The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering HEAT TRANSFER AND FRICTION FACTOR

Transcription

1 The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering HEAT TRANSFER AND FRICTION FACTOR AUGMENTATION IN RIB TURBULATED FLOW A Thesis in Mechanical Engineering by Gaelyn L. Neely Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 009

2 The thesis of Gaelyn L. Neely was reviewed and approved* by the following: Dr. Karen A. Thole Head of the Department of Mechanical and Nuclear Engineering Professor of Mechanical and Nuclear Engineering Thesis Advisor Dr. H. Joseph Sommer III Professor-In-Charge of MNE Graduate Programs Dr. Stefan Thynell Professor of Mechanical and Nuclear Engineering *Signatures are on file in the Graduate School. ii

3 ABSTRACT Current gas turbine airfoils must survive in an environment where operating conditions are approaching extreme levels. Increasing the temperature of the combustion gases entering the turbine improves engine efficiency and power output; consequently, the turbine inlet temperatures have reached levels exceeding the melting point of the blade materials. Internal cooling of the turbine blades is vital to maintaining turbine blade longevity and durability. Ribroughened channels in the blade core are commonly used to increase turbulence and secondary flows that aid the transport of energy. In addition, the ribs increase the convective heat transfer surface area. Past research has focused on two ribbed wall configurations, and worked to identify the most favorable rib design that will produce maximum heat transfer with minimal pressure loss. This paper presents an analysis of various rib configurations for a one ribbed wall configuration, by comparing the effect of pitch, aspect ratio, and rib orientation on both heat transfer and friction augmentation. Heat transfer measurements were made using infared camera thermography in the fully developed region of the channel. Additionally, the effect of total wetted area versus planform area was investigated. Experimental measurements were taken in a closed-loop recirculating channel with a parallel-plate channel test section. The channel had varying aspect ratios of.86 or 5 with a constant blockage ratio of 0.. All ribs were rounded, discontinuous V-shape, at 45 to the flow with pitch-to-rib height ratios of 5 or 10. Results indicate heat transfer augmentation was higher with a pitch-to-rib height ratio of 5 compared to 10. Similarly, the pitch-to-rib height ratio of 5 caused higher friction factor augmentation. The results also indicate aspect ratio did not affect the ribbed side heat transfer augmentation; however, the.86:1 aspect ratio cases had higher augmentation on the unribbed side compared to the 5:1 case. An increase in aspect ratio caused an increase in friction factor augmentation; thus the 5:1 aspect ratio case had the highest friction factor augmentation. iii

4 TABLE OF CONTENTS List of Tables. v List of Figures vii Nomenclature xi Acknowledgements... xiii Chapter 1. INTRODUCTION Motivation for Research 3 1. Research Objectives. 5 Chapter. LITERATURE REVIEW 7.1 Effects of Rib Pitch.. 9. Effects of Blockage and Aspect Ratio Effects of Rib Shape Orientation and Angle of Attack Measurement Methods Used for Rib Studies Uniqueness of Research Chapter 3. DATA ANALYSIS AND EXPERIMENTAL FACILITY Rib Geometries Overall Test Facility Test Section Design Heat Transfer Pressure Penalty Data Reduction Heat Transfer Augmentation Friction Factor Augmentation Uncertainty Analysis. 45 Chapter 4. EXPERIMENTAL RESULTS Benchmarking Heat Transfer Results for Rounded Ribs Friction Factor Results for Rounded Ribs Chapter 5. CONCLUSIONS Rib Spacing Effects Aspect Ratio Effects Area Effects Recommendations for Future Work.. 8 References. 83 Appendix A. Flowrate Calculations Appendix B. Infared Image Data Reduction.. 89 Appendix C. Heat Transfer Uncertainty Calculations 96 Appendix D. Friction Factor Uncertainty Calculations iv

5 LIST OF TABLES Table -1 Table 3-1 Table 3- Table 3-3 Table 3-4 Table 3-5 Table 3-6 Table 3-7 Table 3-8 Table 3-9 Table 4-1 Table 4- Table 4-3 Table A-1 Table B-1 Table B- Table B-3 Table C-1 Table C- Table C-3 Table C-4 Summary of Relevant Rib Studies Summary of Rib Configurations Summary of Rib Configuration Upstream of the IR Window Summary of Power Settings for P/e=10, AR=4:1, e/h=0.15 Thermal Conductivity and Thickness of Materials in the Loss Analysis Losses for Rib Configurations Uncertainty in Ribbed Heat Transfer Uncertainty in Unribbed Heat Transfer Uncertainty in Friction Factor Measurements Summary of the Repeatability Testing Summary of Ribbed Benchmark Configurations Test Matrix for All Configurations Summary of the Geometries Tested and Compared with Literature for Results Parameters for the Orifice and Venturi Flow Meters Calibration Results for Re=40,000, P/e=5, e/h=0.15, AR=5:1, Ribbed Side Calibration Results for Re=40,000, P/e=5, e/h=0.15, AR=5:1, Smooth Side Biot Calculations for Each Rib at High and Low Re Numbers Uncertainty in Reynolds Number Uncertainty in Heat Transfer Coefficient for the Ribbed Channel Wall Uncertainty in Heat Transfer Coefficient for the Smooth Channel Wall Uncertainty in Nusselt Number for the Ribbed Channel Wall v

6 Table C-5 Table C-6 Table C-7 Table C-8 Table D-1 Table D- Table D-3 Table D-4 Uncertainty in Nusselt Number for the Smooth Channel Wall Uncertainty in the Smooth Channel Nusselt Number Uncertainty in Nusselt Number Augmentation for the Ribbed Channel Wall Uncertainty in Nusselt Number Augmentation for the Smooth Channel Wall Uncertainty in Reynolds Number Uncertainty in Friction Factor Uncertainty in Smooth Channel Friction Factor Uncertainty in Friction Factor Augmentation vi

7 LIST OF FIGURES Figure 1-1. Schematic of a turbojet aircraft engine [Hill and Peterson, 199]. Figure 1-. Cut-away of the Pratt & Whitney F119 engine [ 009]. Figure 1-3. Progress of the compression ratio through the years [Han, 000]. Figure 1-4. Progression of the turbine inlet temperature over the years [Han, 000]. Figure 1-5. Figure 1-6. Figure -1. Figure 3-1. Figure 3-. Three methods of turbine blade cooling are jet impingement, rib turbulated channels, and pin fin banks [Liu et al., 006]. Aspect ratios of the passages depend on the location in the blade core [Huh et al., 008]. Schematic defining the rib parameters under investigation in this study. Schematic of a rounded-rib cross-section where all dimensions are normalized to the rib height. Experimental rib configuration shown with discrete V-shaped, rounded crosssection ribs 45 to the flow, P/e=5, AR=5:1, and e/h=0.15. Figure 3-3. Wright et al. [004] rib configuration showing square cross-section, parallel 45 to the flow, P/e=10, AR=4:1, and e/h=0.15. Figure 3-4. Figure 3-5. Figure 3-6. Figure 3-7. Figure 3-8. Figure 3-9. Schematic of closed loop test facility used for rib turbulator testing. Schematic of the interior components of the plenum. Rounded inlet contraction vanes, made from halved PVC pipes, which aided the transition of the flow from the plenum into the test section. Schematic of the test section used for rib turbulator testing. Typical developing augmentation profile at Re=30000, in the streamwise direction for internal channel heat transfer study with rib turbulators configured as P/e=5, AR=.86, and e/h=0.. One side of the channel had rib turbulators (red) present, while the other remained smooth (blue). Schematic of the Inconel foil strip heaters made for the sidewalls. Figure Cross-section schematic of the Kapton heater used in the test section. vii

8 Figure Side and top schematics of the Lexan support added to the IR viewing area. The support reduced the viewing width by.5 cm of the heater. Figure 3-1. Schematic of thermocouples installation in the channel. Thermocouple bead was secured to the backside of the heaters using Duralco 18 two-part epoxy and the wire routed out through a bore hole in the MDF. Figure Diagram of heater and power supply set-up. Voltage is measured across the wire junction, and the current is measured across the precision resistor. Figure Schematic of the heat loss pathways in the test section. Heat that does not enter the flow is lost to the surroundings and modeled with a 1-D conduction analysis. Figure Pressure taps are located upstream and downstream of the ribbed section of the channel; the extra length of channel is accounted for in the friction factor calculations. The upstream and downstream lengths are summed in x. Figure Schematic defining the various areas used in the area-weighted Nusselt number augmentation. Figure 4-1. Figure 4-. Figure 4-3. Figure 4-4. Figure 4-5. Channel average Nusselt number results for a smooth channel plotted with smooth, turbulent, fully developed heat transfer correlations. Channel friction factor results plotted with smooth, turbulent, fully developed correlations. For the benchmark square rib case, two tests were run at Re=30000 to verify heating the sidewalls did not effect the heat transfer augmentation. The augmentation development along the centerline of the channel was the same regardless of whether the sidewalls were heated. Difference between crossed (Mahmood [003]) and parallel (current study) rib orientation is the angle of attack of each side of the channel. Heat transfer augmentation for the benchmark case compared with Wright et al. [004] and Mahmood et al. [00] for P/e=10, AR=4:1, and e/h=0.15. Figure 4-6a. Augmentation contours show the endwall heat transfer for the benchmarking configuration. Figure 4-6b. Augmentation contours show the endwall heat transfer for the benchmarking configuration. Figure 4-7. Heat transfer augmentation contour, for Re=10,000, from Mahmood et al. [00], where the region immediately upstream and downstream of the rib was resolved. viii

9 Figure 4-8. Figure 4-9. Friction factor augmentation for the benchmark case compared with Wright et al. [004] and Mahmood et al. [00] for P/e=10, AR=4:1, and e/h=0.15. The effect of increasing the pitch is an increase in heat transfer. This increase is more prominent at lower Reynolds numbers, as shown by the current study ribbed results (AR=5:1, e/h=0.) and a Liu et al. [006] study. Figure Contours from AR=5:1, e/h=0., P/e=5 show the secondary flow induced by the V-shape ribs. Figure Ribbed side augmentation contours for P/e=10, AR=5:1, e/h=0.. Figure 4-1. Ribbed side augmentation contours for P/e=5, AR=5:1, e/h=0.. Figure Ribbed side augmentation contours for P/e=10, AR=.86:1, e/h=0.. Figure Ribbed side augmentation contours for P/e=5, AR=.86:1, e/h=0.. Figure Smooth side augmentation contours for P/e=10, AR=5:1, e/h=0.. Figure Smooth side augmentation contours for P/e=5, AR=5:1, e/h=0.. Figure Smooth side augmentation contours for P/e=10, AR=.86:1, e/h=0.. Figure Smooth side augmentation contours for P/e=5, AR=.86:1, e/h=0.. Figure Comparing Rhee et al. [003] with the current study confirms that no aspect ratio effect was expected on the ribbed side heat transfer augmentation; however, an increase in pitch from 5 to 10 decreased heat transfer. Figure 4-0. The smooth side augmentation shows that when only one-wall of the channel was ribbed, the aspect ratio had an effect of the augmentation. As the aspect ratio increased, the smooth wall heat transfer decreased. Figure 4-1. Kunstmann et al. [009] tested W-shape ribs in a one-ribbed wall channel; the unribbed side heat transfer augmentation reflected an aspect ratio effect where the largest aspect ratio has the highest augmentation. Figure 4-3. The ribbed side, unribbed side, and channel average augmentation for the.86:1 aspect ratio cased. Figure 4-4. The ribbed side, unribbed side, and channel averaged augmentation for the 5:1 aspect ratio cases. ix

10 Figure 4-5. Channel-averaged heat transfer augmentation reflects the smooth wall contribution; therefore, the channel average does showed aspect ratio effect for this rib orientation. Figure 4-6. Ribbed side heat transfer results for the P/e=10 cases show reduced augmentation when total wetted area was used relative to planform area. Figure 4-7. Ribbed side heat transfer results for the P/e=5 cases show reduced augmentation when total wetted area was used relative to planform area. Figure 4-8. Unribbed side heat transfer results for all cases show minimal change in augmentation when total wetted area was used relative to planform area. Figure 4-9. Global average heat transfer results for the P/e=10 cases show reduced augmentation when total wetted area was used relative to planform area. Figure Global average heat transfer results for the P/e=5 cases show reduced augmentation when total wetted area was used relative to planform area. Figure Friction factor results for the current study show friction factor increased with increasing Reynolds. Also, the highest pressure penalty occurred for the P/e=5 and AR=5 configuration. Figure 4-3. Comparing the current study with the Rhee et al. [003] showed similar aspect ratio trends; as AR was changed from 5 to.86, the friction factor decreased. Figure A comparison of friction factor augmentation for the current study with Liu et al. s [006] study shows that as pitch increased, friction factor decreased. Figure A-1. Figure B-1. Sample performance curve for the orifice and venturi flow meters shows the orifice was better suited for resolving low-flow conditions. Raw infared image captured with the Flir camera, for square cross-section ribs, 45 parallel to the flow, P/e=10, e/h=0.15, AR=4:1. The thermocouple locations, window frame, and ribs are identified. x

11 NOMENCLATURE A = area [m ] A c = cross sectional area of flow [m ] A p = planform (smooth) heater area [m ] A t = total (wetted) area, heater surface, between ribs, and rib surface area [m ] AR = channel aspect ratio, W:H c p = specific heat of air [J/kg K] d = depth of the airgap [m] D H = hydraulic diameter [m] dp = pressure drop [in H O] e = rib height [m] f = Darcy friction factor of test section f o = Blasius friction factor correlations for a smooth pipe g = acceleration due to gravity [m/s ] h = heat transfer coefficient [W/m K] H = channel height [m] I = measured current through the precision resistor [A] k = thermal conductivity [W/mK] L = length [m] m& = mass flow rate in test section [kg/s] Nu = Nusselt number Nu o = Dittus-Boelter smooth channel Nusselt number P = pressure [in H O, psi, or PA] or rib pitch [m] Pr = Prandtl number P w = wetted perimeter of channel [m] q" = heat flux [W/m ] Q = power [W] or volumetric flowrate [SCFM or m 3 /s] R = resistance [Ω] or universal gas constant, 87 [N-m/kg-K] Ra t = Rayleigh number Re = Reynolds number T = temperature [K] u x = uncertainty in value x V = velocity of flow [m/s] or voltage [V] W = channel width [m] x = streamwise length of ribbed section [m] Greek: α = thermal diffusivity [m /s] or rib angle of attack [degrees] β = bore / hydraulic diameter [m] or volumetric expansion coefficient [1/K] η = thermal efficiency µ = dynamic viscosity [N-s/m ] ρ = density [kg/m 3 ] ν = kinematic viscosity [m /s] xi

12 Subscripts: variable variable air airgap amb bulk conv endwall in ins loss mean measured MDF o out rib side std unribbed wall window ZnSe = line average value = area average value = air properties = air gap between the heater and ZnSe window = ambient room conditions = denotes the bulk fluid flow in the channel = convective = denoted ribbed endwall = inlet to test section = insulation = denotes the outer wall of test section = average of inlet and outlet conditions = denotes a measured value = medium density fiberboard = conditions outside the rig = outlet of test section = denotes rib surface = denotes the sidewall = denotes properties at standard temperature and pressure = denotes a non-ribbed wall of the channel = denotes the heat loss pathway through the MDF wall = denotes the heat loss pathway through the ZnSe window = Zinc Selenide window xii

13 ACKNOWLEDGEMENTS When I graduated from Penn State with my undergraduate degrees, I just wasn t ready to leave Happy Valley. Pursuing grad school at Penn State has been challenging and rewarding, and I will always look back with fond memories. There are a few people I need to thank, for my success would not have been feasible without them. First, I would like to thank my advisor, Karen Thole, for the opportunity to work in your lab, PSU Exccl. I have learned many life lessons that I will carry with me in my career as an engineer. You have taught me the value of hard work and persistence, skills that certainly will be useful in life after grad school. I would also like to also acknowledge Pratt & Whitney for the support of my research, specifically Atul Kohli and Chris Lehane. Your motivation and encouragement have been instrumental in my achievements. Spending so many hours in the lab, I couldn t have done it without my fellow lab mates: Grant, Seth, Jason, Steve, Weaver, Alan, Mike, Gina, and Sundar. The unending support and guidance you have all provided me are invaluable. The company during the tough times and the laughs during the celebrations are things I will never forget. I have made lifelong friends, and even as we move apart I know we will keep in touch. A special thanks goes to my parents Mom and Dad, who have never let me forget who I am and what I can achieve. My triumphs are most certainly yours as well. Dad, you have been my role model since I started walking you are one of the most ingenious and brilliant people I know. Mom, I couldn t have stayed on the path without you, you are definitely my biggest fan, and your support has carried me though more than you will ever know. In addition, I need to thank Kathy for all your help with my writing; I have a polished product thanks to you! Gif, my goodness, I don t even know how to start thanking you! From the isponge to cap and gown, you have been supportive and patient with me. You have made me countless dinners, let me vent when it was tough, bought Asti when it was time to celebrate, and given me hugs when I needed them most. Thank you so much for everything, and I can t wait to start this next adventure with you! xiii

14 Chapter 1 INTRODUCTION Gas turbine engines are widely used for land-based power generation, in addition to aircraft and naval ship propulsion. Because of their efficiency and fast response time, gas turbines are ideal for commercial, industrial, and residential electrical power generation because they can accommodate the fluctuations in load. Similarly, for commercial and military aircraft, gas turbines provide a nearly instantaneous response when more power is needed. A turbine is simply comprised of three main components, including the compressor, the combustor, and the turbine. Air is pulled into the compressor through a diffuser. As the compressor rotates, work from the blades causes the air pressure to rise. In the combustor, fuel is mixed with the high-pressure air and is ignited. This generates a highly energetic mixture of combustion products, which exit the combustor into the turbine. The flow expands as it passes through the turbine, causing the blades to rotate. Finally, the gases are exhausted back into the atmosphere. Figure 1-1 shows a basic schematic of a gas turbine engine [Hill and Peterson, 199]. Figure 1-1. Schematic of a turbojet aircraft engine [Hill and Peterson, 199]. The turbine is mechanically coupled to the compressor in order to provide the power necessary to compress the air. All the remaining power is utilized in various manners depending on the application. In military aircraft engines, the combustion gases exit the turbine and are accelerated through a nozzle generating thrust. Figure 1- shows a cut-away of the Pratt and Whitney F119 engine used in the F- Raptor. Commercial aircraft engines use the power 1

15 generated to rotate a large fan. Finally, for land-based power generation applications, the power generated is typically used to rotate a shaft coupled with an electric generator. Compressor Combustor Turbine Figure 1-. Cut-away of the Pratt & Whitney F119 engine [ 009]. There are two main parameters that will increase the thermal efficiency and power output of a gas turbine; they are the compressor pressure ratio and the turbine inlet temperature. Through research, the compression ratio has increased from approximately 5 in the 1940 s to nearly 40 in the 000 s. Work continues to get this value as high as possible in the future. Figure 1-3 shows the progression of the compression ratio over the years. The second parameter, and the focus of this work, is increasing the turbine inlet temperature. By increasing the inlet temperature the specific core power production of the turbine increases. Inlet temperatures exceed the melting point of the turbine blade material; thus, advanced cooling schemes are needed to protect the integrity of the blades. Hot combustion gases pass over the blades and transfer heat to the outer surface; then that heat is conducted through the metal, and internal coolant passages pull the heat away from the metal. The advances in turbine blade cooling and the subsequent increase in turbine inlet temperature are shown in Figure 1-4. By reducing the blade temperature in addition to minimizing the temperature fluctuations, the lifetime of the turbine blades can be doubled. The main goal is to reduce the thermal stresses that lead to fractures in order to increase safety, blade durability, and engine longevity. Many enhancements have been made to the internal and external cooling of blades; however, there is room for improvement.

16 Figure 1-3. Progress of the compression ratio through the years [Han, 000]. Figure 1-4. Progression of the turbine inlet temperature over the years [Han, 000]. 1.1 Motivation for Research Typical blade cooling schemes include thermal barrier coatings, external cooling, and internal cooling. The first goal of turbine blade cooling is to reduce the amount of heat being transferred from the hot combustion gases to the blade; the second goal is that any heat that is transferred to the blade needs to be removed by internal cooling schemes. 3

17 Thermal barrier coatings (TBCs) are applied to the external surface of the blade and act as a layer of insulation against the hot mainstream flow. In addition to TBCs, a passive heat transfer mechanism, the primary active method of external heat transfer is film cooling. Filmcooling holes are placed on the leading edge of the blade in order to reduce the amount of heat transferred from the flow to the blade. Cooling air bleed off the compressor is injected, through the holes, under the boundary layer formed on the blade surface. This creates a protective layer of cooling air surrounding the blade like a sheath. While film-cooling structurally weakens the blade, it is the most effective method of reducing external heat transfer. The remaining two methods, pin-fins and rib turbulated channels, promote internal heat transfer. Figure 1-5 is a schematic indicating where jet impingement, pin-fins, and rib turbulated passages are utilized. Pressurized cooling air is extracted from the compressor stage of the engine and injected into the turbine blade. This air passes through the serpentine passages and the pin-fn banks, eventually exiting the top or rear of the blade. On the trailing edge of the turbine blade are pin-fin banks that not only provide structural support in the thinnest part of the blade but also increase the heat transferred away from the blade. Pin-fins span the area between the suction side and the pressure side of the blade; this causes a large increase in the convective area in the most thermally stressed region of the blade. Figure 1-5. Three methods of turbine blade cooling are jet impingement, rib turbulated channels, and pin fin banks [Liu et al., 006]. Rib turbulated serpentine channels comprise the mid-portion of the blade. The ribs break up the boundary layer in the internal passages, causing turbulence and increased heat transfer. Driving factors in rib turbulated channels are the channel aspect ratio, rib orientation, and flow 4

18 Reynolds number. It should be noted that pin-fins are highly efficient in the trailing edge of the blade, but they would not have the same effectiveness in the mid-portion of the blade. Pin-fins cause a great amount of drag, and any pressure loss reduces the efficiency of the overall engine. Ribs are typically smaller and have much less effect of the pressure relative to a pin-fin. The goal is to obtain a design with the highest overall cooling effectiveness and the lowest possible penalty on the thermodynamic cycle performance. 1. Research Objectives The work presented in this thesis is part of the larger goal to gain a better understanding of the internal cooling of turbine airfoils. Of particular interest in this study were the heat transfer and pressure loss of the serpentine rib turbulated channels in the mid-portion of a turbine blade. The unique aspect of this work was having only one side of the channel ribbed. Traditionally, research has focused on channels with two ribbed walls. A variety of parameters, related to rib channel flow, were varied in order to identify configurations that maximize heat transfer, while minimizing the pressure penalty. The pitch-to-rib height ratios studied were P/e=5 and 10, and the aspect ratios studied were AR=.86:1 and 5:1. The rib height-to-channel height ratio was constant at e/h=0. for all the cases run. Aspect ratio is of particular interest because different parts of the blade have different aspect ratios as a consequence of the airfoil shape, shown in Figure 1-6. When quantifying heat transfer, the area used in defining the heat flux has an effect on the results. Typically, researchers use the planform area of the heaters as the preferred method, thus investigating the effect of the individual rib configuration on heat transfer. However, when the total wetted area is used, the advantage of the additional surface area is removed from the findings. An analysis of both methods is presented in the results. The remainder of this thesis is organized as follows. Chapter discusses a literature review of ribbed channel heat transfer and friction factor studies relevant to turbine airfoil cooling. Also in the review of relevant literature, the various measurement methods used in heat transfer studies is presented. Chapter 3 describes the test facility, test section, and data reduction methodology. Temperature measurements were collected in two different manners, and both are outlined in the methodology section. The rounded rib experimental results are presented in Chapter 4, in addition to the smooth channel and characteristic geometry benchmarking. Finally, conclusions and recommendations for future work are presented in Chapter 5. 5

19 Figure 1-6. Aspect ratios of the passages depend on the location in the blade core [Huh et al., 008]. 6

20 Chapter LITERATURE REVIEW A review of the relevant literature regarding the various parameters in rib turbulated internal flows revealed numerous studies have been done. Table -1, at the end of the chapter, shows a summary of all the rib geometries and data-collection methods. Rib characteristics include pitch-to-rib height ratio (P/e), blockage ratio (e/h), channel aspect ratio, rib shape, orientation, and angle of attack. The data in this thesis is unique, however, because the effects of pitch and aspect ratio are investigated with a complex rounded rib. In addition, the study utilized infared camera thermography to measure spatial heat transfer augmentation on the endwall. Section.1 addresses previous work done regarding pitch-to-rib height ratios (P/e), Section. covers the combined effect of blockage (e/h) and aspect ratio (AR), while in Section.3 gives a review of rib profile effects. Rib orientation and angle of attack are summarized in Section.4. Section.5 highlights the various measurement methods used in experimental work. Finally, Section.6 summarizes the uniqueness of the current study. For internal flow heat transfer and friction factor studies, some common nomenclature and definitions are used throughout the literature. Figure -1 shows a schematic defining the rib parameters of pitch, rib height, and angle of attack. In rib studies, it is common to define the Reynolds number with respect to hydraulic diameter of the channel: Re = D H V ρ µ (-1) Endwall Rib P α e P = pitch e = rib height α = angle of attack Figure -1. Schematic defining the rib parameters under investigation in this study. 7

21 The hydraulic diameter is defined in Equation -. For large aspect ratio channels, this can be estimated by two times the channel height: D H A = 4 P w c (-) Equation -3: Likewise, the Nusselt number is defined by using the hydraulic diameter, as shown in Nu = h D k H (-3) The measured channel Nusselt number is divided by a smooth circular tube correlation. Studies commonly use the fully developed turbulent correlation developed by Dittus-Boelter [Incropera], shown in Equation -4: Nu o = For friction factor, the commonly used correlation is the Blasius correlation shown in Equation -5: f o Re = Re Pr (-4) (-5) One remaining value used to evaluate the efficiency of the rib turbulators is the thermal performance, defined in Equation -6: η = Nu Nu f f o o 1 3 (-6) The thermal performance equation was developed by Webb and Eckert [197] for heat exchangers with repeated-rib roughness tubes. They found generalized friction factor and heat transfer augmentation correlations for these tubes, then developed the effectiveness equations. Equation -6 is specific for either a specified heat flux boundary condition or a prescribed wall temperature boundary condition. The relative friction power relation in the original equation is raised to the one-third power, which originated from the roughness correlations Webb and Eckert 8

22 developed. The thermal performance for a specific rib configuration is affected by the rib orientation and the Reynolds number. Generally speaking, these are the definitions used by the following researchers in discussing rib turbulator internal flow..1 Effects of Rib Pitch One of the goals of this work was to investigate the effect of rib pitch with a complex rib shape. Many studies have looked at the pitch, but not with the same rib shape as the current work. This section summarizes a few representative studies regarding pitch and establishes the expected trends associated with rib spacing. Han and Park [1988] studied pitch-to rib height ratios of 10 to 0. The cases tested were characterized by square, brass ribs on two walls, oriented in a parallel angle configuration. This study used the planform area of the foil heaters in the data reduction, which is consistent with most internal flow rib turbulator studies. Han and Park [1988] found that P/e=10 yielded higher heat transfer and higher pressure drop penalty in all cases when compared with P/e=0. For a P/e=0 ratio the boundary layer was able to redevelop, thus reducing the heat transfer. The pressure drop was also higher for the P/e=10 ratio because the number of ribs in the channel is doubled when the pitch changes from 0 to 10, meaning more obstacles for the flow to encounter. A 006 study by Liu et al. investigated the effect of rib spacing on heat transfer and friction factor, and they summarized their findings as thermal performances (η). Additionally, they examined the effect of using planform area compared to wetted surface area in their definition of heat flux. The test section was a two-pass channel with an aspect ratio of 1: and two ribbed walls. For each pitch tested, the square ribs were parallel angled at 45 to the flow with a blockage ratio held constant at Over the span of Reynolds 5,000 to 40,000, the pitch-to-rib height ratios tested were as follows: 10, 7.5, 5, and 3. To compare Liu et al. s results with the current study, only the first pass data was considered; however, the study does report first-pass, second-pass, and channel-averaged (both passes) values. When using the planform area, Liu et al. [006] found that heat transfer augmentation increased with a decrease in P/e, which is consistent with earlier findings from Han and Park [1988]. When using the total wetted area, all the augmentation plots converged to one value with no effect of pitch reported. Friction factor augmentation increased with decreasing P/e from 10 9

23 to 5. Then as the pitch decreased further to P/e=3, the friction factor augmentation decreased. Han and Park s result are consistent with Liu s, that a decrease in P/e from 10 to 5 caused an increase in friction factor. Rallabandi et al. [009] also found for a square channel with 45 parallel ribs, the heat transfer augmentation decreased when the pitch decreased from 10 to 5. A study done by Huh et al. in 008 examined only the effect of pitch on heat transfer using an average of all the thermocouples placed in the channel. This experiment utilized a twopass channel with an aspect ratio of 1:4. Similar to Liu et al. [006], only results from the first pass of the channel were considered for comparison purposes. The square ribs were parallel at a 45 angle of attack on two walls. Blockage was constant at e/h=0.15 over the range of Reynolds numbers tested. Huh et al. tested P/e ratios of.5, 5, and 10, given that Liu et al. s study showed only a slight variation in heat transfer results when P/e was varied from 7.5 to 10. Huh et al. s study used copper blocks to achieve a constant temperature boundary condition with a lumped capacitance model. Huh et al. [008] found that heat transfer augmentation increased with increasing P/e when the total wetted area was used to reduce the data. The total wetted area was considered to be the smooth area between the ribs and the three sides of the ribs exposed to the flow. Thus, with total wetted area, they found P/e=10 had the highest heat transfer augmentation, contradicting the previous findings from Liu et al. [006] in which they found using the total area does not result in a pitch effect. Huh et al. did, however, found that heat transfer augmentation decreased with increasing P/e when the planform area was used in the data reduction, whereby using planform area, the highest augmentation occurred at P/e=.5. In summary, for all the pitches, the augmentation was lower when planform area was used instead of total wetted area. Using planform area in the data reduction identified a trend where an increase in P/e caused a decrease in heat transfer. The current study uses planform area; therefore, it was expected that as P/e increased from 5 to 10, both the heat transfer and the friction factor would decrease. There is an ideal range of pitch-to-rib height ratios that is desirable for heat transfer augmentation, while keeping thermal performance in mind. With a large spacing between ribs, the boundary layer is able to redevelop, decreasing heat transfer. However, with too little spacing between the ribs, the boundary layer never reattaches, which also decreases heat transfer. With respect to friction factor, the fewer obstacles (ribs) the flow encounters, the lower the pressure penalty. So it was 10

24 expected that a lower P/e would yield a higher pressure drop because there were more ribs present in the channel.. Effects of Blockage and Aspect Ratio Upon examining numerous studies, it became apparent that blockage ratio and aspect ratio effects typically were not isolated during experiments. Most studies utilized one physical set of ribs and changed the channel dimensions. As the channel height was changed to accommodate various aspect ratios, the blockage ratio (e/h) inherently changed. Bunker [008] investigated the effects of manufacturing tolerances on thermal boundary conditions for highly cooled turbine airfoils. For internal flow, he found that blockage was the main contributor to variation in heat transfer when considering aspect ratio, pitch-to-rib height, angle of attack, and blockage ratio. It is surprising that more studies in the literature do not focus solely on the effect of blockage without simultaneously varying the aspect ratio. The current study did not consider various blockage ratios; however, it did investigate the effect of aspect ratio on heat transfer with a constant blockage. The study by Han and Park [1988], summarized in Section.1, evaluated the combined effect of angle of attack and aspect ratio on heat transfer and friction factor. Because a single set of ribs was used, the blockage ratio changed with aspect ratio. The angle of attack was varied from 90 to 30, and the aspect ratio varied from 1:1 to 4:1, with the respective blockage ratios of to Han and Park [1988] found that at a 90 angle of attack, the augmentation development down the centerline of the channel remained constant at x/d H =3; therefore, all the channel-averaged values were averages from data collected downstream of the fully developed region in the channel. They determined that the centerline averaged Nusselt numbers and the averaged friction factors increased with decreasing angles of attack, and the maximum heat transfer occurred at α=60. However, the best thermal performance for a constant pumping power occurred at α=30 for an aspect ratio of 1:1 and α=45 for aspect ratios of :1 and 4:1. When examining the effect of aspect ratio, the friction factor augmentation increased progressively as the aspect ratio increased from 1:1 to 4:1. It should be noted that as the aspect ratio increased, the blockage ratio simultaneously increased. Heat transfer, however, increased only slightly as aspect ratio increased from 1:1 to :1, and there was almost no change when 11

25 aspect ratio increased from :1 to 4:1. It became a consistent trend that aspect ratio had a greater effect on pressure drop than on heat transfer. In 199, Park et al. looked at the combined effect of aspect ratio and blockage ratio on friction factor and heat transfer in a channel with two-ribbed walls that contained square, parallel, angled ribs placed at a pitch-to-rib height ratio of 10 and blockage ratios of to 0.15, respectively. This study used one set of ribs for the rectangular channels and a separate set of ribs for the square channel; so as the channel height was varied, the e/h ratio also changed. Foil heaters were used to create a constant heat flux boundary condition, and the flow was hydrodynamically developing as it contacted the ribs due to a sudden entrance contraction. Park et al. [199] found for the same level of heat transfer augmentation, the pressure drop in the wide aspect ratio channel (4:1) was much larger than in the narrow aspect ratio channel (1:4). Overall, the narrow aspect ratios had higher heat transfer than the wide aspect ratios, which is inconsistent with the finding that heat transfer increases with increased blockage and aspect ratio, as shown by Park [199] and Han and Park [1988]. This study showed that heat transfer augmentation increased slightly as aspect ratio increased. Friction factor augmentation notably increased with increasing aspect ratio and, therefore, increasing blockage ratio. In a naphthalene sublimation study, Rhee et al. [003] studied the combined effect of aspect ratio and blockage ratio on heat transfer and friction factor. The test facility used naphthalene sublimation in the fully developed region to obtain the heat transfer values. The aspect ratio was varied from 3:1 to 6.8:1, while the blockage ratios ranged from 0.06 to 0.136, respectively. The square cross-section ribs were either continuous 60 V-shape or discrete 45 V-shape and both had a constant P/e=10. For both rib orientations, the maximum heat transfer augmentation occurred at the centerline of the V-shape and decreased along the outer edges of the rib. Rhee et al. [003] found that the centerline augmentation of the V-shape was largely affected by the aspect ratio, while the near-wall region was not as sensitive. They determined that the impact of the downward flow decreased as the aspect ratio increased in the centerline region. As expected, Rhee et al. [003] found that as Reynolds number increased, heat transfer augmentation decreased and friction factor augmentation increased. For the channel-averaged values, the heat transfer decreased with increasing aspect ratio. The opposite trend was observed with the pressure drop: friction factor augmentation increased as aspect ratio increased. It is important to keep in mind that as the aspect ratio was increased, the blockage ratio also increased 1

26 in the Rhee et al. study. It is commonly known that an increase in blockage will increase both heat transfer augmentation and friction factor augmentation. Rallabandi [009] confirmed the effect of various blockage ratios on heat transfer and pressure drop measurements with 45 rounded ribs. Distinctively, the aspect ratio was held constant, and the rib height-to-channel height ratio (e/h) varied from 0.19 to He found that with a square channel, as the blockage increased, both the fiction factor augmentation and the heat transfer augmentation increased. Overall, it can be summarized that experimental findings show as aspect ratio increased, there was a larger effect on friction factor augmentation than on heat transfer augmentation. Also, as the aspect ratio was increased, both friction factor augmentation and heat transfer augmentation were expected to increase..3 Effect of Rib Shape Classically, most studies utilize square ribs because of the ease of manufacturing. Complex rib shapes require machining or casting, while a common cross-section shape, such as a square, can be purchased off the shelf. With that in mind, studies on the effect of rib shape on heat transfer and friction factor contribute to a significant amount of research done in gas turbine cooling studies reported in literature. Liou and Hwang [1993] measured heat transfer coefficients and friction factors in a rectangular channel with an aspect ratio of 4:1 for two-ribbed walls with various rib shapes. The configurations were transversely oriented (90 ) ribs with e/h=0.15 and varying P/e=8 to 0. The rib shapes considered were an isosceles triangle, half-circle, and square cross sections. Results showed that the square cross-section ribs had both the highest heat transfer augmentation and the highest pressure drop. Conversely, the half-circle ribs had the lowest heat transfer and the lowest pressure drop. When the data was evaluated for thermal performance, no significant effect was identified as a result of changing the rib shape. This result may be driven by the fact that the heat transfer data reduction used the total wetted rather than the planform area of the channel. The surface area was different for each rib shape, making direct evaluations on the benefits or drawbacks of the specific rib shapes difficult. Viswanathan and Tafti [005] examined computational models using rounded ribs. The configuration under investigation was a two-wall angled, staggered 45 rounded ribs, in a square 13

27 channel (aspect ratio was 1:1), with P/e=10 and e/h=0.1. They investigated only one Reynolds number of 5,000, and the model had a constant heat flux boundary condition. Most studies use square ribs, and Viswanathan and Tafti [005] concluded that the use of rounded ribs in a staggered, angled configuration did not affect the heat transfer but did have a significant effect on the friction factor. From comparing similar experimental results from Johnson et al. [1994] and Chanteloup et al. [00] with computational models from Abdel-Wahab and Tafti [004], Viswanathan and Tafti [005] found the rounded rib friction factor augmentation was 33 percent less than that of the square rib configuration..4 Orientation and Angle of Attack Research began with orthogonal ribs, 90 to the flow with studies including Stephens et al. [1995] and Liou and Hwang [1993]. The focus then shifted to angled ribs at various angles of attack: 45, 60, and 30 including Rhee et al. [003] and Kim et al. [007]. Eventually, more complex orientations developed, including V-shape and W-shape. Experimental studies focused on determining the ideal orientation for best overall heat transfer with minimal pressure loss. This goal drew researchers to investigate parallel versus staggered orientations and continuous (without gaps) versus non-continuous (with gaps) orientations. The current study focused only on 45 orientations as it has been widely shown that this angle of attack is ideal for angled or v- shaped orientations [Johnson et al., 1994]. Han and Park [1988] and Park [199] investigated the effect of angle of attack on heat transfer by varying the angle between 90 and 30. Park et al. [199] found that the angle of attack was dependent on aspect ratio. For aspect ratios less than one, the 45 and 60 attack angle had the highest heat transfer augmentation, while for aspect ratios greater than one, the 90 and 60 yielded a highest heat transfer augmentation. Consistent with the previous research, a 1994 study by Johnson et al. resulted in a recommendation for angled (45 ) over orthogonal (90 ) trips for blade design based on heat transfer results for an aspect ratio of 1:1. Wright et al. [004] focused their study on the effect of different rib orientations on heat transfer and friction factor. Six different rib orientations were investigated: angled, discrete angled, V-shaped, discrete V-shaped, W-shaped, and discrete W-shaped. This approach highlighted the differences in heat transfer augmentation and pressure penalty between a continuous and a non-continuous rib. For each rib orientation, the 4:1 aspect ratio channel had 14

28 two-ribbed walls with an angle of attack at 45, P/e=10, and e/h=0.15. Wright et al. [004] found the W-shape and discrete W-shape had the best heat transfer augmentation; however, these orientations also had the highest frictional loss augmentation. The discrete V-shape and discrete angled ribs had the lowest pressure drop augmentation and, therefore, the lowest friction factor augmentation. When thermal performance was considered, Wright at al. [004] found that for a constant pumping power, the discrete V-shape and discrete W-shape had the best performance, while the angled rib had the worst. This study was selected to benchmark the current study s test rig because of the common rib and channel geometry in addition to the thoroughly reported data. Lee et al. s [005] goal was to determine the effect of rib orientation on heat transfer, mainly comparing parallel to staggered orientations and continuous (without gaps) to noncontinuous (with gaps) orientations. The configurations all had a 45 angle of attack and included parallel V-shape without gaps, staggered V-shape without gaps, parallel V-shape with gaps, parallel angled without gaps, staggered angled without gaps, and parallel angled with gaps. The channel had a 4:1 aspect ratio with two-ribbed walls. Pitch-to rib height spacing was held constant at P/e=10, and the blockage ratio was e/h=0.15. Lee et al. [005] concluded that the V-shaped produced higher heat transfer augmentation than angled ribs. They also found there was a negligible effect on heat transfer augmentation when comparing parallel to staggered orientations without gaps, regardless of whether the ribs were angled or V-shaped. However, parallel V-shaped without gaps had higher heat transfer than parallel V-shape with gaps. Having a continuous versus non-continuous orientation affected the secondary flow mechanisms, thus altering the heat transfer augmentation. The opposite was found for parallel angled orientations, ribs with gaps showed higher heat transfer augmentation than parallel angled without gaps. These findings are consistent with those of Wright et al. [004]. Overall, the V-shaped turbulators had the greatest thermal enhancement and performed well with regard to minimal pressure drop augmentation. The current study utilized this knowledge and went a step further in investigating how only one ribbed wall would affect the heat transfer and friction factor..5 Measurement Methods Used for Rib Studies A variety of measurement methods exist for determining rib heat transfer coefficients. Many studies, including Johnson et al. [1994], Wright et al.[004], Lee et al. [005], Liu et 15

29 al.[006], Ostanek [008], and Huh et al. [008], used a lumped capacitance method that required a constant surface temperature boundary condition. A highly thermal conductive material, such as copper, was typically used to create the walls of the channel. Each copper block had a thermocouple embedded within it, which recorded the temperature of that section of the channel at a steady state. Because the blocks were assumed to be a uniform temperature, an assumption confirmed by a Biot analysis, this lumped capacitance method was an easy and reliable method to capture average global heat transfer coefficients. A need for spatially resolved heat transfer data grew as technology advanced and questions about the secondary flow structures developed. For example, researchers began predicting heat transfer and flow structures with numerical simulations, and these computational results required experimental validation. Additionally, a regionally or globally averaged value does not indicate where areas of lower augmentation were developing along the channel walls. A hot spot could lead to intense localized thermal stress, eventually weakening the airfoil. Methods used in experimental work for spatially averaged data collection include holographic interferometry, naphthalene sublimation, liquid crystals thermography, and infrared camera thermography, which is the technique utilized in the current study. Liou and Hwang [1993] used real-time holographic interferometry to measure the temperature distribution of the airflow and thermocouples to capture local wall temperatures under the constant heat flux boundary condition. This method provides spatially resolved convection coefficients around the perimeter of a two-dimensional rib. Interferometry is not an accurate method of obtaining surface heat transfer measurements. It is difficult to measure the change in air temperature so close to the surface, which is why Liou and Hwang [1993] embedded thermocouples along the surface to capture the near-wall temperature. Similarly, Ostanek [008] measured the surface temperature with embedded thermocouples; however, the focus of that study was to develop a methodology for measuring the heat transfer augmentation on the rib surface. Another data-collection technique better suited for surface temperature measurements is naphthalene sublimation. Naphthalene sublimation utilizes the analogy between heat and mass transfer to determine heat transfer augmentation. Cho et al. [003] coated the leading and trailing surfaces in a channel with naphthalene in order to simulate a cooling channel s two-sided heating condition, representative of a gas turbine blade. The naphthalene coated surfaces are analogous 16

30 to a constant temperature boundary condition, where the uncoated surfaces are comparable to adiabatic surfaces. Sherwood ratios are calculated by measuring the sublimation depth before and after an experiment. One limitation of naphthalene is that sublimation occurs under natural convection; therefore, corrections to the measured depths are needed to account for the time used to measure, install, and disassemble the test facility. Cho et al. [003] used the naphthalene sublimation technique to investigate heat/mass transfer in a two-pass duct for smooth and ribbed surfaces. Kim et al. [007] studied the effects of secondary flow due to angled ribs on heat/mass transfer by using naphthalene sublimation, but they introduced channel rotation and bleed holes into the configuration. In addition to Cho et al. [003] and Kim et al. [007], similar experiments using naphthalene sublimation were conducted by Han et al. [005] and Papa et al. [00]. The surfaces of the test section were cast in naphthalene, and the local sublimation depth was measured to attain mass transfer coefficients at each position by using a linear variable differential transformer. Another common data-collection technique uses liquid crystals thermography (LCT) to obtain iso-contours of the surface temperature. The interior walls of a clear channel are painted with liquid crystal paint. As the paint is heated, the crystals change color, and the changes are recorded with an RGB camera. Temperature changes are recorded and then reduced to a temperature map of the entire interior surface of the channel. Maurer and von Wolfersdorf [006] used liquid crystals thermography to measure heat transfer on V-shaped ribs in a :1 aspect ratio channel. With the LCT, they were able to obtain spatial augmentation maps for the ribbed walls instead of only channel-averaged or regional augmentations. Diette et al. [004] also used liquid crystals thermography to map iso-contours of Nusselt numbers on a rib, ribbed wall, and the opposing smooth wall. The bottom of the rib was filleted and manufactured from Plexiglass. The constant heat flux boundary condition was achieved with Inconel foil sheets. Diette et al. [004] concluded that there was good qualitative agreement between the numerical simulation and the iso-contours obtained with the liquid crystals; however, the numerical simulation quantitatively under predicted the heat transfer levels as was also observed in the Maurer and von Wolfersdorf [006] study. The liquid crystal thermography method is limited by the temperature range the crystals can register at a given time. To record a full spectrum of temperatures, the data is collected in stages and then combined into one image. 17

31 Infared camera thermography has no limitations on the temperature range that can be recorded at any given time. Ames et al. [007] and Lyall [006] used infrared camera thermography to take fullsurface endwall heat transfer distributions for pin fin arrays. These studies used a constant heat flux boundary condition, which was achieved with foil heaters. Both used a zinc selenide window in order to insulate the heater surface, allowing the infared radiation to pass through. The test surfaces were coated with flat black paint to reduce issues related to the uncertainty. Mahmood et al. [00] used infared camera thermography to image a ribbed channel wall in order to obtain spatially average Nusselt numbers. A portion of the top channel wall was removed, and a zinc selenide window was installed in order to image the inside ribbed channel wall. This provided spatial data on the top surface of the rib. This approach is different from the Lyall [006] and Ames et al. [007] studies, which imaged the back side of the heater. When the zinc selenide was not in place, an insert with ribs exactly matching the adjacent ribs was installed. The walls were heated with an etched foil heater, creating a constant heat flux boundary condition, which is necessary in an IR camera study. This study was selected for comparison because the configuration is identical to the one used in the current study as well as the Wright et al. [004] study. Globally averaged values were determined by spatially averaging the Nusselt numbers in the fully developed region of the test section, which was reported to be in the x/d H = range. This method allowed the researchers to analyze the secondary flow effects of the surface heat transfer occurring on and around the rib..6 Uniqueness of Research As aforementioned, the focus of this work was to identify the effect of pitch and aspect ratio on heat transfer and friction factor with a complex rounded rib shape. Additionally, the study focused on a one-ribbed wall configuration, which is uncommon in previously reported experimental work. The one-ribbed wall work completed showed improved thermal performance over a two-ribbed wall configuration. Finally, the measurement method utilized infared camera thermography to provide spatially averaged endwall heat transfer data. It also allowed the current researcher to examine the secondary flow effects on the endwalls of the channel with minimal limitations. 18

32 Table -1 Summary of Relevant Rib Studies Investigator Cho et al. [003] Diette et al. [004] Han & Park [1988] Huh et al. [008] Johnson et al. [1994] Kim et al. [007] Kunstmann et al. [009] Lee et al. [005] Liu et al. [006] Liou & Hwang [1993] Mahmood et al. [00] Maurer & von Wolfersdorf [006] Ostanek [008] Park et al. [199] Data-Collection Method Naphtalene Sublimation Liquid Crystal Thermography Thermocouples w/ Foil Heaters Lumped Capacitance Lumped Capacitance Naphtalene Sublimation Liquid Crystal Thermography Lumped Capacitance Lumped Capacitance Holographic Interferometry Infared Camera Thermography Liquid Crystal Thermography Lumped Capacitance Thermocouples w/ Foil Heaters Aspect Ratio (W:H) P/e e/h α 1: Rib Shape Rectangle (:3) Orientation Arrangment Angled Parallel Crossed Discrete No. Ribbed Walls Continuous 4.67: Rounded Transverse - Continuous 1 1: : : : Square Angled Parallel Continuous 1: Half-circle Angled Staggered Continuous 1: : W-Shape 4: Square W-Shape 8: W-Shape Square Transverse Parallel Continuous V-Shape Parallel Discrete V-Shape Parallel Continuous V-Shape Staggered Continuous 4: Square Angled Parallel Discrete 1: 4: Angled Parallel Continuous Angled Staggered Continuous Square Angled Parallel Continuous Isosceles Triangle Half-circle Square 4: Square Angled Crossed Continuous : Square V-Shape Parallel Continuous 1.7: Rounded V-Shape Staggered Discrete 1: : : : : Square Angled Parallel Continuous Square Transverse Angled - Parallel Parallel Continuous Continuous Continuous 1 1 Rallabandi et al. [009] Rhee et al. [003] Viswanathan & Tafti [005] Wright et al. [004] Neely [009] Lumped Capacitance Naphtalene Sublimation Numerical Simulation Lumped Capacitance Infared Camera Thermography 1:1 3: : : : Rounded Angled Staggered Continuous.86:1 5: : Rounded Angled Parallel Continuous Square V-Shape Parallel Square Angled Angled V-Shape V-Shape W-Shape W-Shape Parallel Discrete (45 only) Continuous (60 only) Discrete Continuous Discrete Continuous Discrete Continuous Rounded V-Shape - Discrete 1 4: Square Angled Parallel Continuous 19

33 Chapter 3 EXPERIMENTAL FACILITY AND DATA ANALYSIS The goal of this project was to obtain heat transfer and friction factor measurements for a variety of rib turbulator configurations by examining the effects of pitch, blockage, aspect ratio, rib shape, and rib orientation. Because the actual size of the channel in a turbine blade is too small to spatially resolve the physics, the test section was scaled up from actual engine size in order to obtain the desired measurements with sufficient resolution. Benchmark testing was done with a smooth channel and a characteristic geometry of parallel square-cross section ribs 45 to the flow on two opposing walls. The remaining geometries tested were discontinuous, V- shaped, rounded ribs at 45 to the flow on one wall only. This chapter explains the design of the experimental facility as well as the various data reduction methods. All the rib geometries tested are summarized in Section 3.1. The overall experimental facility used was built by a previous graduate student [Lyall, 006] and was designed to allow test sections to be interchangeable while maintaining the basic structure of the rig. Lyall et al. [006] describe in detail the specifications for all components used in the permanent experimental facility. A summary of the components used in the experimental facility and instrumentation is offered in Section 3.. In Section 3.3, the test section design is explained in detail. Once raw data was collected, it was reduced from temperature and pressure readings to heat transfer coefficients and friction factors. Section 3.4 summarizes heat transfers augmentation data reduction for both the line and spatial measurements. Section 3.5 presents the friction factor augmentation data reduction. 3.1 Rib Geometries The various rib configurations under investigation are summarized in Table 3-1. Figure -1, in the previous chapter, defines the rib parameters used and varied in the experiments. Four configurations were rounded cross-section ribs oriented in a discontinuous V-shape at 45 to the flow. The pitch-to-rib height ratio was varied from 5 to 10, while the trip-height-to-channelheight remained constant at 0.. The rib cross-sectional area with normalized dimensions is shown in Figure

34 Table 3-1 Summary of Rib Configurations Rib Orientation Rib Shape Aspect Ratio Length-to- Hydraulic Diameter No. of Ribs Pitch-to-Height Ratio Blockage Ratio α No. Ribbed Walls Entry Lengthto-Hydrualic Diameter Entry Condition w/h L/D H P/e e/h L entry /D H V-shaped rounded Heated V-shaped rounded Heated V-shaped rounded Unheated V-shaped rounded Unheated parallel square Unheated Radius = 0.5 Wall Length = Height = 1.0 Width = 1.09 Figure 3-1. Schematic of a rounded-rib cross-section where all dimensions are normalized to the rib height. The dimensions are given in a normalized format because the actual dimensions of the ribs changed from configuration to configuration, while the shape remained constant. Finally, the aspect ratio was varied between.86 and 5 for the rounded rib studies. Figure 3- shows a sample rib installation for rounded-cross section, parallel 45 to the flow, P/e=5, AR=.86, and e/h=0.. For all the rounded rib tests, the ribs were installed on one side of the channel, with the remaining three walls left smooth. Because of the complex rib shape, the ribs were milled at the machine shop to obtain the proper cross-sectional area shape. Copper alloy 110 was used for all ribs because of the material s high thermal conductivity, 400 W/m-K. 1

35 Figure 3-. Experimental rib configuration shown with discrete V-shaped, rounded crosssection ribs 45 to the flow, P/e=5, AR=5:1, and e/h=0.15. The remaining configuration was a square cross-section, parallel 45 to the flow, P/e=10, AR=4.0, and e/h=0.15. This specific configuration was designed to replicate a study done by Wright et al [004] in order to benchmark the test section. Because the cross section on the rib was square, copper alloy 110 barstock was purchased in the exact width and height needed, and then cut to length in the machine shop. Figure 3-3 shows this benchmark configuration. Figure 3-3. Wright et al. [004] rib configuration showing square cross-section, parallel 45 to the flow, P/e=10, AR=4:1, and e/h=0.15. Because many rib configurations were being tested, the ribs needed to be installed in the channel with an impermanent technique. Contronics manufactures Duralco 13, a two-part

36 resin-hardener epoxy that is highly thermally conductive. The epoxy has a thermal conductivity of 5.76 W/m-K. To install the rib, the epoxy was applied to the underside of the rib and then placed on the clean, dry heater. Once all the ribs were installed, cinderblock weights were used to hold the ribs in place until the epoxy was completely cured. According to Cotronics [008], cure time ranges from 16 to 4 hours depending on the ambient temperature. After a specific configuration was completely tested, the ribs were removed carefully with Klean Strip adhesive remover. Some residual epoxy remained on the heater surface, and it was cleaned off using the same adhesive remover. After the heater was cleaned, it was ready for the next rib installation. 3. Overall Test Facility The overall test facility was a closed-loop, recirculating channel. Figure 3-4 shows a schematic of the facility with flow moving in the clockwise direction. The system includes a Model D53-J4 high pressure, low flowrate blower manufactured by Chicago Blower. A Baldor Motor ID15H415-E variable frequency drive control was used to adjust the mass flowrate in 0.01 Hz increments [Lyall, 006]. The flow exited the blower through 0.15 meter diameter 40 PVC piping, which was used throughout the rig and continued to the plenum. Downstream of the blower, but prior to entering the plenum, a relief valve in the system was left open to allow the pressure differential between ambient room conditions and the test section to be nearly zero during testing. The plenum conditioned the flow aerodynamically and thermally before it entered the test section. Downstream of the test section, there was a square-to-round expansion joint manufactured by Bolland Machine of Pittsburgh, Pennsylvania. This joint connected the rectangular test section to the circular PVC piping leading to the flow meter. A calibrated Oripac model 4150-P orifice flow meter, manufactured by Lambda Square Inc., was used to calculate the mass flow rate traveling through the test section. Using the orifice meter limited the flowrate to SCFM, which corresponded to a maximum obtainable Reynolds number of approximately 40,000. The manufacturers specifications require ten pipe hydraulic diameters of smooth pipe upstream and six pipe hydraulic diameters downstream to ensure flowrate measurements within a specified accuracy of ±0.6% [Lambda Square Inc.]. Finally, the flow reentered the blower for recirculation. 3

37 Plenum FLOW Test Section FLOW IR Camera Viewing Area L = 7.98 m Flow Meter Relief Valve Blower Figure 3-4. Schematic of closed loop test facility used for rib turbulator testing. 4

38 In the plenum, flow encountered a splash plate and then passed through a heat exchanger before passing through inlet contraction vanes to the test section. Figure 3-5 shows a schematic of the interior of the plenum. The inside dimensions of the plenum measured 1. m in the flow direction, 1. m in the spanwise direction, and 0.55 m high. The splash plate prevented jets from forming and aided in expanding the fluid. Aerodynamically, the dispersion of the flow created uniformity inside the plenum by expanding the flow to ensure a zero-velocity inlet condition for the test section. The plenum had a cross sectional area of 0.67 m, which was 46:1 to 81:1 times greater than the test section flow area, depending on the specific aspect ratio being tested. In general, a ratio of 10:1 is considered acceptable for plenum design. Next the flow passed through a water-to-air heat exchanger, which was used to maintain a consistent inlet temperature. The closed loop nature of the test necessitated a heat exchanger because heat was added to the flow in the test section via viscous and electrical heating. Without a steady inlet temperature, the bulk fluid temperature would have increased gradually throughout the duration of a test. The inlet temperature was measured by two type E thermocouples placed downstream of the heat exchanger, and the maximum variation present in the readings was 0.3 C at steady state. 1. m 1. m FLOW 0.55 m Pressure Tap Thermocouple Splash Plate Heat Exchanger Figure 3-5. Schematic of the interior components of the plenum. 5

39 Finally, the flow passed through inlet contraction vanes to aid in the transition from the plenum to the test channel. The vanes were made from halved pieces of PVC pipe secured to the interior of the front face of the plenum, as shown in Figure 3-6. They were adjustable in order to accommodate the various channel aspect ratios studied. A pressure tap was mounted on the front face of the plenum in order to measure the pressure differential between the plenum and various test section locations and also the ambient room conditions. The tap itself consisted of a small brass tube in inserted flush with the medium density fiberboard wall. For more accurate pressure readings, the interior end of the brass tube was chamfered, creating a seamless joint between the wood and the tubing. Figure 3-6. Rounded inlet contraction vanes, made from halved PVC pipes, which aided the transition of the flow from the plenum into the test section. Temperature and pressure data were collected by National Instruments (NI) signal conditioning hardware and software. An SCXI 1100 signal conditioner was used in conjunction with SCXI 1303 and SCXI 110 terminal blocks to capture voltage signals from the thermocouples and pressure transducers, respectively. The single SCXI 1000 chassis housed the terminal blocks and a Hz low pass filter in order to reduce unwanted noise and frequency content in the signal. Analog signals were converted to digital signals via a PCI-6034E 16 bit data acquisition card. LabView 8.0 software was used to make a user-friendly interface for data acquisition manipulation and viewing the outputs. 6

40 Type E thermocouples were manufactured in the lab and calibrated in an ice bath with a maximum bias uncertainty of ±0. C. The thermocouples were positioned along the centerline of the channel and provided line-averaged data. In the IR viewing area the calibration thermocouples were also type E and manufactured in the lab. Various pressure drops throughout the rig were measured by using two Setra Model 64 pressure transducers. The accuracy was quoted to ±1.0% of the full scale in ambient conditions [Setra Systems, 008a]. A in H O range transducer was used across the orifice flowrate meter, and a in H O range transducer was used for test section measurements. Because there were various pressure taps at one streamwise location, a mechanical fluid wafer from Scanivalve was used to switch easily between the different tap locations for data collection. To obtain the plenum pressure with respect to atmospheric pressure, a Meriam 100F smart gauge with a 0-0 in H O range and accuracy of ±0.05% of full scale was used [Meriam Instruments]. This gauge was also used to measure the high pressure side of the orifice with respect to the room atmospheric pressure. Atmospheric pressure in the lab was obtained by using a Setra Model 370 barometric pressure gauge with a range of kpa and an accuracy of ±0.0% full scale [Setra Systems, 008b]. While the Setra Model 64 transducers were wired to the NI data acquisition system, the Meriam 100F and the Setra Model 370 gauges gave digital readouts that were used to obtain the pressure data. The next section outlines the details of the test section design. 3.3 Test Section Design The test section was designed to fit easily into the overall test facility. A parallel plate channel was built in order to examine the effects of various rib parameters on heat transfer augmentation and friction factor. The test section was constructed to accommodate changing channel dimensions and rib configurations while maintaining the ability to obtain measurements. The Reynolds numbers of interest were in the range 1000 < Re < These numbers were representative of the operational Reynolds numbers for internal cooling of a turbine blade. A channel was built with a 0.3 cm wide endwall and interchangeable sidewalls of heights 4.1 cm, 5.1 cm, and 7.1 cm. To change the aspect ratio, width-to-height of the channel, the sidewalls were replaced by the appropriate height sidewall, while the endwall remained a constant width of 0.3 cm. 7

41 The components of the test section are depicted in Figure 3-7. The flow exited the plenum passing through rounded contraction vanes. Two trip wires that had a mm diameter were used to ensure that the flow was transitioned to a hydrodynamically fully turbulent profile prior to the start of the rib turbulators. The wires were placed 5 cm downstream of the inlet of the channel, spanning the 0.3 cm endwalls. Medium density fiberboard (MDF) was used to make the channel walls because it was readily available, easy to build with, and capable of rigidly supporting the heaters. Furthermore, MDF has a relatively low thermal conductivity of 0.1 W/m-K, making it a good insulator. Trip Wire Pressure Tap Copper Ribs Air Gap Insulation Pressure Tap FLOW Contraction Vanes MDF Heater IR Window L =. m Figure 3-7. Schematic of the test section used for rib turbulator testing Heat Transfer To create a constant heat flux boundary condition, heaters were installed on all four walls of the test section. Rib turbulators disturb the flow by adding increased mixing motions and disrupting the boundary layer. Early tests led to the finding that an insufficient length of heated and ribbed channel existed upstream of the IR camera window. Initial channel configurations permitted only 4 ribs, or.7 hydraulic diameters, upstream of the IR camera viewing area. Flow was not reaching a fully developed state prior to the area where IR measurements were collected, thus creating misleading results. Because the location of the IR camera viewing area could not be changed, additional heaters and ribs were installed upstream of the initial heater location in order to gain the extra hydraulic diameters needed to collect data in the fully developed region. For the rounded rib configurations with an aspect ratio of.86:1, the entry region was heated and 7.3 hydraulic diameters long. The rounded rib configuration with an aspect ratio of 5:1 had an 8

42 unheated entry region that was 18 hydraulic diameters long. Finally, the square rib configuration had an unheated entry region that was 17.7 hydraulic diameters long. Typically, a rib turbulated channel requires approximately five to six rib pitches before becoming thermally and hydrodynamically fully developed turbulent flow. Graham, Sewall, and Thole [004] showed that based on friction factor measurements, the flow became hydrodynamically fully developed by the third to fifth rib. Similarly, Han and Park [1988] showed that the flow is thermally fully developed by the sixth rib based on surface heat transfer measurements. After retrofitting the channel, the IR camera window was positioned a minimum of 7 ribs downstream for the rounded rib cases; however, this length varied from 7 to 14 pitches depending on the specific configuration being tested. Table 3- summarizes the original and extended rib configurations. A plot of the general heat transfer augmentation development in a ribbed channel along the streamwise axis is show in Figure 3-8. Heat transfer augmentation is on the ordinate, and the distance along the streamwise direction normalized by hydraulic diameter is on the abscissa. The augmentation development is for a rib configuration characterized by P/e = 5, AR =.86:1, and e/h = 0. with ribs on one wall only. Thermocouples were permanently installed 6.6 cm apart down the centerline of the channel on both endwalls; this length corresponded to one of the hydraulic diameters of a specific configuration. The hydraulic diameter varied depending on the aspect ratio being tested, and 6.6 cm was selected as the thermocouple spacing because it was the smallest hydraulic diameter being tested. Table 3- Summary of Rib Configuration Upstream of the IR Window Rib Orientation Rib Shape Aspect Ratio No. Ribs Upstream of IR Original Length-to- Hydraulic Diameter Upstream of IR No. Ribs Upstream of IR Extended Length-to- Hydraulic Diameter Upstream of IR w/h V-shaped rounded V-shaped rounded V-shaped rounded V-shaped rounded parallel square The flow underwent entrance and exit effects caused by the transition from the plenum to the test section and similarly from the test section to round PVC pipe, as shown in Figure 3-8. For this example, the entrance length was heated, and the ribs began at x/d H =4.4, causing a large 9

43 jump in augmentation on the ribbed side of the channel at x/d H =4.4. The augmentation development on the ribbed wall was characterized by a spike; then it converged to a constant value in the fully developed region. On the unribbed wall, the augmentation gradually increased until it remained level in the fully developed region. Augmentation on both sides of the channel converged at the same x/d H distance from the start of the ribs, confirming that the flow was thermally fully developed. Slight variations in augmentation values in the fully developed region were the result of the sensitivity of thermocouple placement Entrance Effects Rib Side No Rib Side Fully Developed Region Nu Nu o 4 3 Exit Effects x D H Figure 3-8. Typical developing augmentation profile at Re=30000, in the streamwise direction for internal channel heat transfer study with rib turbulators configured as P/e=5, AR=.86, and e/h=0.. One side of the channel had rib turbulators (red) present, while the other remained smooth (blue). Kapton resistance heaters, manufactured by Electrofilm in Valencia, California, were purchased for the permanent endwalls, and Inconel strip heaters were manufactured in the lab for the smaller interchangeable sidewalls. Each 0.3 cm by 97.5 cm Kapton heater was rated to watts; thus, each heater was able to generate 35 W/m. For the sidewalls, single strip Inconel foil heaters were manufactured in the lab. As shown in Figure 3-9, a strip of Inconel foil was cut to 1 hydraulic diameter in height. Due to the thin foil, a 0.8 mm thick copper busbar was soldered to the end of the strip for stability so that a lead wire could be soldered securely to the 30

44 heater. The individual strip heaters ranged in resistance depending on the height and length of the strip. For example, the 7.1 cm wide heaters had a resistance of 1.1 Ω, while the 4.1 cm wide heaters had a resistance of 1.3 Ω. H = 1 D H Copper strip Inconel foil Lead wire Figure 3-9. Schematic of the Inconel foil strip heaters made for the sidewalls. A cross-section schematic of the Kapton heater is shown in Figure Serpentine inconel strips were laminated between layers of Kapton and then backed with a 8.3 gram layer of copper. The copper backing created a more uniform heat flux distribution than the Kapton/Inconel surface alone. Finally, the copper side was spray painted black in the IR window viewing area in order to create a highly emissive surface. A typical emissivity value for the heater was 0.96, and the background temperature ranged from 0 to 8 C. MDF 1.9 cm Copper Kapton Inconel Kapton 50.8 µm 76. µm 50.8 µm 76. µm Flow Side Figure Cross-section schematic of the Kapton heater used in the test section. To image the heater, a portion of the MDF endwall was removed so the backside of the heater was visible. The window area was oriented at 45 to the flow in order to image the entire length of a rib spanning the channel at 45 to the flow. A zinc selenide (ZnSe) window, measuring 9. cm by 14.0 cm, was installed in the opening to prevent losses yet still allow infared waves to pass through. Outside the IR viewing area, the heater was adhered to the MDF 31

45 wall with model 401B double-sided paper tape manufactured by 3M Company. This siliconbased adhesive stuck well to both the copper side of the heater and the MDF sidewall. In the IR viewing area, the ZnSe window extended past the edges of the channel. Because the heater was the exact width of the channel, 0.3 cm, Lexan supports were added to provide rigidity to the heater. This adjustment prevented the heater from wrinkling and limited vibrations during testing. IR images taken with the supports were of higher quality than those taken without supports, thus justifying their need. Figure 3-11 shows a schematic of the heater supports. At the edge of the heater, 1.3 cm of viewing area on each side was sacrificed in order to install the support. This trade-off was determined to be acceptable because of the resulting improvements in data collection. The footprint of the supports matched that of the IR window in order to prevent any surfaces from coming into contact with, and damaging, the surface of the ZnSe. Side View Top View Heater Air Gap Lexan Support MDF MDF Insulation ZnSe 0.3cm 0.6cm 17.8 cm 0.3 cm Rib Lexan Support Figure Side and top schematics of the Lexan support added to the IR viewing area. The support reduced the viewing width by.5 cm of the heater. Prior to installing the heaters in the channel, the Type E thermocouples were placed at equidistant locations, 6.6 cm, along the streamwise centerline of the heater. Duralco 18, highly thermal conductive, electrically resistive epoxy, was used to secure the thermocouple bead to the backside of the heater. Each thermocouple was placed in the center of an inconel strip to yield the most accurate readings. Then the thermocouple wires were routed out through a bore hole in the MDF channel wall, as shown in Figure 3-1. A small counter sink was drilled in the channel wall on the flow side of the bore hole so that the thermocouple bead would not disrupt the 3

46 smoothness of the heater surface. Strips of the 401B double-sided tape were placed along the length of the channel, and small areas were removed, to accommodate the counter sinks for the thermocouples. To mount the heater in the channel, the thermocouple wires were fed through the channel walls. Gradually, the backing of the tape was removed as the heater was rolled into place with consistent pressure from a hand-held roller. This ensured solid contact and minimal air gaps among the MDF channel wall, the tape, and the heater. 9 µm 54 µm Flow Heater Tape 1.9 cm MDF Thermocouple Bead Bore Hole with Countersink Duralco Epoxy Thermocouple Wire Figure 3-1. Schematic of thermocouples installation in the channel. Thermocouple bead was secured to the backside of the heaters using Duralco 18 two-part epoxy and the wire routed out through a bore hole in the MDF. Because of slight variations in the individual heater resistances, all the heaters were independently powered by Lambda EMI Model GEN DC power supplies. During testing each heater was connected in series with a Lambda power supply and 1 Ω precision resistor. Figure 3-13 shows the circuit for the heaters, power supplies, and precision resistors. A voltage and current were passed through the heater in order to generate a heat flux. To accurately quantify the power generated by each heater, the current was measured across the 1 Ω precision resistor, and the voltage was measured across the heater itself with a digital multimeter. Because the system was connected in series, the current passing through the resistor was equal to the current passing through the heater. Equation 3-1 shows how the heater power was calculated. Q = V I (3-1) 33

47 Wire Junction Voltage Measured Here 1Ω Precision Resistor Current Measured Here - + Power Supply Heater Figure Diagram of heater and power supply set-up. Voltage is measured across the wire junction, and the current is measured across the precision resistor. Measured voltages were in the range of 5-50 volts, and currents were in the range of amps. Table 3-3 shows a sample of the power settings for the following rib configuration: P/e=10, AR = 4:1, e/h=0.15, square ribs on two walls. Most of the heat generated went into the flow; however, some losses were associated with the test section. Table 3-3 Summary of Power Settings for P/e=10, AR=4:1, e/h=0.15 Reynolds Voltage Current Power V A W Figure 3-14 shows a schematic of the two heat loss pathways. The first pathway went through the solid wall where heat flux flowed from the heater surface through the MDF wall through the insulation, ultimately being exposed to ambient room conditions. The second pathway went from the surface of the heater through an air gap through the ZnSe window, finally 34

48 being exposed to ambient room conditions. In order to image the backside of the heater, a barrier was needed that would allow IR radiation to pass through for imaging while still insulating the heater to prevent excess losses. When the viewing area was not in use, the ZnSe window was covered with insulation to prevent further losses. When the insulation was removed from the ZnSe window to take a picture, the temperature decreased by up to 0.4 C. The actual temperatures recorded during the IR picture taking were used in the data reduction process, which is explained in Appendix B. The effect was minimized by removing the insulation over the window for the least amount of time possible, and it was replaced while the IR camera was reset between images. Loss thermocouples ZnSe Air Gap 1.3 cm 0.6 cm FLOW MDF q" flow Heater 1.9 cm 0.03 cm Insulation.5 cm q" loss,wall q" loss,window Figure Schematic of the heat loss pathways in the test section. Heat that does not enter the flow is lost to the surroundings and modeled with a 1-D conduction analysis. Losses were calculated by placing thermocouples on the outer surface of the channel, between the MDF and insulation, equidistantly, at 1. cm apart, in the streamwise direction. This placement created a streamwise temperature profile used to calculate spatial losses. With a constant heat flux boundary condition, the losses increased with increasing streamwise direction. The surface of the ZnSe window was susceptible to scratches, so no thermocouple measurements could be obtained on the window surface to calculate the actual losses occurring through the window. If the window surface had blemishes, it would affect the quality of the IR images. 35

49 In order to determine if the losses calculated through the MDF walls of the channel were an accurate representation of the losses occurring in the IR window area, a thermal resistance analysis was conducted. A one-dimensional conduction analysis was used because the test rig walls could be treated like a composite wall where each layer had an individual thermal resistance. Table 3-4 shows the values for thermal conductivity and length of the various materials in the loss pathways. Table 3-4 Thermal Conductivity and Thickness of Materials in the Loss Analysis MDF Insulation Air Gap ZnSe Thermal Conductivity, k W/m-K Thickness, L m For the wall pathway, the thermal resistance is shown by Equation 3-. R wall = L k MDF MDF L + k ins ins 1 + h amb (3-) For the window pathway, the thermal resistance is shown by Equation 3-3. R window = L k air air L + k ZnSe ZnSe L + k ins ins 1 + h amb (3-3) The thermal resistances were found to be R wall = 1.4 m -K/W and R window =1.33 m -K/W. The difference of 6.6% is small enough that the losses through the IR window could be calculated by using the spatially developed losses through the MDF walls of the channel. The actual losses used in the data reduction were found by using the thermal resistance and the temperature gradient of the MDF wall. Recall, the loss thermocouples were located between the MDF and the insulation. These calculations are shown by Equations 3-4 and 3-5, respectively. L R MDF = k MDF MDF (3-4) q " loss T = endwall R MDF T o (3-5) 36

50 The value of R MDF was calculated to be m -K/W. At the lowest Reynolds number of 1,000, the losses ranged from -10% depending on the configuration. For the highest Reynolds number of 40,000, the losses decreased to a range of 1-8%. Losses on the ribbed side were expected to be lower than losses on the unribbed side as a result of the increased heat transfer caused by the turbulators. Table 3-5 shows each configuration and the respective losses for high and low Reynolds numbers, in addition to the ribbed versus unribbed losses. Because of the enhanced heat transfer on the ribbed side of the channel, the loss on the ribbed endwall was found to be approximately half the loss of the unribbed endwall. Table 3-5 Losses for Rib Configurations Re=40,000 Heat Flux [W/m ] Ribbed Side Loss [W/m ] Ribbed Percent Loss [W/m ] Unribbed Side Loss [W/m ] Unribbed Percent Loss [W/m ] P/e=10, AR=5, e/h= % 34. % P/e=5, AR=5, e/h=0. Discrete One Ribbed % 36.0 % P/e=10, AR=.86, e/h=0. V-Shaped Wall % % P/e=5, AR=.86, e/h= % 6.3 5% P/e=10, AR=4, e/h=0.15 Parallel Two Ribbed Walls % - - Smooth Channel No Ribs % 18 8% Re=1,000 Configuration Configuration Heat Flux [W/m ] Ribbed Side Loss [W/m ] Ribbed Percent Loss [W/m ] Unribbed Side Loss [W/m ] Unribbed Percent Loss [W/m ] P/e=10, AR=5, e/h= % % P/e=5, AR=5, e/h=0. Discrete One Ribbed % 3.6 3% P/e=10, AR=.86, e/h=0. V-Shaped Wall % 4.8 8% P/e=5, AR=.86, e/h= % % P/e=10, AR=4, e/h=0.15 Parallel Two Ribbed Walls % - - Smooth Channel No Ribs % 1 10% The 0.6 cm air gap between heater surface and ZnSe window was designed to minimize losses and also to prevent natural convection from occurring (see Figure 3-14). To check that instabilities did not develop into natural convection cells, the Rayleigh number had to be less than the critical value of Ra t = g β ( T T ) endwall α ν airgap d 4 (3-6) In Equation 3-6, the Rayleigh equation, g is the acceleration due to gravity, β is the volume expansion coefficient, T endwall is the endwall heater temperature, T airgap is the temperature in the air gap, d is the depth of the air gap, α is the thermal diffusivity, and ν is the kinematic 37

51 viscosity. A conservative temperature difference of 30 K was used in the analysis. For the ZnSe window air gap, the Rayleigh number was approximately 680. Therefore, a 1D conduction analysis was determined to be a valid approximation for the heat loss calculations, and no instabilities in the air gap would result in natural convection cells Pressure Penalty To calculate friction factor, the pressure drop across the ribbed portion of the test was needed. Pressure taps were installed in the sidewall, 1 hydraulic diameter upstream of the start of the ribs. Downstream of the ribbed portion, there were two sets of three pressure taps located 3.5 and 4 hydraulic diameters aft of the heater. All pressure taps were installed and manufactured by using the same method described in Section 3.. The smooth channel between the taps and ribs was subtracted in order to obtain the true friction factor of just the ribbed region. The Blasius equations, for a smooth channel, were used to calculate the friction factor in the smooth portions of the channel. The pressure losses due to the smooth portion of the channel then were subtracted from the overall measured value as shown in Equation 3-7. dp = dp measured f o 1 ρ V x DH (3-7) Figure 3-15 shows the how the x length was calculated in the previous equation. The pressure drop, dp flow, was further reduced to a friction, which will be described in detail in Section

52 Pressure taps Ribbed section FLOW L 1 x L x = L 1 +L Figure Pressure taps are located upstream and downstream of the ribbed section of the channel; the extra length of channel is accounted for in the friction factor calculations. The upstream and downstream lengths are summed in x. Prior to running the rounded rib configurations, the test section underwent benchmarking to ensure the channel construction and data reduction were accurate. In the next section, the data reduction for heat transfer and friction factor is covered. 3.4 Data Reduction For each rib configuration, the experiment was run at various Reynolds numbers ranging from 1000 to To obtain the different flow conditions, the mass flow rate was adjusted while the remaining parameters were held constant. An orifice plate flow meter was used to calculate volumetric flow rate through the orifice, and then the value was converted to a test section volumetric flow rate. Reynolds number was then calculated from the flow velocity in the test section. The volumetric flow rate through the orifice was found by using the line flow conditions and correlations provided by the manufacturer. The detailed calculations for determining volumetric flow rate are shown in Appendix A. Once the volumetric flow rate, Q std, though the orifice was determined, the mass flow rate for the experimental facility was calculated by using Equation 3-8. m& = Q std ρ std (3-8) 39

53 The standard density of air, ρ std =1.3 kg/m 3, was found by using Equation 3-9, the ideal gas law, where P amb was Pa and T amb was 15.6 C. The base ambient conditions were provided by the orifice plate flow meter specifications [Lamba Square, Inc.]. ρ std = P R T amb amb (3-9) Once the mass flow rate of the test facility was known, the volumetric flow rate of the test section was found by using Equation Mass flow rate was constant throughout the entire test facility, so it could be used to find the volumetric flow rate, Q, in the test section. Q = ρ m & (3-10) The density of the flow, ρ, in the test section was found by using the ideal gas law with the inlet pressure and temperature of the test section. Finally, the area-dependent velocity of the flow in the test section, V, was calculated by using Equation 3-11, where A c is the cross sectional area of the test section. V = Q A c (3-11) Equation 3-1. The Reynolds number based on hydraulic diameter was finally calculated by using Re = D H V ρ µ (3-1) The dynamic viscosity of air, µ, was interpolated from tables in Incropera and DeWitt [00] using the mean temperature of the flow defined in Equation T mean T = in + T out (3-13) Heat transfer and friction factor augmentation values varied with Reynolds number; thus, it was the central calculation in the data reduction process. 40

54 3.4.1 Heat Transfer Augmentation Temperature and pressure measurements were continuously recorded throughout the duration of a test, but only data collected during steady state was used in the final reduction process. Typically, a test starting at ambient conditions would require three hours to come to steady state. When the temperature values leveled and began to alternate around a mean reading, the thermocouple standard deviation was checked to ensure it was approximately 0. C. At this point the test section was assumed to be at steady state, and measurements were collected. Heat transfer calculations were obtained in two different manners. First, thermocouples were embedded along the centerline of the test section. Second, infared (IR) camera images were used to calculate spatially averaged heat transfer coefficients. Regardless of the method by which temperature data was collected, the heat transfer reduction began by calculating the amount of heat entering the flow. The heater power, Q, was found by measuring the current and voltage across the heater with a digital multimeter. The heat flux of each heater, shown in Equation 3-14, was calculated by using the planform surface area of the heater, A p. q " = Q A p (3-14) The total heat flux entering the flow took into account the heat loss out of the channel. In Section 3.3 a detailed analysis of the heat loss is presented. From this analysis, it was possible to conclude that the total heat entering the flow, q" conv, is defined as follows: q " = q" q" conv loss (3-15) 16. The bulk temperature was calculated by using a first law analysis shown in Equation 3- T bulk = T in q" conv Ap + m& c p (3-16) The heat transfer coefficient, shown in Equation 3-17, was calculated at each thermocouple location. h = A endwall + 1 A side Qconv 1 + A side ( T T ) endwall bulk (3-17) 41

55 The area used in the heat transfer coefficient calculation did not account for the added surface area of the ribs in the channel; instead, it was accounted for later in the Nusselt number weighting. Planform area was the smooth surface area of the heaters, while the total, or wetted, area represented the actual surface area the flow encountered. Therefore, the total area included the heater surface between the ribs and the exposed top and side surfaces of the ribs. In Equation 3-17, a planform area representing the endwall and half of each sidewall was used. Depending on the specific configuration, ribs were installed on one or two endwalls in the channel, leaving the sidewalls smooth in all cases. The ribbed endwall had a higher total surface area compared to a smooth wall and, by using the planform area in the data reduction, the analysis remained consistent regardless of the configuration under consideration. Using the planform area also allowed for uniform comparison between ribbed and smooth walls. It was important to calculate a heat transfer coefficient for each wall because of the difference in the magnitude between a turbulated and a smooth wall. Finally, the channel Nusselt number was calculated by using Equation 3-18; this number represents the temperature gradient at the wall. h D Nu = k air H (3-18) Augmentation is a nondimensional number that characterizes the heat transfer caused by the addition of turbulators. The measured channel Nusselt number is divided by a smooth circular tube correlation. For this study, the fully developed turbulent correlation used was Dittus-Boelter [Incropera], shown in Equation Nu o = Re Any augmentation value above 1.0 means the heat transfer was enhanced by the turbulator feature. The augmentation was calculated for the ribbed channel walls, the unribbed channel walls, and finally a global channel area-averaged value, given in Equation 3-0. Pr 0.4 (3-19) Nu Nu o = Nu endwall A + Nu + Nu + Nu ( A + A + A + A ) 0.03 Re Pr endwall endwall rib rib A rib unribbed unribbed side A unribbed unribbed A side (3-0) 4

56 Figure 3-16 is a schematic defining the areas A endwall, A rib, A unribbed, and A side used in the area weighted augmentation. The A endwall did not include the heater surface covered by the ribs, only the exposed area between the ribs. A rib was the surface area of the rib not including the bottom surface that was in contact with the heater. A unribbed was the viewable area on the smooth side of the channel. Finally, A side was the smooth sidewall area consistent with the length of the IR window viewing area Rib A endwall 0 A rib 0 Augmentation Cropped A side W 40 A unribbed 0 H Figure Schematic defining the various areas used in the area-weighted Nusselt number augmentation. The thermocouple values along the centerline of the channel provided only streamwise dependent point values. In order to obtain spatial averages, temperature maps were collected at a specified location in the channel. Each pixel in the image represented a temperature at that coordinate location. Using all the pixels, a full map of the heat transfer was provided, and spatially averaged values were calculated. For each test, five IR images of the backside of the heater were collected at each of the two viewing locations. Multiple images were captured to 43

57 reduce the pixel-to-pixel noise and the measurement uncertainty. A full description of the image capture process, calibration, and reduction are provided in Appendix B. In addition to heat transfer data, pressure measurements were made across the test section to determine friction factors Friction Factor Augmentation Darcy friction factor across a ribbed channel is shown in Equation 3-1. f = L D H dp 1 ρ V (3-1) The pressure drop across the ribbed portion of the test section was calculated by measuring the pressure drop from the plenum to the pressure taps downstream of the ribs and then subtracting the pressure drop from the plenum to pressure taps upstream of the ribs. The difference between the measurements was the pressure drop across the ribbed section only. The measurement was verified by directly measuring the pressure drop across the ribbed section, from the upstream to downstream taps, during the test channel development. During testing, the pressure drop across the ribbed portion of the channel was not directly measured because the data-acquisition system had a limited number of channels available for use. In order to accurately resolve the pressure drops at various Reynolds numbers, various pressure transducers with the appropriate differential ranges were used. The number of measurements needed, however, exceeded the available channels on the data-acquisition system. Therefore, a pressure manifold was designed to accommodate multiple measurements on one pressure transducer. The pressure transducers used are described in detail in Section 3.. Because the pressure taps were not located immediately upstream and downstream of the ribs, there were some smooth wall contributions to the pressure drop, as explained in Section 3.3. The pressure drop across the smooth endwalls was calculated by using the Blasius correlations for a smooth surface tube and then subtracting them from the measured pressure drop. Detailed explanations of the rig set-up and pressure measurement methods are presented in Section 3.. Blasius correlations are Reynolds dependent, with different equations for flow conditions above or below Re=0,000. Both correlations are shown in Equations 3- and

58 f o f o = Re = Re Re 0,000 Re < 0,000 (3-) (3-3) The friction factor augmentation is a nondimensional way to characterize the effects of the turbulators on the pressure drop across each unique rib configuration, and it is given by f/f o. 3.5 Uncertainty Analysis Uncertainty analyses were calculated for heat transfer and friction factor calculations in order to quantify how well the experimental data represented the actual physics of the flow. Because a range of Reynolds numbers was tested, the analysis was carried out for the highest and lowest values in order to obtain a range of uncertainties. Equation 3-4 is the method described by Kline and McKintock [1953] and Moffat [1985] for single sample measurement uncertainty. u R = ± N i= 1 R u xi x i (3-4) The uncertainty in measurement R is given by the square root of the sum of the squares of the partial derivative of R with respect to variable x i multiplied by the uncertainty in variable x i. With many different measured quantities used to calculate one variable of interest, this equation accounts for the propagation of experimental error due to the uncertainty present in the various measured quantities. For the heat transfer results, the uncertainty was calculated for the Reynolds number, the heat transfer coefficient, the Nusselt number, and the Nusselt number augmentation. Furthermore, the calculations were broken down into a high and low Reynolds number, as well as ribbed and unribbed values. Table 3-6 summarizes the ribbed uncertainty values, and Table 3-7 summarizes the unribbed uncertainty values. Detailed calculations for heat transfer uncertainty are presented in Appendix C. For the ribbed Nusselt augmentation, the uncertainty ranged from %, while the unribbed uncertainty ranged from.9 3.9%. Because the range of Reynolds numbers tested was only 1,000 to 40,000, little variation in uncertainty existed over the entire spectrum of Reynolds numbers tested. 45

59 Table 3-6 Uncertainty in Ribbed Heat Transfer Variable Target Reynolds Value Uncertainty Uncertainty (%) 13, % Re 40, % h Nu Nu o Nu/Nu o 13, % 40, % 13, % 40, % 13, % 40, % 13, % 40, % Table 3-7 Uncertainty in Unribbed Heat Transfer Variable Target Reynolds Value Uncertainty Uncertainty (%) Re h Nu 13,000 13,000 13, % 0.9% 4.1% 40,000 40,000 40, % 0.8% 4.1% Nu o Nu/Nu o 13, % 40, % 13, % 40, % Similarly, the friction factor uncertainties were broken down into four components: Reynolds number, channel friction factor, smooth channel friction factor, and friction factor augmentation. The uncertainty calculated for these values is shown in Table 3-8, and detailed calculations are presented in Appendix D. Both heat transfer and friction factor augmentations are Reynolds dependent, and the range of uncertainty in Reynolds was.8 4.% for values of 1,000 to 40,000, respectively. Uncertainty in the friction factor augmentation was % over the range of Reynolds numbers tested. One of the highest contributors to the uncertainty in the heat transfer augmentation was the use of the Dittus-Boelter correlation. To reduce this contribution, smooth channel benchmark testing was conducted. Smooth channel testing not only verified the rig was operational, but proved that any additional heat transfer was due to the addition of the ribs in the channel. 46

60 Table 3-8 Uncertainty in Friction Factor Measurements Variable Target Reynolds Value Uncertainty Uncertainty (%) Re f f o 13,000 13,000 13, E-0 4.7E % 1.5% 1.6% 40,000 40,000 40, E-0 3.1E % 8.6% 1.4% f/f o 13, % 40, % One final evaluation was completed in order to reduce the uncertainty in the measurements, and that was repeatability testing. On the first ribbed configuration tested (P/e=5, AR=.86:1, e/h=0., and one ribbed wall), repeatability cases were run at the highest and lowest Reynolds numbers. Two cases were run under the exact same conditions, and a third case was run with 5% higher heat flux on each heater. Heat transfer coefficients are independent of the amount of power put into the heater under a constant heat flux boundary condition; therefore, it was expected that this increase in heat flux would not affect the heat transfer results. The first repeatability test, run under the exact same conditions, yielded the same augmentations for the ribbed wall, smooth wall, and channel average. At a Re=9500, the ribbed side augmentation varied 0.6% between the two tests, 1.3% for the smooth wall, and 0.4% for the channel average. When the heat flux was increased by 5% from 918 W/m to 1164 W/m, the percent difference on the ribbed wall increased slightly to.1%. The percent difference from the original case to the higher heat flux case for the smooth wall was 0% and 1.1% for the channel average. Table 3-9 summarizes the augmentation values and the percent difference for the repeatability testing. 47

61 Table 3-9 Summary of the Repeatability testing Reynolds Rib Augmenation Percent Difference Average Augmentation Percent Difference Smooth Augmentation Percent Difference % %.9 0.0% Condition 5% more heat flux % %.6 1.3% Exact repeat Original % % % Exact repeat Original % % % 5% more heat flux 48

62 Chapter 4 EXPERIMENTAL RESULTS This chapter presents the experimental heat transfer and friction factor results for the benchmarking and the rounded rib configurations over a Reynolds number range of 1,000 < Re < 40,000. As established in the previous chapter, thermal measurements were taken with thermocouples and also infared camera thermography. The friction factor was determined from the pressure drop inside the channel. Section 4.1 presents the smooth channel and characteristic geometry benchmarking. Section 4. summarizes the heat transfers results and the effects of rib spacing and aspect ratio. Finally, Section 4.3 shows similar effects of rib spacing and aspect ratio on the friction factor results. 4.1 Benchmarking Two methods of benchmarking were completed: a smooth channel and a characteristic open literature rib geometry [Wright, 004]. The first benchmark case was heat transfer and friction factor tests in a smooth channel. No ribs were installed in the channel, but the data acquisition occurred in the same manner. Heat transfer coefficients and friction factor measurements were obtained and then compared with correlations published in open literature. The heat transfer results for the baseline testing of a 4:1 aspect ratio channel are presented in Figure 4-1 with various turbulent, fully developed correlations for a smooth channel. The maximum percent difference between the Dittus-Boelter () correlation, shown in Equation 4-1, and the current study s channel averaged Nusselt number was 9.% at the lowest Reynolds number. Then as Reynolds numbers increased, the deviation from Dittus-Boelter () decreased to 0.3%. Nu o = Re Pr 0.4 (4-1) The Dittus-Boelter (1), found in Incropera [00] and shown in Equation 3-19, is a modified version of the original correlation Dittus-Boelter (), found in Kakaç [1987]. For the smooth channel benchmarking, the Nusselt number at the lowest Reynolds was 4.0% different relative to the Dittus-Boelter (1) correlations. At the highest Reynolds number, the Nusselt 49

63 number deviated by 13.5%. In open literature, Dittus-Boelter (1) is used commonly to define augmentation, and in the current study it was used to calculate the heat transfer augmentation for all the configurations. In a smooth, rectangular duct with symmetric heating, the channel Nusselt number is insensitive to aspect ratio, including very wide channels [Kakaç, 1987]. Benchmarking at an aspect ratio of 4:1 was thereby inconsequential. Kakaç also concluded that with a smooth channel and symmetric heating, the Nusselt number can be determined to within ±10% of the smooth, circular correlations. The use of the Dittus-Boelter correlations was significant source of uncertainty. By conducting the smooth channel testing, any heat transfer enhancements can be attributed to the addition of the rib turbulators Nu Current Study Dittus-Boelter (1) [Incropera] Dittus-Boelter () [Kakac] Nusselt [Kakac] Drexel & McAdams [Kakac] Gnielinski [Incropera] Re [10 3 ] Figure 4-1. Channel average Nusselt number results for a smooth channel plotted with smooth, turbulent, fully developed heat transfer correlations. In addition to heat transfer data, friction factor was calculated and compared with open literature correlations. In Figure 4-, the channel friction factor is plotted with various turbulent, fully developed correlations for a smooth channel. The maximum percent difference between the channel friction factor and Blasius correlation, shown in Equations 3- and 3-3, was 1.4% at the highest Reynolds number. At the lowest Reynolds number, the percent difference was.7%. Unlike the Nusselt comparison, the percent difference in friction factor increased with 50

64 increasing Reynolds. Correlations indicated that as the aspect ratio of the smooth channel increased, the friction factor would increase [Kakac, 1987]. This trend was also observed once ribs were introduced to the channel Current Study Blasius [Incropera] Colebrook [Kakac] Drew et al. [Kakac] Kakac [Kakac] 0.03 f Re [10 3 ] Figure 4-. Channel friction factor results plotted with smooth, turbulent, fully developed correlations. To ensure that the ribbed channel measurements would be characterized accurately in the experiments, benchmarking was done against a study published by Wright et al. [004]. To quantitatively compare the Wright results with those obtained in the current study, the nondimensional parameters of the test section and ribs were matched. Both studies had an aspect ratio of 4:1 with ribs on two opposing walls. The ribs were square in cross-section with a rib height-to-channel height ratio of e/h = All ribs were parallel spanning the width of the channel and placed at a 45 angle to the flow. Figure 3-3, in the previous chapter, showed the benchmark rib configuration in the channel. Only the ribbed walls were heated, and the sidewall remained unheated consistent with Wright s test facility. Testing was done to ensure the heat transfer remained independent of the sidewall heating. In Figure 4-3, the heat transfer augmentation along the centerline of the channel is plotted for a test run with heated sidewalls and a test run with unheated sidewalls. There is a negligible difference in the heat transfer 51

65 augmentation, and the remaining cases were run without the sidewalls heated consistent with Wright. 5 4 Nu Nu o 3 1 Heated Sidewalls: Top Endwall Heated Sidewalls: Bottom Endwall Unheated Sidewalls: Top Endwall Unheated Sidewalls: Bottom Endwall x D H Figure 4-3. For the benchmark square rib case, two tests were run at Re=30000 to verify heating the sidewalls did not effect the heat transfer augmentation. The augmentation development along the centerline of the channel was the same regardless of whether the sidewalls were heated. The current study was scaled up four times from the Wright experiment for ease of manufacturing the components and overall test facility compatibility. In addition to the physical non-dimensional parameters, the flow conditions were also matched. Both studies had unheated entrance lengths and a heated test section that was 7.5D H long. This heated length corresponded to testing over nine rib pitches. Wright et al. used a constant surface temperature boundary condition on the two ribbed walls. This boundary condition was achieved by using 0.3 cm thick copper plates with heaters on the backside. Each copper plate had an embedded thermocouple, which measured the block temperature. From each thermocouple reading, an average augmentation value was calculated for that copper block. Prior to testing, Wright et al. conducted a Biot analysis to ensure the lumped capacitance model was accurate. There were 4 blocks in the channel, and all the individual copper block augmentations were averaged to obtain a channel-averaged augmentation. 5

66 The current study used a constant surface heat flux boundary condition, which was achieved with the foil heaters. The thermocouple readings in a constant surface heat flux boundary condition experiment are not spatial averages but rather represent only a point value. Therefore, the thermocouple reading was sensitive to its placement relative to the rib, which is not the case with a constant surface temperature boundary condition. To have an accurate comparison with Wright et al. s results, the IR spatially averaged values were used from the fully developed region. Spatially averaged augmentations are an average of the entire channel endwall and thus are directly comparable with Wright et al. s results. In addition to the Wright study, Mahmood et al. [00] used nearly the same configuration, but collected the temperature data using infared camera thermography instead of the lumped capacitance method. The difference between the current study and Mahmood et al. is the rib orientation. Instead of parallel in the case of the current study, where the ribs are angled the same direction on each endwall, the Mahmood configuration had crossed ribs of perpendicular angles on each endwall. Figure 4-4 illustrates the difference between a parallel and crossed rib orientation. Because the remaining rib configuration parameters are the same, the results of the Mahmood et al., Wright et al., and the current study are compared for benchmarking. Table 4-1 shows a summary of the parameters in the current study, Wright et al., and Mahmood et al. Crossed Orientation Parallel Orientation Ribs on top wall Ribs on bottom wall Figure 4-4. Difference between crossed (Mahmood [003]) and parallel (current study) rib orientation is the angle of attack of each side of the channel. 53

67 Table 4-1 Summary of Ribbed Benchmark Configurations Current Study Wright et al. Mahmood et al. Rib Profile Rib Shape Angled Angled Angled Orientation Parallel Parallel Crossed No. Ribbed Walls P/e e/h AR 4:1 4:1 4:1 α Measurement Method IR Camera Lumped Capacitance IR Camera The heat transfer augmentations were calculated and compared with the open literature studies, shown in Figure 4-5. The agreement is within the uncertainty reported by Wright and the uncertainty calculated for this experiment, but the values were consistently higher for the current study. The range of Reynolds numbers was defined by the data available in the Wright et al. study. At the highest Reynolds number of 40,000, the augmentation was.8, and Wright reported an augmentation of.3. Both the current study and Mahmood et al. found an augmentation of.9 at a Reynolds number of 6,000. For the low Reynolds number of 1,000, the augmentation was 3.3, while Wright and Mahmood both reported augmentations for Reynolds as low as 10,000, with augmentations.7 and 3.4, respectively. Between Wright and the current study the trend seen was similar, and the actual values were within the 10% uncertainty of the augmentation value, although consistently higher. However, Mahmood and the current study reported similar trends and similar augmentation levels. 54

68 5 4 Current Study Wright [004] Mahmood [00] Nu Nu o Re [10-3 ] Figure 4-5. Heat transfer augmentation for the benchmark case compared with Wright et al. [004] and Mahmood et al. [00] for P/e=10, AR=4:1, and e/h=0.15. Heat transfer augmentation contours for the benchmark study are shown in Figure 4-6a and Figure 4-6b. Immediately downstream of the rib, the heat transfer augmentation decreased due to the presence of a recirculating flow. Moving further downstream from the rib, the augmentation increases due to the reattachment of the boundary layer. Mahmood et al. [00] reported a small area of recirculation just upstream of the rib. This was not easily observed in the current study because of the resolution of the images. In Mahmood et al. s study, the viewing area was concentrated on one rib, not several rib pitches; therefore, they were able to finely resolve the near-rib area of the endwall. 55

69 Top Endwall Bottom Endwall Re=39175 Nu Nu o 7 6 Re= Re=30783 Re=5064 Figure 4-6a. Augmentation contours show the endwall heat transfer for the benchmarking configuration. 56

70 Top Endwall Bottom Endwall Re=0876 Nu Nu o Re= Re=189 Figure 4-6b. Augmentation contours show the endwall heat transfer for the benchmarking configuration. A heat transfer augmentation contour from Mahmood s study is shown in Figure 4-7. Behind the rib, the flow formed a vortex that travelled up the length of the angled rib and impinged on the sidewall. For the current study, the area of highest heat transfer was directly 57

71 downstream of the streamwise leading end of the rib. Here, the rib caused the most disruption of the flow, and the boundary layer was the least developed. Moving along the angle of the rib, the boundary layer is free to redevelop until it impinges on the sidewall. The nature of the rib orientation generated a warmer and cooler side to the channel, shown as lower augmentation and higher augmentation in the contours of Figure 4-6. Figure 4-7. Heat transfer augmentation contour, for Re=10,000, from Mahmood et al. [00], where the region immediately upstream and downstream of the rib was resolved. In addition to heat transfer augmentation, friction factor augmentation was compared with the Wright and Mahmood results shown in Figure 4-8. The variation between the current study and both the open literature studies was within the uncertainty in the experiment, and the results in the current study were consistent with findings in open literature. Friction factor agreement between the current study and the Wright study was very good, with only minimal deviation at the highest Reynolds number. For Re=40,000, the friction factor was 8.8, and Wright s value was 9.0. At the lowest Reynolds number of 1,000, both studies found friction factors of 7.0. Between Mahmood and the current study, the friction factor augmentation did not agree as well as the heat transfer data; however, this can be attributed to the difference in rib 58