An Experimental Study of Heat Transfer Coefficients and Friction Factors in Airfoil Leading Edge Cooling Cavities Roughened with Slanted Ribs

Transcription

1 An Experimental Study of Heat Transfer oefficients and Friction Factors in Airfoil Leading Edge ooling avities Roughened with Slanted Ribs A Thesis Presented By Benjamin S. Tom To The Department of Mechanical and Industrial Engineering in partial fulfillment of the requirements for the degree of Master of Science In Mechanical Engineering Northeastern University Boston, Massachusetts June 2014

2 Table of ontents Nomenclature... 6 Abstract... 9 Introduction... 9 Theory Test Environment Test Section Rig Rig Rig 3A Rig 3B Turbulator Geometry Heater Arrangement Source Pressure Network The Plenum Power Source Test Procedure Liquid rystal alibration old and Heat Transfer Tests old Test Procedure Heat Transfer Test Procedure Data Post-Processing Procedure Image Processing FORTRAN ode: Determining Average Nusselt Number, Friction Factor, and Enhancement Factor Results and Discussion Test Rig Test Rig Test Rig 3A Test Rig 3B omparative Study: Rigs 1, 2, 3A, and 3B onclusions References

3 Appendix A.1: FORTRAN ode for Rig heck.f File Reduce.F File Rig1-reduce-friction.f File Appendix A.2: FORTRAN odes for Rig heck.f Reduce.F Rig2-reduce-friction.f Appendix A.3: FORTRAN odes for Rig 3A heck.f Rig3a-Reduce-Heat-Transfer.f Rig3a-reduce-friction.f Appendix A.4: FORTRAN odes for Rig 3B Reduce.f Rig3b-Reduce-Heat-Transfer.f Rig3b-reduce-friction.f Appendix B.1: Rig 1 Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal Performance) Appendix B.2: Rig 2 Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal Performance) Appendix B.3: Rig 3A Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal Performance) Appendix B.4: Rig 3B Results (Nusselt Number, Enhancement Factor, Friction Factor, and Thermal Performance)

4 Table of Figures Figure 1: High Bypass Turbofan Jet Engine and Turbine Blade [16], [17] Figure 2: Thermal Resistance Network (Rig 1) Figure 3: Test Section Experimental Setup Figure 4: ross-section of Test Section Figure 5: Layers of Material on Fiberglass Wall Figure 6: ross Section of Test Section Figure 7: ross Section of Test Section 3A Figure 8: ross Section of Test Section 3B Figure 9: Staggered 45 Turbulator Arrangement on Sidewalls Figure 10: Heater Arrangement for Test Rig Figure 11: Heater Arrangement for Test Rig Figure 12: Heater Arrangement for Test Rig 3A Figure 13: Heater Arrangement for Test Rig 3B Figure 14: Parallel Network of Pressure Pipes in Laboratory Figure 15: Plenum Structure Figure 16: Multi-hannel Power Source Figure 17: Liquid rystal alibration Figure 18: Example of image taken by camera of the backwall and nose surfaces used for image processing Figure 19: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall) Figure 20: Rig 1 Nusselt Number Vs Reynolds Number (Nose) Figure 21: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) Figure 22: Rig 1 Enhancement Factor Vs. Reynolds Number (Backwall) Figure 23: Rig 1 Enhancement Factor Vs. Reynolds Number (Nose) Figure 24: Rig 1 Friction Factor Vs. Reynolds Number Figure 25: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall) Figure 26: Rig 2 Nusselt Number Vs. Reynolds Number (Nose) Figure 27: Rig 2 Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) Figure 28: Rig 2 Enhancement Factor Vs. Reynolds Number (Backwall) Figure 29: Rig 2 Enhancement Factor Vs. Reynolds Number (Nose) Figure 30: Rig 2 Friction Factor Vs. Reynolds Number Figure 31: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall) Figure 32: Rig 3A Nusselt Number Vs. Reynolds Number (Nose) Figure 33: Rig 3A Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) Figure 34: Rig 3A Enhancement Factor Vs. Reynolds Number (Backwall) Figure 35: Rig 3A Enhancement Factor Vs. Reynolds Number (Nose) Figure 36: Rig 3A Friction Factor Vs. Reynolds Number Figure 37: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall) Figure 38: Rig 3B Nusselt Number Vs. Reynolds Number (Backwall Vs. Nose) Figure 39: Rig 3B Enhancement Vs. Reynolds Number (Backwall)

5 Figure 40: Rig 3B Friction Factor Vs. Reynolds Number Figure 41: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall) Figure 42: Nusselt Number Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose) Figure 43: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Backwall) Figure 44: Enhancement Factor Vs. Reynolds Number For All Rigs at All Blockage Ratios (Nose) Figure 45: Friction Factor Vs Reynolds Number for All Rigs at All Blockage Ratios Figure 46: Thermal Performance of All Four Test Sections at Backwall at All Blockage Ratios Figure 47: Thermal Performance of All Four Test Sections at Nose at All Blockage Ratios Figure 48: Rig 1 Thermal Performance Vs. Re (Backwall and Nose) Figure 49: Rig 2 Thermal Performance Vs. Re (Backwall and Nose) Figure 50: Rig 3A Thermal Performance Vs. Re (Backwall and Nose) Figure 51: Rig 3B Thermal Performance vs. Re (Backwall and Nose)

6 Nomenclature = ross-section area of the test section = Heater area = Venturi throat cross-sectional area = Specific heat at constant pressure = Hydraulic diameter e = Turbulator height = Blockage ratio EF = Enhancement factor = Darcy friction factor = Smooth wall friction factor = Proportionality onstant in Newton s 2 nd Law (32.2 ) h = Heat transfer coefficient h = Heat transfer coefficient of air at ambient temperature!= urrent applied to heater i ",! = Thermal conductivity of air at ambient conditions $ = Length of the heater Nu = Nusselt number for roughened surface %& = Nusselt number for smooth wall ' ( = Number of turbulators P = Perimeter of test section ) = Ambient pressure )!* = Inlet pressure to test section ) +* = Venturi pressure 6

7 Pr = Prandtl number,-. = Heat transfer rate from the heater to the ambient air at middle of test section,-* = Heat transfer rate from heater to the heated wall surface within leading edge cavity,-!* = Incoming heat transfer rate from heaters,- = Heat transfer rate of losses,-!// = Heat transfer rate at middle of test section at camera location,-* = Heat transfer rate at nose,0! = Heat flux emitted by surface i,0!* = Incoming heat flux,0 = Heat flux losses Re = Reynolds number 1! = Resistance value of material designated by i S = Turbulator pitch (spacing from center of one rib to next) = Turbulator pitch to Turbulator height ratio 2 3 = Heated wall surface for radiation calculation 2 4 = Top wall surface for radiation calculation 2 5 = View wall surface for radiation calculation 2 6 = Nose projected surface for radiation calculation 7 = Temperature of the heater 7!* = Average inlet temperature to the test section 7!*3 = Temperature measured by thermocouple #1 at inlet to the test section 7!*4 = Temperature measured by thermocouple #2 at inlet to the test section 7!8(!/ = Liquid crystal temperature 7 * = Mean temperature at middle of test section (at camera location) 7 +* = Venturi temperature 7

8 TP = Thermal performance 7 ( = Surface temperature at surface of heated wall at middle of test section 9! = Voltage applied to heater i 9 = Flow mean velocity μ = Air dynamic viscosity ρ = Density of air 8

9 Abstract In turbine blade design, the use of turbulators in airfoil cavities has been a preferred means to cool the metal temperatures within the airfoil. Temperatures in the turbine section of a jet engine can easily reach beyond material temperature capability limits and without any internal cooling, the turbine blades will begin to creep and eventually lead to engine failure. The introduction of turbulators has provided a means to increase the heat transfer coefficient within the airfoil cavities and help promote turbulence and better mixing to facilitate convective cooling. In this study, 4 different test rigs were experimented upon with each test rig assessing 3 different turbulator blockage ratios (e/dh). Each test section s cross section was based on leading edge cavity geometry scaled up from a real-life airfoil. Turbulators were placed along the backwall and also along the leading edge nose. The backwall turbulators had rounded corners and staggered, and were placed 45 along the surface of the wall. The nose turbulators also had rounded corners and staggered, but, unlike the wall turbulators, were placed at 90 along the nose surface. To determine the reference temperature of the measured wall and nose surfaces, liquid crystals were used. The liquid crystals were laid on top of the wall and nose surfaces on one wall of the test section. Electric foil heaters were placed beneath the liquid crystals to simulate a heated wall boundary condition. The remaining walls were insulated from the environment to simulate adiabatic conditions. For this study, the heat transfer coefficient, friction factors, enhancement factors, and thermal performance were calculated based on experimental data collected on the backwall and nose surfaces. Upon conclusion of this study, it was found that: (a) Rig 1 has the highest thermal performance at the nose at all blockage ratios. Rig 3A has the highest thermal performance at the backwall at low and high blockage ratios. (b) Rig 1 had the highest friction factor across the range of Reynolds Numbers. Rig 2 had the lowest. (c) As the blockage ratio increased, so did the heat transfer coefficient and friction factors. It was noted, however, in some cases, that as the blockage ratio increased to the maximum blockage the heat transfer benefit was reduced. (d) The turbulator spacing was suggested to have a potential impact on the overall heat transfer coefficient as demonstrated by looking at the results between rigs 2 and 3A and 3B. (e) To validate the test results and trends seen from this experiment, it is recommended that a FD analysis be performed on each test section. Introduction The use of turbulators in turbine airfoils has been the preferred means of cooling the airfoil metal temperatures to achieve the design part life. In jet engine design, the leading edge of an airfoil can be the life limiting location due to high thermal stress. Figure 1 below shows a picture of a high bypass ratio turbofan jet engine and highlights where in the engine, turbine airfoils are generally located. 9

10 Figure 1: High Bypass Turbofan Jet Engine and Turbine Blade [16], [17] As shown in Figure 1, the turbine airfoils are downstream of the combustor module and thus, are exposed to the extremely high temperatures in the flowpath. To reduce the metal temperature along the airfoil s internal walls, it is necessary to provide a means of convectively cooling the internal passages of an airfoil. This is where the use of turbulators is effective. Turbulators are used to help facilitate turbulence and enhanced mixing within the internal cavities of the airfoil by tripping the flow. Tripping the flow enhances mixing and the heat transfer coefficient to facilitate heat transfer from the hot wall to the cooling flow. Taslim and Lengkong [1] studied the heat transfer coefficient on the surfaces of 45 degree angled ribs with sharp and rounded corners within a square channel. A comparison was also done to look at the heat transfer effectiveness of 45 degree vs 90 degree angled turbulators. Taslim and Lengkong investigated into 3 different blockage ratios ( ) of 0.133, 0.167, and 0.25 and for rib pitch-to-height ratios (S/e) of 5, 8.5, and 10. The experiment involved measuring the average temperatures on an electric heated copper rib upstream and midstream location. It was concluded that sharp cornered turbulators produced higher heat transfer coefficient. In addition, 45 turbulators proved more beneficial from heat transfer standpoint at smaller blockage ratio. Moreover, Taslim and Lengkong also showed that small rib pitch to height ratios led to lower thermal performance. Domaschke et al [2] performed experiments looking at the heat transfer coefficient and pressure drop measurement for leading edge geometry consisting of both smooth and rib roughened channels. Staggered 45 angled turbulators were placed on suction and pressure backwalls with constant pitch and blockage ratio for Reynolds numbers between 20,000 and 50,000. Using the Transient Liquid rystal Method, originally developed by Ireland and Jones, Domaschke et al showed that introducing turbulators increased the local heat transfer at the walls and at the leading edge. The pressure and suction backwalls showed an increase up to 350%, while the leading edge only showed a 1.5x increase 10

11 over the smooth wall. The maximum local heat transfer was seen behind the turbulators away from the leading edge. Overall thermal performance increased with the introduction of the turbulators, but decreased with increasing Reynolds Numbers. Rallabandi et al [3] looked at the heat transfer coefficients and frictions factors for a square channel with 45 round-edged ribs at high Reynolds Numbers for land-based gas turbine applications. They looked at various high blockage ratios and pitch for Reynolds Numbers ranging from 30,000 to 400,000. Using copper plates and thermocouples, Rallabandi et al found that larger blockage ratios and smaller rib pitch led to a higher heat transfer coefficient, but also higher pressure drop. Also, increasing the number of ribs increased the surface area, which enhanced the heat transfer coefficient. In terms of the friction factor, Rallabandi et al saw that the rounded edge ribs had lower friction factors than that of the sharp edged ribs. Lau et al [4] also looked at turbulent heat transfer and friction in a square channel with discrete turbulator configurations for two rib to pitch ratios and various angles of attack for Reynolds Number of 10,000 to 80,000. Using brass ribs and heated walls, Lau et al determined the Stanton Number and friction factors for the different rib configurations. Lau et al concluded that the 90 discrete rib case had about 10-15% higher average Stanton Number than the 90 transverse rib case and that turning the ribs in the same direction of the core flow increased it further by another 10-20%. Moreover, the thermal performances of the parallel oblique ribs with 30, 45, and 60 angle of attack was about 20% higher than the 90 discrete rib configuration. The crossed oblique discrete ribs performed the poorest. Some other works in the field of turbulator heat transfer for 90 ribs included Dees et al [5]. Dees et al conducted experiments in a closed loop wind tunnel using a three-vane, two passage cascade test section. Rib turbulators were placed within the test airfoil section, which included two different types of passages; one being of u-bend shape and the other just a straight radial passage. Dees et al concluded that rib turbulators increased the overall heat transfer effectiveness in both u-bend and radial channels, with the ribbed radial channel showing between 40-50% increase in effectiveness. Dees et al also compared the experimental results to their FD analysis, and concluded that the FD analysis under predicted the overall effectiveness, but the trends were similar. In addition to square channels, there also have been experiments performed on triangular leading edge shaped channels. Liu et al [6] investigated internal cooling of a triangular channel with 45 angled ribs at high rotation numbers for P/e = 8 and e/dh = Reynolds numbers ranged from 10,000 to 40,000 and the rotational speeds ranged from RPM. They concluded that in a rotational channel, the trailing edge had higher heat transfer coefficient, while in a stationary channel, the leading edge had a higher heat transfer coefficient. Luo et al [7] also investigated into triangular ducts with ribbed internal surfaces for blockage ratios of 0.11 to 0.21, and rib spacing to rib height ratios of 3.41 to for Reynolds number range of 4,000 to 23,000. The test section was uniformly heated using electrically heated nichrome wire around the triangular duct and temperatures and pressures were taken using thermocouples and pressure taps along the axial length of the test section. Luo et al concluded that blockage ratio of 0.18 provided the 11

12 maximum forced convection and pressure drop increased with blockage ratio. In addition, a rib to rib spacing of 7.22 provided the best thermal performance. Taslim and Bethka [8] looked at impingement on the leading edge of an airfoil with axial cross flow. The experiment measured the heat transfer impact for a range of axial to jet mass flow rates of 1.4 to 6.4 and jet Reynolds Numbers from 8,000 to 48,000. Two types of inlet flows were tested; one in the same direction as the crossflow and one in the opposite direction of the crossflow. Using copper plates and thermocouples to measure the local temperature, Taslim et Bethka concluded that (1) For both inlet flow configurations, the sidewall showed a higher heat transfer coefficient than the leading edge nose. (2) The heat transfer coefficient for impinging jets with crossflow is less than that of impinging jets without crossflow. Bunker and Metzger [9] also performed some studies looking at local heat transfer at airfoil leading edge with impingement cooling without film cooling extraction. Thin temperature coating was sprayed at the leading edge and variations in jet Reynolds Number, airfoil leading edge sharpness, jet pitch-to-diameter ratios, and jet nozzle to-apex travel distances were tested. 4 different types of airfoils were used with radius of curvature of 0 (sharp edge), 0.2, 0.4, and 1.0. Pitch-to-jet diameter ratios of 4.67, 3.33, and 0 were tested. Jet nozzle-to-airfoil apex distance to width of slot jet ratios of 18, 24, 30, 36, and 42 were also tested. Experimental results showed that (1) as the pitch to jet nozzle diameter ratio decreases, the leading edge heat transfer increased, but severely degrades at pitch to jet nozzle diameter ratio of 0. (2) Heat transfer at the leading edge apex is increased as the nose radius is increased from 0 to 1. Bunker and Metzger [10] as a follow-up experiment looked at the local heat transfer at airfoil leading edge with impingement cooling and film cooling extraction. Similar, to the setup described in the experiment without film cooling extraction, the only difference was that two rows of bleed holes were added at +/-45 from the apex centerline for film cooling extraction. ases were the bleed holes were directly in-line and out of phase with the impingement jet hole were assessed to determine any differences in heat transfer performance. Bunker et Metzger concluded that the level of heat transfer was mainly affected by the impinging jets and secondarily by the amount of bleed air. When the bleed holes were in-line with the jet holes, the local heat transfer coefficient increased by as much as 50%. When the bleed holes were 180 out of phase with the impingement jets, the local heat transfer coefficient decreased. Thus, observations showed that alignment of the bleed holes relative to the jet holes played an important factor in the local heat transfer coefficient. Different shaped turbulators and bumps have also been investigated to see what shape turbulator or bump will provide the optimal thermal performance. Taslim et al [11] investigated into convective heat transfer coefficient of impingement for 4 different typed surfaces on the leading edge of a channel. The four different types of surfaces included smooth wall, finely roughened wall, conical surface bumps, and longitudinal ribs. One sided and two sided inflow, and two sided outflow, crossflow, and one sided outflow were considered. Thermocouples were embedded into brass test plates that simulated the backwalls and the nose to measure the surface temperatures. onclusions showed that (1) crossflow had a strong impact on the heat transfer coefficient and reduced the heat transfer at the leading edge. 12

13 (2) The conical shaped bumps proved to be most beneficial out of all the types of surfaces and improved the heat transfer by 40 percent. Moreover, Taslim et al [12] also looked at the heat transfer of 45 angled, V-shaped, and discrete ribs using the liquid crystal methodology to determine surface temperatures. The conclusions of this study entailed the following: (1) 45 and discrete ribs of lowest blockage had the best thermal performance, while the 90 angled ribs performed the worst. (2) Low blockage ratio V-shaped ribs facing downstream produced the highest heat transfer enhancement and friction factors. For all other blockage ratios, the 45 ribs showed the highest heat transfer enhancements with friction factors less than those of the V- shaped ribs. Besides looking at heat transfer for a ribbed surface, there have been also a lot of studies on other types of cooling configurations. One such configuration is looking at heat transfer in a leading edge channel with crossflow with jet impingment. A study was done by Andrei et al [13] to look at heat transfer of a trapezoidal channel with racetrack holes and film cooling extraction. Using the thermochromic liquid crystal method, Andrei et al determined the Nusselt Number for jet Re range of 10k to 40k along the span of the leading edge. They concluded that the heat transfer coefficient peaks towards the tip of the blade, where the ratio of jet to crossflow velocity is highest, and that Reynolds number plays a critical factor in the heat transfer coefficient. Building upon the works of those aforementioned, this paper will look at 45 staggered rounded corner wall turbulators and 90 staggered rounded corner nose turbulators for 4 triangular shaped leading edge test sections at 3 different blockage ratios. This experiment will only be concerned with measuring and calculating the heat transfer and friction factor at the middle of the test section. Since, each test section is slightly different from each other, the blockage ratios will be dependent on the hydraulic diameter of the test section and will change with each test section, except rigs 3A and 3B. Rigs 3A and 3B are essentially the same test section, but the measured backwall surface for rig 3A is opposite that of rig 3B. This study will make observations on how the different test section and turbulator geometries impact the heat transfer coefficient, friction factor of the channel, the enhancement factors at the backwall and nose surfaces between the turbulators, and the overall thermal performance of each test section. Theory In this study, the four major parameters of interest are the Nusselt Number, friction factor, enhancement factor, and the thermal performance. The Nusselt Number, enhancement factor, and thermal performance can be determined by first defining the thermal resistance network within the given system. In terms of the friction factor, there are two types of friction factors of concern. The first being the Darcy Friction Factor and the second one being the smooth wall friction factor, which can be expressed by the Dittus-Boelter correlation. This section will briefly explain the details and the main equations used to determine the Nusselt Number, friction factor, enhancement factor, and the thermal performance. 13

14 Before performing the heat transfer calculations, it is necessary to determine the characteristics of the flow and the heat input into the system. This includes the mass flow rate, the inlet temperature and pressure, the ambient temperature and pressure, and the upstream venturi temperature and pressure. The mass flow rate can be determined by equation 1.1 for critical venturi. : ; DEF (1.1) Once the mass flow rate is known, the Reynolds Number can also be determined by equation 1.2 below. 1I = where μ = viscosity of air and P = Test Section Perimeter (1.2) K The inlet temperature is the average of the measured inlet temperature readings from the two thermocouples placed at the inlet to the test section in the plenum as denoted by equation 1.3 below 7!* = H LBM H LB 4 (1.3) In addition to the flow characteristics, the heat transfer rate generated by the heaters also needs to be known to determine the heat transfer coefficient. To determine the heat transfer rate at the middle of the test section, the measured voltage and amperage need to be known. The heat transfer rate at the middle of the test section can be expressed by equation 1.4.,-!// = 3.413P T (1.4) Now, since the input flow characteristics are known and the amount of heat input is calculated, the next steps are to determine the heat losses due to the radiation, conduction, and convection. To determine amount of heat loss to the environment, a thermal resistance network needs to be constructed. Figure 2 shows the thermal resistance network for rig 1. Note this thermal resistance system can be modified and applied to any of the four different test sections. For simplicity, test section 1 is chosen here to show the thermal resistance network due to its symmetrical nature. Figure 2 below shows the thermal resistance network of the given system. 14

15 Figure 2: Thermal Resistance Network (Rig 1) The thermal resistance network consists of the three different modes of heat transfer: conduction, convection, and radiation. onduction occurs in the layers between the leading edge cavity and outside ambient air. onvection occurs only on the ambient surfaces of the test section walls. Radiation occurs within the leading edge cavity. To determine the rate at which heat is leaving the heater due to conduction, a thermal balance needs to be performed per figure 2. This results in equation 1.5 and 1.6,-. =,-* = PH AD?AUH VDEF T W FDXY (1.5),-* = ZH AD?AUH V[\U]^ W ]U_B? (1.6) Furthermore, the equations below indicate which elements compose the conductive resistance network. 1 ` = 1 +!a = 1 b! + 1 *+ (1.7) 1 * =0.51!* Q 1 /!+3 Q1.` * Q1 /!+4 Q1. Q1!8(!/ (1.8) 15

16 1. = 0.51!* + 1 /! ` * + 1 /!+5 + 1!c + 1 *+ (1.9) The convective resistance of air can be calculated at room temperature by equation 1.10 below 1 *+ = 3 d, where h =.5e. f (Osisik, 443) (1.10) Where, k= Thermal conductivity of air at ambient temperature and $ = Length of heater The radiative resistance network is constructed under the assumption of a 4 sided enclosure. It is important to note that for the nose, the wall projected from the actual nose surface is assumed to absorb all the radiation emitted from the actual nose surface. This projected nose surface is represented by a dashed line in Figure 2. This assumption helps to simplify the geometry of the test section for the radiative heat transfer calculations. To calculate the radiation view factors in rig 1, we take advantage of the symmetrical nature of the test section, and also use the view factor correlation for two perpendicular rectangles with a common edge. This simplifies the problem and only view factors, F1-2 and F2-1 need to be calculated. The remaining view factors can be determined by assuming symmetry. Once the fractions of radiation leaving the surface i is determined, equation 1.11 is used to determine the radiative heat flux leaving surface i and radiated away to surfaces j,0/,!g = hi l Lj L H k\u],l l i m j m H k\u],m n 3i L (1.11) Then, an iterative scheme is used to guess the heat transfer coefficient and the temperatures at the top, view wall, and the projected nose surface. This iterative scheme is run 30 times or until thermal equilibrium is reached at both the top and front view walls (net heat transfer rate <.001). Using this iterative scheme, the total heat loss from each surface can be determined. Knowing the amount of heat loss, one can calculate the rate at which heat is lost at through each of the four surfaces (top, bottom, front, and back). In addition, the mean temperature at the middle of the test section can also be calculated by reducing the 1 st Law of Thermodynamics to equation 1.12 below P,-!*,-T = : + `P7 * 7 ( T (1.12) Where 7 ( = 7!8(!/,-* 1 Utilizing the mean temperature and the knowing the total heat loss, one can determine the heat transfer coefficient at the wall using equation 1.13 h = 80 LB80p_[[A[ H [\U] H EADB (1.13) Then, the Nusselt Number at the roughened wall can be calculated using equation %& = PTP T. DLU,DEF (1.14) 16

17 To calculate the smooth wall Nusselt Number, the Dittus-Boelter correlation is used as expressed by equation %& = I.q )r.6 (1.15) Once the roughened and smooth wall Nusselt Numbers are known, the enhancement factor (EF) also can be calculated using equation st = u( u( k (1.16) To determine the thermal performance of a particular test configuration, it is necessary to know the friction factor besides the enhancement factor. The Darcy and smooth wall friction factors can be determined by equations 1.17 and Equation 1.18 is called the Blasius orrelation. = 4v = wh *?\UF nh LBpA? DEF.=x; E ny (1.17) =.53e W d.z (1.18) Where v = Fanning oefficient of Friction and = Proportionality onstant in Newton s 2 nd Law h32.2 n. Lastly, the thermal performance (TP) of the system can be determined using equations 1.16, 1.17, and 1.18 and can be expressed by equation ) = { w ] } ~DUX ]} ke? y M/ (1.19) The calculations and general equations in this section can be applied for the other test sections as well. The only differences are in the input flow characteristics and the test section geometry, which are unique to each test configuration. Test Environment Test Section The experimental setup consisted of multiple parts. Figure 3 below shows the individual parts that comprise together to make up the entire test section. 17

18 Figure 3: Test Section Experimental Setup The flow enters the plenum from the venturi network through a 1 ¼ pipe. Once in the plenum, the flow goes through a flow straightener, which makes the flow uniform prior to entering the actual test section. The test section is insulated all around with the exception of the front and top viewing windows, which are transparent to capture images of the liquid crystal surfaces on the heated backwall and nose. The flow then finally exits out of the test section into atmospheric conditions. Supports are used to hold up the test section relieving the bending stress created by hanging it off of the plenum forward face. There are also two cameras set up to take pictures of the liquid crystal color at the backwall and nose section. The cameras are focused near the center of the test section at one particular section between two consecutive backwall turbulators. Rig 1 The cross sectional area of test section 1 is shown below in Figure 4. 18

19 Figure 4: ross-section of Test Section 1 Test section 1 is composed of two see-through plexi-glass wall and a fiberglass wall. One of the plexiglass walls is positioned directly facing the backwall with the liquid crystal and the other one is positioned at the top wall directly over the nose. They are see-through, so pictures of the liquid crystal can be taken with a camera normal to the surface of the nose and sidewall. The sidewall and nose sections, where the liquid crystal, are located are made of fiberglass. On the backside of the fiberglass, polyurethane foam is sprayed to provide insulation and prevent heat loss to the environment from the backside. Figure 5 below shows, in general, the different layers that compose the fiberglass backwall and nose sections. Figure 5: Layers of Material on Fiberglass Wall On the front side of the fiberglass wall sits the heaters. They span across the length of the test section. On top of the heaters is the layer of liquid crystal. It also spans across the entire length of the channel. It is important to keep the temperature of the heater below the melting temperature of the liquid crystal, otherwise, the liquid crystal will be damaged. Thus, whenever the heaters are on, cooling air should always be flowing through the channel. 19

20 Rig 2 Figure 6 below shows the general composition of test section 2. Unlike test section 1, test section 2 is slightly asymmetric, however, the composition of test section 2 is same as test section 1. Figure 6: ross Section of Test Section 2 Rig 3A Figure 7 below shows the composition of test section 3A. Only notable difference between test sections 1,2, and 3A is the cross sectional area. Figure 7: ross Section of Test Section 3A 20

21 Rig 3B Figure 8 below shows the composition of test section 3B. In terms of geometry, test sections 3A and 3B are exactly the same. Test Section 3B is different from 3A in that 3B examines the heat transfer in what is 3A s plexiglass sidewall and fiberglass nose. Figure 8: ross Section of Test Section 3B Turbulator Geometry The wall turbulator geometry for all four test sections are staggered one after the other on opposing walls with an angle of attack of 45 and pointing away from inflow as shown in Figure 9 below. The nose turbulators, however, are staggered and 90 to the flow. 21

22 Figure 9: Staggered 45 Turbulator Arrangement on Sidewalls This study investigated into four different test sections. In this paper, they are designated as rigs 1,2, 3A, and 3B. All the rigs had different cross sectional areas, except for 3A and 3B, which had the same cross sectional areas and were basically mirror images of each other. Table 1 below outlines the test points and turbulator geometry for rig 1. Test Re Rib Angle ( ) S/e e/dh

23 Table 1: Test Points and Turbulator Specifications for Rig 1 Likewise, Table 2 below outlines the test points and turbulator geometry for rig 2. Test Re Rib Angle ( ) S/e e/dh Table 2: Test Points and Turbulator Specifications for Rig 2 23

24 Lastly, Table 3 outlines the test points and turbulator geometries for rig 3A and 3B. Test Re Rib Angle ( ) S/e e/dh Table 3: Test Points and Turbulator Specifications for Rig 3A and 3B For all the test sections, it can be seen from tables 1, 2, and 3 that the non-variable elements of the experiments are the Reynolds Number and the rib angle. The variable elements between each test section are the pitch or turbulator spacing, rib height, and the cross sectional areas of the test sections themselves. By carefully observing and comparing the turbulator specifications in tables 1, 2, and 3, it can be deduced that rig 1 will have the highest blockage ratio (e/dh) and pitch to rib height ratio (S/e) out of all the test sections. Rig 2 has the next highest blockage ratio and pitch to rib height ratios and Rigs 3A and 3B have the lowest. Higher blockage ratios usually result in higher heat transfer coefficients, however, from previous studies by Taslim and Lengkong (1999), it can be shown that too high of a blockage ratio can also lead to a decrease in thermal performance due to higher pressure drop. Heater Arrangement For each of the 4 test rigs, the heater sizes are chosen based on the sidewall and nose geometries. Figure 10 below depicts the heater arrangement and sizes for test rig 1: 24

25 Figure 10: Heater Arrangement for Test Rig 1 For test rig 1, the test section is broken up into 3 equal parts, an inlet, middle, and exit section. A separate heater is used for each section, and each heater is large enough in width to cover both the sidewall and nose segments. The use of a single heater for each section is recommended to facilitate in the amount of heat flux applied to both the sidewalls and nose segments. If 2 separate heaters were used, the amount of voltage applied to each heater would need to be adjusted to account for the different heater areas. Figure 11 below depicts the heater arrangement for test rig 2: Figure 11: Heater Arrangement for Test Rig 2 The heater arrangement for test rig 2 is different than test rig 1. The most apparent difference is in the number of heaters used. Unlike test rig 1, test rig 2 has a separate heater for the wall and the nose. The main reason for using 2 separate heaters is that the heaters only come in certain standard sizes, which would not be large enough to cover both the wall and nose segments alone. Thus, to facilitate the application of a constant heat flux across the wall and nose heaters, respectively, three 3 x11 size heaters were chosen for the wall sections and three 2 x11 heaters were chosen for the nose sections. It is important to note that since the wall and nose heaters are of different areas, the power applied to the nose heaters must be a certain amount less than that of the wall heaters in order to output the same heat flux as the wall heaters. 25

26 Figure 12 below depicts the heater arrangement for test rig 3A: Figure 12: Heater Arrangement for Test Rig 3A For test rig 3A, the heater arrangement is similar to rig 2. Separate heaters are used for each of the wall and nose sections. They are of equal areas in order to facilitate the application of constant heat across all the wall and nose sections. Figure 13 below depicts the heater arrangement for test rig 3B: Figure 13: Heater Arrangement for Test Rig 3B The heater arrangement for test rig 3B is similar to rigs 2 and 3A. Some of the notable difference is in the outlet wall and nose sections of the test section. In the outlet section, there is no nose heater. The reason for no nose heater in the outlet section is that at the time of the experiment, a 2 x11 heater was not available. In the absence of a 2 x11 heater, a 3 x11 heater was used to replace it. Source Pressure Network The source pressure is generated by a compressor in the mechanical room outside the laboratory. It is then fed through an air tank which acts as a temporary air storage unit for excess air as it is discharged and routed to the laboratory for usage. Once the air reaches the laboratory, it enters through a regulator valve, which controls the amount of air entering the downstream pipe. In the lab, there is a parallel network of pipes, but only one circuit is used at a time to feed the air downstream towards the test rig as depicted in Figure 14 below: 26

27 Figure 14: Parallel Network of Pressure Pipes in Laboratory Before the air enters the test rig, it is further regulated by a nozzle venturi of a specific diameter. For this experiment, the two venturi nozzle diameters used were Ø.225 and Ø.320. These specific diameter venturis were used mainly because they covered the range of Reynolds Number in concern for this experiment. There are also drain valves at the bottom right and left of the pressure network as depicted in Figure 14 to facilitate the draining of any additional moisture and condensation. In addition, there is also a cold water cooling system in place to help cool the passing air during hot and humid days. It is recommended the air temperature in the system remain relatively cool to the ambient temperature in the room, because the temperature affects the pressure measured in the system, which in turns impacts the friction factor calculations. The Plenum Figure 15 below shows the general setup of the plenum. Figure 15: Plenum Structure 27

28 The plenum is the section of the test rig in between the pressure source and the actual test section. The plenum is a six-sided enclosure composed of 6 plexi-glass see-thru walls. It is tightened down by bolts at all interfaces and is sealed up using silicon. The air is supplied to the plenum equally from the left and right sidewalls of the plenum as shown in Figure 3 by PV tubes. Once in the plenum, the air is then straightened and filtered through a honeycomb diffuser or straightener. After the air has been filtered and straightened, it then enters the inlet of the test section. Power Source A multi-channel power source was used to provide current to the foil heaters within the test sections. Each heater was connected to a separate channel and two voltmeters were used to measure the voltage and current through each channel. There were two different types of dials on the power source. One was the master dial, which controlled all the channels. The second was the fine tuning dial, which varied the voltage at much finer resolution, and only controlled a particular channel. In cases, where the flux needed to be controlled individually for each heater, the fine tuning dial was used. Figure 16 below shows a picture of the multi-channel power source that was used for this experiment. Figure 16: Multi-hannel Power Source Test Procedure Liquid rystal alibration A liquid crystal calibration was performed to determine the reference temperature and color prior to the start of any testing on any test section. The liquid crystal calibration is important, because the reference temperature of the liquid crystal will be used to determine the surface temperature. Figure 17 below shows a still-image of liquid crystal calibration video. In the image, one can see that the calibration is performed in a hot-water bath, and using a thermocouple probe, the temperature is measured as the bath is cooled naturally by ambient air and induced stirring. The calibration is done until the liquid crystal has turned from black to dark blue (very hot) and to black again (cool). During the entire calibration, it is important to record the reference temperature at the reference color, which in this case is green. Note there are different shades of green, so the color green is subjective to the 28

29 experimenter, but it is essential that the experimenter be consistent in determining the color green throughout the image processing step for each test section. Figure 17: Liquid rystal alibration old and Heat Transfer Tests Two different types of tests were performed for this experiment, heat transfer and cold tests. The cold tests were done to determine the friction factor at ambient conditions without any effect from heated wall conditions. Heat transfer tests were done to determine the heat transfer coefficient, enhancement factors, and also the friction factor at heated wall condition. old Test Procedure For the cold test, venturi pressure, plenum pressure and temperature, and inlet and exit pressures of the test sections were measured. The venturi pressures that were decided on encompassed the range of Reynolds Numbers from the heat transfer tests, and data was taken at increments of 5 psi. In some cases, two different venturis (Ø and Ø 0.32 ) needed to be used to cover the range of Reynolds Numbers of interest. Below outlines the steps in performing the cold test to determine the cold friction factor at ambient conditions: 1. Turn on the air compressor and wait 2 minutes for the air in the channel to come to equilibrium 2. Set the first test venturi pressure 3. Record the ambient temperature and pressure, venturi pressure and temperature, plenum temperature, and inlet and exit pressures of the test section. 4. Go to next higher venturi pressure. 5. Repeat steps 3 and 4 until all Reynolds Numbers have been tested. Switch out venturi diameters if necessary. 29

30 Heat Transfer Test Procedure For the heat transfer tests, a range of Reynolds Numbers (Re~6000, 10000, 15000, 20000, 30000, 40000) were covered. Venturi pressures were determined based on the Reynolds Numbers of concern and the geometry of the test section. Below outlines the steps in performing the heat transfer tests to determine the heat transfer coefficient: 1. Turn on the air compressor and set the first test venturi pressure. 2. Turn on the multi-channel power source to turn on the heaters. 3. Wait 5-10 min for thermal equilibrium to be reached within the test section 4. Set the minimum voltage to each heater until a hint of color is seen on liquid crystal at the midstream wall and nose sections. Note the wall and nose sections liquid crystal may not start to show color at the same time. If color is seen at either the backwall or nose section, set that as the minimum voltage. 5. Run the voltage up to the maximum voltage until the nose and backwall liquid crystals are all blue colored. Wait 1-2 min for the liquid crystal color to stabilize. Record this as your maximum voltage. 6. Go back to the minimum voltage and wait for 5 minutes until thermal equilibrium is reached. 7. Record voltage and amperage for each heater, ambient temperature and pressure, venturi pressure, plenum temperature and pressure, and inlet and exit pressure of the test section 8. Take a picture using a digital camera of the liquid crystal of the backwall and nose surfaces. 9. Increment the voltage to each heater using following rule of thumb: a. Voltage increment = (max voltage min voltage)/20 i. The voltage increment can be adjusted depending on how quickly the liquid crystal seems to heat up 10. Repeat steps 7-9 until the liquid crystal on both the backwall and nose sections are all blue colored. 11. Repeat steps 1-10 for all other venturi test pressures. Data Post-Processing Procedure Image Processing Following the data collection, the next step is to process the data. One of the data processing steps is to digitize the images collected during the test. Previously, it was noted that to determine the reference temperature of the liquid crystal, a liquid crystal calibration needs to be done. This calibration determines the reference temperature and color of the liquid crystal, which will be used for digitizing the pictures. In this experiment, the color green is chosen as the reference color. Using an image digitizing software tool called Sigma Scan, the image is processed to calculate the number of pixels that 30

31 the reference color green takes up in the area of the red box defined in Figure 18 below. The red box defines one repeated segment of the entire test section or equivalent to the pitch from the center of one turbulator to the next. The number of pixels is used to determine the weighted-average Nusselt Number and heat transfer coefficient. This image digitization is repeated for the nose as well as shown in the second picture in Figure 18. Figure 18: Example of image taken by camera of the backwall and nose surfaces used for image processing 31

32 FORTRAN ode: Determining Average Nusselt Number, Friction Factor, and Enhancement Factor Three FORTRAN codes were used in the data processing. One was called the heck.f file, which read the data input file and searched for any typos or errors. The second code was called the Reduce.f file. The Reduce.f file processed the input file and calculated the heat transfer coefficient, Nusselt Number, Enhancement Factors, and the friction factor at heated wall condition. The last code used was called Reduce-Friction.F, which determined the cold friction factor at ambient conditions. Once all the results were processed, the output was inputted into Microsoft Excel, which calculated a weightedaverage Nusselt Number, Friction Factor, and Enhancement Factor using the number of pixels determined from the image processing. Results and Discussion The following results will be presented for rigs 1, 2, 3A, and 3B. Nusselt Number Vs. Reynolds Number (sidewall and nose sections) Midstream location Enhancement Factor Vs. Reynolds Number (sidewall and nose sections) Midstream location Friction Factor Vs. Reynolds Number Test Rig 1 For test rig 1, there were 3 heaters; one for the inlet, the midsection, and the exit. Each heater spanned across the wall and nose sections. The results that follow for all test sections are representative of the midstream section backwall and nose sections. Figure 19 below shows a plot of Nusselt Number Vs. Reynolds Number for the backwall for all three blockage ratios. The three blockage ratios are 0.114, 0.142, and

33 Rig 1 Nusselt Number Vs. Re (Backwall) Nu e/dh = e/dh = e/dh = Re Figure 19: Rig 1 Nusselt Number Vs. Reynolds Number (Backwall) Figure 19 shows that the Nusselt Number trends upwards with blockage ratio. There is some slight variation in the data as indicated at the higher Reynolds Number cases, where the medium blockage data point is nearly the same as the maximum blockage data point. The two Reynolds Numbers, where this occurrence is seen is at Re ~20,000 and 30,000. Overall the data shows that as the height and width of the turbulator increases, so does the Nusselt Number, which is as expected. The taller and wider the turbulator, flow turbulence increases and thus, improving mixing and cooling due to convection at the backwall. Figure 20 below shows the Nusselt Number vs. Re plot at the nose for the 3 different blockages. 33