. For the case with the partial pins attached only to the bottom wall, data are shown only for the wall with the pins. The heat transfer from the wall with the pins remains almost unaffected with the changing gap, however, the friction factor decreases significantly. For the case with rows of partial pins bonded alternatively to the bottom and top walls, the heat transfer for the bottom wall is higher than the top wall. The friction factor for the array with G/H =.15 decreases by about 35% whereas the sselt number decreased by about 4%. The array with the gap at the centre of the pins is geometrically symmetric and the heat transfer also shows a symmetric behaviour for the two walls. The corresponding sselt number and the friction factor ratios show a linear relationship. 7

8 U 1f1; = 0.8 b 0.6 G/H Base case 0 Open symbols Bottom wall.15 for the topwall A Bottom wall.47 Data for the bottom wall ' n n n transfer for the wall with the partial length pin fins. REFERENCES Arora, S.C. and Abdel-Messeh, W., 1983, "Heat Transfer Experiments in High Aspect Ratio ctangular Channel with Epoxied Short Pin Fins", ASME Paper No. 83-GT-57. Arora, S.C., and Abdel-Messeh, W., 1985, "Pressure Drop and Heat Transfer Characteristics of Circular and Oblong Low Aspect Ratio Pin Fins", AGARD Conference Proceedings 390, PEP Symposium, Bergen, Norway b b ^ I. -'n is the average ' of top & bottom walls 6.0 L fr/fr b FIGURE 14: RELATIVE PERFORMANCE OF PARTIAL LENGTH PIN FINS FUR RE = 0,000 O Kline, S.J. and McClintock, F.A., 1953, "Describing Uncertainties in Single Sample Experiments", Mechanical Engineering, Vol. 75, January. Peng, Y., 1983, "Heat Transfer and Friction Loss Characteristics of Pin Fin Cooling Configurations", ASME Paper No. 83-GT-13. Sparrow, E.M. and Ramsey, J.W., 1978, "Heat Transfer and Pressure Drop for a Staggered Wall - Attached Array of Cylinders with Tip Clearance", Int. J. Heat Mass Transfer, Vol. 1, pp Steuber, G.D., and Metzger, D.E., 1986, "Heat Transfer and pressure loss Performance for Families of Partial Length Pin Fin Arrays in High Aspect Ratio ctangular Ducts", Proceedings of Eight International Heat Transfer Conference 6, Zukauskas, A., 197, "Heat Transfer from Tubes in Crossflow" Advances in Heat Transfer, 8, pp CONCLUSIONS The array average heat transfer rate decreases with increasing clearance between the partial length pins and the endwall and varies linearly from the full pin value to that for the smooth channel. Therefore the array averaged sselt number for the pin fin arrays with varying gaps can be interpolated from the full pin and the smooth channel data. Large differences in the sselt numbers for the two walls were observed for the asymmetric partial length pin fin array geometries. The friction factor also decreases with increasing clearance. The geometry with all pins attached to one wall had the lowest friction factor with no significant change in the heat J