Static Pressure Characteristics in a Pin-Fin Channel With Shaped Cylindrical Pins

Static Pressure Characteristics H. J. Pretorius in a Pin-Fin Channel With Mechanical and Aeronautical Engineering Department, University of Pretoria, Shaped Cylindrical Pins Pretoria 0028, South Africa Standard pin-fins in the heat transfer channels are shaped to reduce the pressure penalty 1 and increase the thermal performance. The paper presents experimental results of the G. I. Mahmood wall-static pressure distributions in an array of modified cylindrical short pin-fins in a Mechanical and Aeronautical channel. Standard cylindrical pin-fins with a smooth surface and a similar array configu- Engineering Department, ration are also evaluated as a baseline for comparisons. The pin-fins with a height to University of Pretoria, diameter ratio of 1.28 are arranged in a staggered array consisting of 13 rows in a rec- Pretoria 0028, South Africa tangular channel of aspect ratio 1:7.8. The cylindrical pins are modified by the machined slots at the tips. The slots in the pins are aligned in the streamwise direction. The static J. P. Meyer pressure distributions are measured on the endwall between the pin-rows and on the pin Mechanical and Aeronautical surface. The Reynolds number based on the channel hydraulic diameter ranges from Engineering Department, 10,000 to 50,000. The slots in the pins reduce the friction factor and wall-static pressure University of Pretoria, drop between the pin-rows by up to 50%. The objectives of the investigation are to reduce Pretoria 0028, South Africa the pressure penalty in the cylindrical pin-fin channel to provide increased thermal performance. [DOI: 10.1115/1.4036671] Keywords: slotted pins, flow blockage, friction factor, pressure coefficient 1 Introduction clearance for the pin-fin array in the cooling passages of many applications is not practical as the pin-fins form an integral struc- Short pin-fins with H/D  4 in channel flows promote local tural support for the passage walls. The numerical results of accelerations and strong secondary flows near the endwall to Ref. [11] show the shear-stress distributions along the endwall enhance the convective heat transfer, but also result in the high with the pin-fins attached on one endwall to explain the local heat pressure penalty [1,2]. Typical cooling channels employing the transfer enhancements along the endwall. The arrays of highly pin-fins in gas turbine blades, combustion liners, high-speed bear- porous pins of the numerical model of Yang et al. [12] reduce the ings, fuel-cells, and micro-electronics suffer from low thermal pressure drop and increase the thermal efficiency and performance performances compared to the other internal fin structures [2] in the channel. Eren and Caliskan [13] report the experimental because of the very high friction factors or pressure drop. The friction factor and enhanced thermal performance with the wall pressure distributions are primarily responsible for the local grooved pin-fins, where the groove splits the pin-fins completely flow structures and high friction factors in the pin-fin channels. along the height. The objectives of this study are to reduce the pressure penalty in The recent studies report the local flow field and overall pres- the pin-fin channels employing the slotted circular pins. The sure drop across the pin-fin array without much attention on the results can be beneficial in improving the thermal performance of wall static pressure distributions. The optimal geometry of shaped the pin-fin channels. circular pins depends on the wall pressure distributions to mini- Recent flow-field investigations along the cylindrical pin-fin mize the friction factor and provide the best thermal performance arrays in channels are reported by Refs. [3–7]. The turbulent struc- in the pin-fin channel. For the present experiments, the channel ture near the pin-fins and pressure distributions on the pin surface employs an array of circular pin-fins. The frontal area of the circu- in Ames and Dvorak [3] explain the turbulent mixing in the pin- lar pin-fins is reduced by cutting slots through the pin-tips on both fin arrays. Ostanek and Thole [4,5] measured the horseshoe vortex ends to produce the shaped circular pins. The slot direction is at pin-row upstream and wake-field at pin-row downstream. The aligned to the mean flow. Static pressure distributions are meas- friction factors across a micro-pin-fin channel in Ref. [6] are com- ured on the pin surface and endwall at different Reynolds num- pared with the existing correlations. The details of local vortex bers. The results can contribute to the pressure penalty reductions shedding downstream of the micropin rows and the pressure drop in the common pin-fin channel by means of simple geometric along the pin-fin array are reported by Mita and Qu [7]. modifications of the pins. The shaping of cylindrical pin-fins to tailor the flow characteris- tics and reduce the pressure drop in channel with the minimum effects on the heat transfer has been the subject of numerous 2 Experimental Setup and Procedure investigations for several years. The recent measurements of pres- The pin-fin test section is housed in a low-speed open circuit sure drop and heat transfer with the detached pin arrays are atmospheric wind tunnel, where the air-flow is provided by the reported in Refs. [8–10]. The pin arrays in the studies are attached suction of two axial-fans in series located downstream of the test to one endwall only creating a clearance gap between the free pin- facility shown schematically in Fig. 1. The channel cross section tip and other endwall. The results of Refs. [8–10] indicate both is rectangular from the inlet to exit of the test section with a height the friction factor and heat transfer decrease as the clearance gap of 64 mm and aspect ratio of 1:7.8. The metered pipe section con- between the pin-tip and endwall increases. However, the tip nected to the fan inlet as shown in Fig. 1 includes an ISO standard 5167-1 orifice plate to provide the mass flow rate. The fan speed is controlled with a frequency controller to vary the mass flow 1 Corresponding author. rate and Reynolds number in the test section. The channel walls Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 20, 2016; final are made of commercial clear polycarbonate. manuscript received April 3, 2017; published online June 28, 2017. Assoc. Editor: Figure 2 shows the pin-fin geometry and configuration of the Mark F. Tachie. pin-fin arrays in the test section. The pins are arranged in 13 Journal of Fluids Engineering Copyright V C 2017 by ASME SEPTEMBER 2017, Vol. 139 / 091104-1 Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jfega4/936296/ on 07/30/2017 Terms of Use: http://www.asme.org/a  Table 1 Reference property values Re  103 q (kg/m3) l (Pas) Pso (Pa, gage) V (m/s) 5 10–50 1.04 1.85  10 4–54 1.6–8 Fig. 1 Schematic of the experimental setup calculated quantities as described by Moffat [14]. The maximum staggered rows streamwise with the number of pins per row alter- uncertainty in the measured pressure data including the transducer nated between 5 and 4. Baseline tests are conducted with the solid accuracy and calibration is 8.6% and in the mass flow rate is circular pins of diameter, D ¼ 50 mm and height, H ¼ 1.28D. The 1.5%. The uncertainty in the Cp ranges between 9.2% at Re slotted pin is machined from the solid circular pin with rectangu- ¼ 10,000 and 1% at Re ¼ 50,000. lar slots cut-out from both tips of the pin. The geometry (w, h) given to the slots are shown in Fig. 2. The slot-axis is oriented 3 Results and Discussion along the mean flow direction. The slotted pins replace the solid The results are presented for both the smooth solid pin-fins and circular pins in the test section in the same array configuration as slotted pin-fins at Re ¼ 10,000–50,000. The solid pins are referred in Fig. 2 for the measurements with the slotted pin-fins. The to as the smooth pins in the discussions. slotted pins, therefore, provide 36% less frontal area and flow blockage in the channel than the solid pins. The pin spacing of two-dimensional (2D) is used in both the streamwise (X) and 3.1 Cp and f Along Pin-Fin Array. Figure 3 presents the var- spanwise (S) directions in the pin-fin rows. The same polycarbon- iations of the pressure coefficients, Cp, along the pin-fin array at ate material as the channel walls is used to fabricate the pin-fins. Re ¼ 10,000 for the smooth pins and slotted pins. The relative The pressure tap locations on the endwall and sidewall are locations of the pin-rows (row 1, 3, 5,…, 13) along the endwall shown by the black dots in Fig. 2. The taps are spaced one- are indicated in the figure by the black solid-circles. The averages dimensional apart. Pressure taps are also drilled in the pin wall of of the sidewall and endwall Cp at the corresponding X/2D loca- the center pin in row 11. The pin pressure taps are located at every tions are presented in Fig. 3. The Cp values are negative as 2 mm along the pin-height and 15 deg interval circumferentially. Ps < Pso in Eq. (1). The Cp values in Fig. 3 change little upstream A grid of pressure taps is drilled on one endwall in the black (X/2D < 0.0) and downstream (X/2D > 12) of the pin array. region of Fig. 2 in between pin-rows 11 and 12 with a spacing of Within the pin array, the negative Cp for the smooth pins are 0.2D in the streamwise and spanwise directions for detailed pres- much higher in magnitudes than those for the slotted pins indicat- sure distribution measurements. ing larger pressure drop along the smooth pin rows. This is caused All the wall pressure taps are connected to a differential pres- by the higher flow blockage and form drag provided by the sure transducer via two separate electromechanical scanners smooth pins. through the plastic tubings. As the scanner rotates, a single pres- The straight lines in Fig. 3 between locations 3  (X/2D)  12 sure tap is connected to the pressure transducer to obtain the local represent the least-square fit of the data from the linear-regression pressure signal from the test section. The output from the pressure analysis. One line corresponds to the data points located just transducer is recorded via an Agilent 34790ATM data acquisition downstream of rows 5, 7, 9, and 11; the second line corresponds system using a LabVIEWTM computer program. The pressure sig- to the data points in rows 6, 8, 10, and 12; the third line corre- nals are recorded at 2 Hz for 25 s at each location and then time sponds to the data points located just upstream of rows 7, 9, 11, averaged to convert into the pressure unit by applying the appro- and 13. The average slope of the three straight lines is then used priate calibration curve. Thermocouples are placed at the test sec- as (þDPs/DX) in Eq. (2) for the data in Fig. 4. The friction factors, tion exit and orifice plate to measure the air flow temperature. All f for smooth and slotted pins presented in Fig. 4 at different Re are the measurements are obtained when the channel flow reaches a obtained from Eq. (2). The slope, (DPs/DX), in Eq. (2) is calcu- quasi-steady state at the atmospheric conditions of the laboratory. lated separately for each Re from the Cp versus (X/2D) data and The measured wall-static pressures are presented in the form of represents the pressure drop in the fully developed flow region normalized pressure coefficients, Cp, determined from Eq. (1). downstream of the pin-row 5. The reference pressure, Pso, in Eq. (1) is measured 6D upstream of the first pin-fin row as shown in Fig. 2. The measured reference properties at the reference location of Fig. 2 are provided in ðDh =4Þ ðDPs =DXÞ f ¼ (2) Table 1. 0:5 q V 2 ðPs  Pso Þ As shown in Fig. 4, the friction factor, f, deceases as the Re Cp ¼ (1) increases for both smooth and slotted pin-fins. However, the 0:5 q V 2 dependence of f on Re is significantly higher for the smooth pin- The uncertainties are estimated based on the 95% confidence fins than for slotted pin-fins as f decreases by 45% from interval in the measured data and the propagation of errors in the Re ¼ 10,000 to Re ¼ 50,000 for the smooth pin-fins and about by Fig. 2 Configurations of the pin-fin array and the slotted pin with dimensions in mm 091104-2 / Vol. 139, SEPTEMBER 2017 Transactions of the ASME Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jfega4/936296/ on 07/30/2017 Terms of Use: http://www.asme.org/a  the symmetric flow conditions about the pin diameter along streamwise, the data are then mirrored about Y/2D ¼ 2.5 to create the contour plots in Fig. 5. The locations of the pins in row 11–12 are shown by the thick-black circular lines in the plots. No data are measured on the endwall in close vicinity around the pins. The Cp distributions in Fig. 5 are for the fully developed flow region in the array. The contour magnitudes are all negative as Ps < Pso in Eq. (1) due to the pressure drop along the channel. The highly negative Cp contours indicate the high-pressure drop or low- pressure region between the pin rows. As shown in Fig. 5, the neg- ative Cp values decrease from X/2D ¼ 10 to the next row location (i.e., X/2D ¼ 10.7) for both smooth and slotted pins. The stagna- tion flow region upstream of the pin-row 12 increases the pressure to lower the negative values of Cp in Fig. 5. The negative Cp val- ues then increases at X/2D > 10.7 between the locations of two pins in the row 12 as the mean flow accelerates. When compared between the smooth pins and slotted pins at the corresponding Fig. 3 Pressure coefficient, Cp, along the pin-fin rows for locations in Fig. 5, the highly negative Cp values around the pin- smooth and slotted pins at Re 5 10,000 row 11 are always smaller for the slotted pins. The jet effects of the local flow coming out of the slot at the trailing edge of the 28% for the slotted pin-fins. Higher the f larger the flow separation slotted pin increase the flow pressure and decrease the negative and form drag in the pin-fin channel. In Fig. 4, the friction factors values of Cp in the pin neighborhood. The negative values of Cp for the smooth pin-fin channel are always higher than for the slot- contours in Fig. 5 are also generally smaller for the slotted pins ted pin-fin channel as the slotted pins provide significantly less than for the smooth pins indicating smaller pressure drop along flow blockage and form drag. The difference in f between the the slotted pin-fin rows primarily caused by the reduced flow smooth and slotted pins reduces as the Re increases. Equations (3) blockage. and (4) provide simple correlations between f and Re for the The local Cp values of Fig. 5 along the spanwise Y/2D locations smooth pin-fins and slotted pin-fins in the channel, respectively. at a given X/2D position are averaged and then plotted as Cp,av The solid lines in Fig. 4 represent these correlations. Note that along X/2D for different Re in Fig. 6. The Cp,av data in Fig. 6 are Fig. 4 and Eqs. (3) and (4) provide the friction factors in the pin- shown between row 11 and row 12 for both smooth and slotted fin channel for the fully developed flow region and are independ- pins. As expected, the negative Cp,av decreases along X/2D from ent of the number of pin-fin rows. The correlation of Metzger row 11 location (X/2D ¼ 10) to the upstream of row 12 location et al. [15] is also plotted in Fig. 4 for the present smooth pin-fin (X/2D ¼ 10.7) because of the flow decelerations in the stagnation channel to compare with the measured data. The Metzger correla- region. The negative Cp,av then increases at X/2D > 10.7 between tion [15] is defined based on the overall pressure drop across the the locations of two pins in row 12 due to the flow accelerations. pin array and hence depends on the number of pin-fin rows. The negative Cp,av distributions decrease in magnitudes as the Re increases in Fig. 6 for both smooth and slotted pins. However, the fsmooth ¼ 0:118 lnðReÞ þ 1:5135; for 10; 000  Re  50; 000 magnitudes of negative Cp,av for the slotted pins are more than (3) 50% lower than the smooth pins at all locations at a Re. This sig- nifies the strong influence of the slotted pin-fins on the flow to fslotted ¼ 0:03 lnðReÞ þ 0:455; for 10; 000  Re  50; 000 (4) reduce the pressure drop along the channel. 3.3 Cp on Pin-Fin Surface. The pressure drop along the pin- 3.2 Cp in Pin-Fin Vicinity. The distributions of pressure fin rows in the channel is influenced by the blockage and location coefficients, Cp, in Fig. 5 for Re ¼ 10,000 are obtained from the of the adverse pressure gradient on the pin surface. The wake grid of local wall-static pressures in the black region between pin- region downstream of the pin is generally large when the locations rows 11 and 12 (refer to Fig. 2). The cases for smooth and slotted of the resulting flow separation are positioned closer to the stagna- pins are shown side-by-side in Fig. 5 for comparisons. To deter- tion region on the pin surface. Consequently, the flow experiences mine Cp from Eq. (1) for Fig. 5, the Pso in the equation is replaced high pressure losses along the pin rows. The pressure distributions by the average of local wall-static pressures at X/2D ¼ 10. Using on the pin surface identify the flow separation region. Figure 7 presents the normalized pressure distributions, DP*, along the pin circumference at the height H/2 and H/4. The results are compared at Re ¼ 20,000 and 50,000 between the smooth pin and slotted pin at the 11th row. In Fig. 7, the pin leading edge is located at h ¼ 0 deg, and the trailing edge is at h ¼ 180 deg. For the slotted pin, the pressure taps are only present between 50 deg  h  135 deg at H/4 on the pin surface. Equation (1) is used to define DP* in Fig. 7 with Pso measured at the pin leading edge. The Pso at H/2 is used in DP* at H/4 for the slotted pin. The DP* in Fig. 7 for the smooth pin show the adverse pressure gradient between 75 deg  h  130 deg as the negative value of DP* decreases from the local minima along the pin surface. The apparent flow separation region is then present between 135 deg  h  180 deg on the smooth pin where the DP* changes little. For the slotted pin, the DP* in Fig. 7 decreases at h  90 deg indicating the adverse pressure gradient, but the flow separation region is not clearly identifiable with the constant DP* values. This results in the smaller form drag and negative Cp values for Fig. 4 Friction factor, f, as dependent upon Re for the pin-fin the slotted pin-fins than for the smooth pin-fins as shown earlier. channel Also, the DP* values for the slotted pin-fins are about half of those Journal of Fluids Engineering SEPTEMBER 2017, Vol. 139 / 091104-3 Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jfega4/936296/ on 07/30/2017 Terms of Use: http://www.asme.org/a  Fig. 5 Endwall pressure coefficient, Cp, contours at Re 5 10,000 for smooth pins (left) and slotted pins (right) in locations of rows 11–12 Fig. 6 Averaged spanwise pressure coefficient, Cp,av, on endwall at Re 5 10,000–50,000 for smooth pins (left) and slotted pins (right) in locations of rows 11–12. Legends are shown in left plot. Fig. 7 Pin-surface normalized pressure distributions, DP*, in 11th row at pin-height of H/2 and H/4 for smooth pins (left) and slotted pins (right). Legends are shown in left plot. for the smooth pin-fins for a Re. At H/2, the negative DP* in the on the pin surface is thus stronger in the smooth pin-fin channel adverse pressure gradient region decreases by 11–24% for the than in the slotted pin-fin channel. slotted pin compared to the decrease by 21–44% for the smooth pin. This occurs as: (i) the mass flow is divided between the slot flow and the boundary layer on the pin circumference and (ii) the 4 Conclusions flow exits the pin slot as a jet affecting the pressure distribution on The measured wall-static pressure distributions in an array of the pin surface at h  90 deg. The adverse pressure gradient region modified cylindrical short pin-fins are compared with those in an 091104-4 / Vol. 139, SEPTEMBER 2017 Transactions of the ASME Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jfega4/936296/ on 07/30/2017 Terms of Use: http://www.asme.org/a  array of smooth pin-fins in a channel. The smooth cylindrical pins h ¼ angular position on pin surface relative to pin-axis are modified by machined slots along the diameter at both tips. l, q ¼ dynamic viscosity, density of air The slot-axis in the pin array is oriented along the channel mean flow to reduce the frontal blockage by 36%. The Reynolds number is varied between 10,000 and 50,000 for the measurements. The results show that the friction factors and surface pressure coeffi- References cient distributions can be decreased by 50% when the smooth pins [1] Won, S. Y., Mahmood, G. I., and Ligrani, P. M., 2004, “Spatially-Resolved are replaced by the slotted pins. A correlation between the friction Heat Transfer and Flow Structure in a Rectangular Channel With Pin Fins,” Int. J. Heat Mass Transfer, 47(8–9), pp. 1731–1743. factor and Reynolds number is derived for both smooth and slot- [2] Ligrani, P., 2013, “Heat Transfer Augmentation Technologies for Internal Cool- ted pin array in the fully developed flow region. The correlation ing of Turbine Components of Gas Turbine Engines,” Int. J. Rotating Mach., predicts the friction factor in the present configuration of pin-fin 2013, pp. 1–32. array quite reasonably and independently of the number of pin- [3] Ames, F. E., and Dvorak, L. A., 2006, “Turbulent Transport in Pin Fin Arrays: Experimental Data and Predictions,” ASME J. Turbomach., 128(1), pp. 71–81. rows. The results can be beneficial to improve the thermal per- [4] Ostanek, J. K., and Thole, K. A., 2012, “Wake Development in Staggered Short formance of the cylindrical pin-fin channel. Cylinder Arrays Within a Channel,” J. Exp. Fluids, 53(3), pp. 673–697. [5] Ostanek, J. K., and Thole, K. A., 2012, “Flowfield Measurements in a Single Row of Low Aspect Ratio Pin Fins,” ASME J. Turbomach., 134(5), p. 0510341. [6] Renfer, A., Tiwari, M. K., Brunschwiler, T., Michel, B., and Poulikakos, D., 2011, Funding “Experimental Investigation Into Vortex Structure and Pressure Drop Across Funding for the research project was provided by the ARMS- Microcavities in 3D Integrated Electronics,” J. Exp. Fluids, 51(3), pp. 731–741. [7] Mita, J., and Qu, W., 2015, “Pressure Drop of Water Flow Across a Micro- COR South Africa and National Research Foundation (NRF) of Pin–Fin Array—Part 1: Isothermal Liquid Single-Phase Flow,” Int. J. Heat South Africa. Mass Transfer, 89, pp. 1073–1082. [8] Chang, S. W., Yang, T. L., Huang, C. C., and Chiang, K. F., 2008, “Endwall Heat Transfer and Pressure Drop in Rectangular Channels With Attached and Detached Circular Pin-Fin Array,” Int. J. Heat Mass Transfer, 51(21–22), pp. 5247–5259. Nomenclature [9] Siw, S. C., Chyu, M. K., Shih, T. I.-P., and Alvin, M. A., 2012, “Effects of Pin A ¼ channel cross-sectional area Detached Space on Heat Transfer and Pin-Fin Arrays,” ASME J. Heat Transfer, 134(8), p. 0819021. Cp, Cp,av ¼ pressure coefficient and average pressure coefficient [10] Moores, A., Kim, J., and Joshi, Y., 2009, “Heat Transfer and Fluid Flow in D, Dh ¼ pin diameter and hydraulic diameter of smooth Shrouded Pin Fin Arrays With and Without Tip Clearance,” Int. J. Heat Mass channel Transfer, 52(25–26), pp. 5978–5989. f ¼ Darcy friction coefficient [11] Chi, X., Shih, T. I.-P., Bryden, K. M., Siw, S., Chyu, M. K., Ames, R., and Den- nis, R. A., 2011, “Effects of Pin-Fin Height on Flow and Heat Transfer in a H, h, w ¼ channel or pin height, slot height, and slot width Rectangular Duct,” ASME Paper No. GT2011-46014. m ¼ average mass flow rate [12] Yang, J., Zeng, M., Wang, Q., and Nakayama, A., 2010, “Forced Convection Ps, Pso ¼ local wall-static pressure and reference static pressure Heat Transfer Enhancement by Porous Pin Fins in Rectangular Channels,” Re ¼ Reynolds number ¼ [mDh/(Al)] ASME J. Heat Transfer, 132(5), p. 0517021. [13] Eren, M., and Caliskan, S., 2016, “Effect of Grooved Pin-Fins in a Rectangular S, X ¼ pin spacing in spanwise direction and in streamwise Channel on Heat Transfer Augmentation and Friction Factor Using Taguchi direction Method,” Int. J. Heat Mass Transfer, 102, pp. 1108–1122. V ¼ mean velocity without pins ¼ [m/(Aq)] [14] Moffat, R. J., 1988, “Describing the Uncertainties in Experimental Results,” (X, Y, Z) ¼ Cartesian coordinates Exp. Therm. Fluid Sci., 1(1), pp. 3–17. [15] Metzger, D. E., Fan, Z. X., and Shepard, W. B., 1982, “Pressure Loss and Heat D ¼ difference in quantities Transfer Through Multiple Rows of Short Pin Fins,” Seventh International Heat DP* ¼ normalized pressure on pin surface Transfer Conference, Munich, Germany, Sept. 6–10, Vol. 3, pp. 137–142. Journal of Fluids Engineering SEPTEMBER 2017, Vol. 139 / 091104-5 Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jfega4/936296/ on 07/30/2017 Terms of Use: http://www.asme.org/a