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Effect of Dimple Depth on Heat Transfer Enhancement in a Rectangular Channel (AR = 3:1) with Hemispherical Dimples

Lance C. Case1, C. Neil Jordan2, and Lesley M. Wright3 Baylor University, Waco, TX, 76798-7356

Over the past decade, the use of dimples has shown promise as an alternative to the traditional ribs for internal heat transfer enhancement of gas turbine blades and vanes. Studies have shown that dimpled channels provide reduced heat transfer enhancement compared to ribbed channels; however, dimpled channels are advantageous due to the reduced pressure drop incurred through the channel. The current experimental investigation uses both detailed and regionally averaged heat transfer coefficient distributions to compare traditional hemispherical dimple configurations. One wide wall of a rectangular channel (AR = 3:1) is lined with hemispherical dimples. While the effect of dimple depth is primarily considered (δ / D = 0.15 – 0.30), the changing depth also indirectly varies the dimple spacing. In addition to the variation in dimple configurations, Reynolds numbers ranging from 10,000 – 40,000 are investigated. Detailed heat transfer coefficient distributions are obtained on the dimpled surface using a transient temperature sensitive paint (TSP) technique. This technique is validated by comparing heat transfer coefficients obtained in a similar channel using traditional copper plate and thermocouple measurements. Measurements indicate the average heat transfer coefficients, for both dimple depths, are relatively insensitive to coolant Reynolds number. Decreasing the depth of the dimple yields less variation in the heat transfer coefficients across the diameter of the dimple; in other words, with reduced dimple depth the difference between the minimum and maximum heat transfer coefficients is reduced.

Nomenclature A = area AR = aspect ratio D = dimple diameter Dh = hydraulic diameter f = friction factor h = heat transfer coefficient I = emission intensity k = thermal conductivity L = channel length �� = mass flow rate Nu = Nusselt number ∆P = pressure drop Pr = Prandtl number Qnet = net rate of heat transfer Re = Reynolds number S = dimple pitch T = temperature

t = time v = velocity w = width of channel x = streamwise location y = location into semi-infinite solid z = spanwise location α = thermal diffusivity δ = dimple depth η = thermal performance τ = time step change Subscripts 0 = smooth b = bulk or black i = initial ref = reference w = wall

1 Undergraduate Research Assistant, Department of Mechanical Engineering, AIAA Student Member. 2 Undergraduate Research Assistant, Department of Mechanical Engineering, AIAA Student Member. 3 Professor, Department of Mechanical Engineering, Lesley_Wright@Baylor.edu, AIAA Member

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-825

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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I. Introduction

Gas turbines, used for power generation and propulsion, are vital to the world’s industrialized society. As the worldwide demand for power increases, it is imperative that the gas turbines operate as efficiently as possible. In advanced gas turbines, the turbine inlet temperature can be as high as 3500°F; such extreme temperatures exceed the melting point of the turbine’s components, specifically its vanes and blades. Heat must be removed from these turbine components so they can withstand such high operating temperatures. This is accomplished in part by passing relatively cool air through internal cooling passages as shown in Fig. 1. This coolant air convects heat away from the blade material and is then ejected out of the cooling passages into the mainstream in the form of film cooling gas. Much research has been conducted to improve the efficiency of internal cooling in gas turbine blades. Han et al.1 gave an extensive overview of cooling techniques and experimental observation methods. This work covers several techniques for experimentally investigating and constructing both internal and external cooling technology. Several types of internal passage surface geometries have been experimentally considered, including the largely-accepted rib turbulators (ribs), as well as the more recent surface geometry of concavities (dimples). Extensive research has been done to improve the effectiveness of both geometries. Initial studies of internal surface geometries have mostly been focused on ribs, which have been shown to provide relatively high heat transfer; however, they incur a high pressure loss through the turbine blade. Wright and Gohardani2 and Chandra et al.3 studied heat transfer enhancement through adjusting the spacing, number of rib turbulators, and height of rib; however, as heat transfer increases with optimized size and spacing of the ribs, the pressure losses associated with the larger ribs also increases. Much recent research has been conducted to find a comparably-effective dimpled surface geometry. Dimples have been proven to incur a lower pressure penalty compared to ribs. Moon et al.4 investigated the effect of channel height on the heat transfer coefficient and friction factor in a channel with one dimpled wall. Using a thermochromic liquid crystal technique, and measuring over relative channel heights – the ratios of channel height to dimple print diameter – ranging from 0.37 to 1.49 and Reynolds numbers from 12,000 to 60,000, the authors found that the heat transfer coefficient was invariant with both Reynolds number and relative channel height. The authors also found that the friction factor only increased to at most two times the corresponding smooth channel's value. They concluded that "the heat transfer enhancement with [dimples] can be achieved with a relatively low-pressure penalty." Mahmood et al.5 used flow visualizations and infrared thermography techniques on a dimpled surface in a channel to observe how vortex structures augment local Nusselt numbers in and around each dimple. The authors describe how the vortical fluid acts to advect mainstream fluid to regions near the dimpled surface and how downstream heat transfer enhancement is caused by this effect. As the air passes over the dimple, the flow detaches and causes low heat transfer, while on the trailing edge of the dimple, the flow reattaches and causes high heat transfer. As vortices travel out of the dimple, they cause a lot of mixing which increases heat transfer downstream of the dimple. As Griffith et al.6 describe, dimpled surface geometries act to trip the boundary layer of the coolant flow and allows for reattachment and regions of high heat transfer to occur. Near the upstream part of the dimple, separation and recirculation occur. At the downstream part of the dimple, the flow reattaches and acts as a small impingement jet, causing an area of high heat transfer. As the flow leaves the dimple, a significant upwash region is created that, as described above, advects cooler air to the surface, causing another area of high heat transfer to occur downstream and diagonal from the dimple. Griffith et al.6 also observed dimpled channel behavior similar to a 45-degree angled rib channel with less spanwise heat transfer variations by using a rectangular channel (AR = 4:1) and a dimple depth-to-diameter ratio of 0.3. Varying dimple depth and diameter is an effective method in altering the overall heat transfer enhancement. Burgess and Ligrani7 observe that increasing the ratio of dimple depth to dimple print diameter increases Nusselt number augmentation at Reynolds numbers ranging from 9,940 to 74,800. There are several experimental measurement techniques which have been employed in previous studies. A traditional measurement technique is the copper plate and thermocouple technique. This technique, used by Griffith et al.6 and Wright and Gohardani8, as well as others, uses copper plates of a uniform geometry and attached thermocouples to obtain regionally-averaged heat transfer coefficients by measuring the temperatures at each copper plate location as well as air inlet and exit conditions, and adjusting the voltage supplied to heating elements placed

Figure 1. Multi- pass Turbine Blade Internal Cooling Passages. Han et al.1

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directly beneath each region of copper plates. Although the more traditional experimental method of using a channel with copper plates and thermocouples has been used extensively, another approach that has recently gained some popularity is temperature sensitive paint (TSP). Wright et al.9 give an assessment of several measurement techniques, including this TSP method. The present study focuses on varying dimple depth (δ / D) over Reynolds numbers between 10,000 and 40,000. The study will employ the two separate measurement techniques described above, regionally-averaged copper plate measurements and TSP, to individually measure the same flow scenario.

II. Experimental Facilities As mentioned previously, this study involves two methods to obtain heat transfer coefficients. For each test, air

is supplied from a compressor, through a 1 in. ASME orifice plate, then through a pipe heater, where, for the TSP technique, the air is heated to a constant temperature (the heater is not used for the copper plate technique). The power input to the heater is regulated with a variable transformer. The air then runs through a three-way valve where it is either vented to the surroundings or it is diverted to the test channel. The inlet of the test channel is connected to the outlet of the three-way valve via 1 in. inner diameter rubber tubing, which splits into two smaller diameter tubes prior to entering the test section. All tubing between the outlet of the heater and inlet of the test channel is wrapped in black neoprene foam insulation to minimize heat losses. Preceding the test section is a 2.699 cm by 7.779 cm by 45.72 cm long smooth, unheated entrance to provide hydrodynamically fully developed flow at the entrance of the test section. Each method has a separate test section that can be attached to the hydrodynamic entry section. Each test section is equivalent in length, aspect ratio, and dimple geometry, as shown in Fig. 2.

For the copper plate method, the rectangular channel used for the current study has been modified from the work of Wright and Gohardani2. The test section is a 2.699 cm by 7.779 cm by 45.72 cm long one-pass rectangular channel of aspect ratio 3:1 with a hydraulic diameter of 4.007 cm. Square copper plates of sides measuring 2.381 cm are machined according to the required surface geometries described below. Figure 3 describes the manner in which the copper plates are installed in the test section. Although two walls – the bottom, wide wall and one narrow wall - of the test section are made of copper plates and have heaters installed beneath the copper plates, only the bottom, wide wall of the test section is dimpled and heated during the tests. This wide wall is divided into three distinct regions, inner, middle and outer, to provide a more resolved spanwise heat transfer distribution. Fifteen copper plates aligned in the flow direction are used to collect temperature data for each region, for a total of 45 separate copper plate readings. T-type thermocouples are inserted with a thermal epoxy to a small hole on the bottom side of each copper plate to provide these readings. A silicone-based caulk is used to insulate the gap between each copper plate and is carved out with the same dimple pattern to provide a

Figure 2. Overview of Experimental Facilities

Figure 3. Cross-Sectional View of Copper Plate Test Section

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surface geometry condition similar to that of a single dimpled section of copper. Due to the high thermal conductivity of copper, and the relatively small volume of a single copper plate, each

piece of copper is at a constant temperature. A fluid inlet temperature, as well as three exit temperatures corresponding to each spanwise region and two separate room temperatures, are measured using additional thermocouples. Each thermocouple reading is measured with National Instruments’ LabVIEW software. Each spanwise region of copper plates has a resistance heater embedded beneath the copper plates to provide the heat source. These heaters are attached to 3 separate variable-voltage transformers that allows each heater to be adjusted. Voltages applied to the heaters are measured using a Fluke 8808A 5-1/2 digit multimeter. During the test for each flow scenario, the voltages are varied in order to reach a steady-state copper plate temperature of about 150°F. These voltages are recorded, in addition to heater resistance and current, along with the thermocouple temperatures.

For the TSP method, the test section (same length and cross-section as the copper plate method), is made of plexiglas; Figure 4a is a 2-D layout of the dimpled surface for TSP measurements. For the bulk air temperature, two T-type thermocouples are are placed in the center of the channel – prior to and after the viewing window of the CCD camera. Reference wall temperatures are taken using three T-type thermocouples. The thermocouple readings are measured with National Intstruments’ LabVIEW software.

Two arrays of different dimple depths are considered for this study: δ/D = 0.3 and δ/D = 0.15. Each array consists of 89 rows of staggered dimples employed in the streamwise direction, with 6 or 7 dimples in each row. Each row is offset by S = 0.508 cm in both the streamwise and spanwise directions. The pitch of the dimpled pattern is conserved between the two different dimple depth scenarios. Figure 4 presents geometric details of the dimple configurations. The dimples were machined onto each test section with a 0.635 cm ball mill.

III. Data Reduction

A. Regional Heat Transfer Enhancement with Copper Plates

This study observes both the regionally-averaged and the transient TSP heat transfer coefficients. For a steady state heat transfer experiment, the heat transfer coefficient is given as follows:

� � ���� ⁄��,� � ��,� (1)

Net heat transfer for the copper plates is calculated using the voltages and currents supplied by the variable-voltage transformers, and measured at each heater region by the multimeter. The supplied power is then divided among the 15 copper plates for a given heater, and the external heat losses are subtracted from this power supplied. A heat loss calibration is performed for each surface geometry by insulating the test section to prevent natural

Figure 4. Experimental Surface Geometry a) Schematic Diagram of Dimpled Test Surface b) Dimple Depth Geometry c) Dimple Geometry Details (δ/D = 0.30) d) Dimple Geometry Details (δ/D = 0.15)

a)

b) c) d)

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convection and measuring the power required from the transformers for a measured regional surface temperature. From conservation of energy, the heat lost to the environment is able to be calculated.

The geometric surface areas considered are the projected smooth areas of the channel. Regionally averaged wall temperatures are directly measured using the thermocouples epoxied into the copper plates, as stated above making the assumption that the temperature of the entire copper plate is constant due to the high thermal conductivity of copper. The bulk temperatures were calculated by measuring one inlet and three exit temperatures and linearly interpolating for each flow location x/Dh. This calculation was checked against the conservation of energy principle and thus the energy balance equation:

��,� = ��,� + ∑���������

�� ��� , � = 1,2, … ,15 (2)

The linear interpolation method is thus validated after comparisons yielded small differences in the results of each calculation method, and it is the linear interpolation method used in the remainder of this study. As a common reference for each analysis, the Nusselt numbers calculated are compared against a fully developed, turbulent flow in a smooth tube as given by the Dittus-Boelter correlation for heating10 at the same Reynolds number:

#$

#$%=

ℎ&'

()�*

1

�0.023 /0%.123%.4� (3)

All air properties are taken based on the bulk air temperature with a Prandtl number (Pr) for air of 0.71. Another consideration in the study of the effectiveness of the dimpled surface geometry is the extra pressure loss caused by the dimpled surface, which occurs over the length of the channel. This is accounted for in the friction factor, f:

5 =62

489:)�*;)�*

9 <&'

(4)

Pressure taps on the top side of the test section at a known distance, L, from one another are used to measure pressure differentials across the entire length of the test channel for each Reynolds number and surface geometry tested using a Scanivalve pressure sensor. The air velocities are calculated from each Reynolds number case. These friction factors are also compared in a ratio to the smooth-channeled case, f0, found using the Blausius equation10:

5

5%=

62

489:)�*;)�*

9 <&'

=

1

0.079 /0�8 4⁄ (5)

These two nondimensionalized ratios can be combined into a single expression called the thermal performance, η:

@ =�#$ #$%⁄ �

�5 5%⁄ �8 A⁄ (6)

This ratio, derived from heat exchanger design, is a metric to describe the ratio of benefit to cost of a particular design. As can be seen, more emphasis is placed on higher heat transfer rather than the incurred pressure penalties, which have an exponent of 1/3.

B. Detailed Nusselt Number Distributions using Temperature Sensitive Paint (TSP)

Thermocouple setups can give accurate temperature measurements; however they cannot provide detailed heat transfer coefficient distributions. As a result, the use of optical techniques to determine heat transfer coefficients is becoming more prevalent. Optical techniques involve the use of cameras to capture surface temperature changes over time; this allows for detailed heat transfer coefficient distributions. This portion of the study utilizes temperature sensitive paint (TSP) to determine detailed heat transfer coefficient distributions.

TSP is thermally quenched photoluminescent paint. As the luminescent molecules are excited by the absorption of a photon, the molecules try to return to their ground state by emitting a photon at a lower wavelength, as temperature increases, the emission intensity of the paint decreases11. By measuring the light intensity with a CCD (charged couple device) camera and excitation source (for this study, a 400-nm LED array), detailed surface temperature distributions can be obtained. A 570-nm filter is used to filter out the light from the excitation source, as well as any ambient light that may distort the image.

The intensity of light emitted by the TSP is proportional to the temperature of the paint. Introducing a reference condition enhances the functionality of TSP; generally the room temperature at which the tests are run is set to be the reference temperature. Along with the reference condition, a black image (no excitation source) is used to eliminate any background intensity associated with optical components. The emission intensity is related to the surface temperature as shown in Eqn. 7.

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B��� � B�

B���*�C � B�= 5��� (7)

A calibration of the TSP must be performed to determine the relationship between emission intensity and surface temperature. The calibration involves attaching a thermocouple to a TSP coated copper block, taking a black image of the block, heating the block from room temperature to 125°F, and recording the intensity at known temperatures. Figure 5 shows the calibration curve developed for this study. Note that TSP degrades due to time and light exposure, coating both the copper block and test section with the same batch of TSP at the same time allows for minimal error between the calibration sample and the test section.

Wright et al.9 gives a detailed setup for TSP measurements. The focus of this study is to determine detailed heat transfer coefficient distributions. To accurately determine heat transfer coefficients, four images are required. First, a black image (no excitation source, no air flow) is taken to eliminate any noise within the instrumentation. The second is a reference image where the excitation source is on, but no air is flowing through the channel. The third is an initial image (includes the excitation source, but no air flow) that takes into account any possible fluctuations in room temperature while the air is being vented into the surroundings. The fourth “image” is actually a set of test images taken at set intervals during the transient experiment. These images have the heated air flowing through the channel and the excitation source

running. Heat transfer coefficients are obtained using a transient TSP technique. Transient heat transfer experiments rely

on the assumption of 1-D conduction through a semi-infinite solid. To ensure this is a viable assumption, materials that minimize heat conduction must be used, and each test must be a minimal length of time. For this study, the dimpled surface is made from Plexiglas (α = 0.1073*10-6 m2/s and k = 0.1812 W/m-K). The governing equation for the 1D semi-infinite solid is shown in equation 810.

D9�

DE9 =1F D�DG (8)

Solving Eqn. 8 requires knowledge of an initial condition and two boundary conditions. The initial image provides the wall temperature just before the test starts; eqn. 9 shows the initial condition. The first boundary condition, a convective boundary at the surface, is given by eqn. 10, and the second is that far from the plate, the temperature is equal to the initial temperature, eqn. 11. ��E, G � 0� � �� (9)

�( HD�DEIJK% � ���� � ��� (10)

��E → ∞� � �� (11) Solving eqn. 8 at y = 0, and using the given boundary and initial conditions, eqn. 12 is obtained. The

experimental setup does not allow for an instantaneous step change in air temperature; as a result, equation 12 must be modified – eqn. 13 – using Duhamel’s superposition theorem. ���G� � ���� � �� � 1 � N0OP Q�9FG(9 RS N035T Q�√FG( RS (12)

���G� � �� � VWXXY1 � 0OP Q�9FZG � [\](9 R 035T

^_�`FZG � [\]

( ab

cddef

\K8g6���\, \�8�h (13)

The only unknown in eqn. 13 is the heat transfer coefficient, h, which can be solved numerically. With the heat transfer coefficient, refer to Eqn. 3 to obtain corresponding Nusselt number ratios.

Figure 5: TSP Calibration Curve

0.99

1.01

1.03

1.05

1.07

1.09

1.11

0.45 0.65 0.85 1.05

T/T

ref

I/Iref

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IV. Results and Discussion The experimental results will be presented according to measurement technique. The regionally-averaged heat

transfer enhancement results will be discussed first, followed by the results for the detailed heat transfer distributions. Additional thermal performance comparisons will also be discussed.

A. Regionally Averaged Heat Transfer Enhancement

Figure 6 shows the Nusselt number ratios for the 30% dimple depth surface geometry. For each Reynolds number examined, the same trend in the Nusselt number ratios may be observed. High heat transfer due to thermal boundary layer development may be observed at the entry of the test section. Near approximately 6 diameters into the channel, the Nusselt number ratios reach a constant value of about 1.8. For every Reynolds number, each spanwise region is approximately equal to the others, and the Nusselt number ratios are shown to be relatively insensitive to Reynolds number. At Re = 10,000, there is a larger distribution in Nusselt number ratios than in the other flow cases, but this is to be expected because a larger percentage of the supplied heat is lost to the environment as opposed to convected through the flow.

Figure 7 shows the Nusselt number ratios for the 15% dimple depth surface geometry. The same trends described for the 30% dimple geometry are also apparent for the 15% geometry. A thermal entry length of high heat transfer is observed through channel distances of about 6 diameters. The Nusselt number ratios at each spanwise region are approximately the same value as those of the other spanwise regions. For the Re = 10,000 case, the same larger distribution is observed in the 30% dimple depth surface geometry is observed, and occurs for the same reason described above. A thermally fully-developed Nusselt number ratio of about 1.5 is observed for the other flow cases of the 15% dimple depth geometry, which is expectedly less than that of the 30% dimple depth geometry.

B. Detailed Heat Transfer Enhancement Distributions

Figure 8 gives detailed Nusselt number ratio distributions for δ /D = 0.3. In each image, the flow is going from left to right. In order to help with understanding of the dimple position and corresponding Nusselt number ratio, each full dimple print is over laid on the plot. Note the areas of low heat transfer enhancement inside each dimple. Similar to Mahmood et al.5 as the flow goes over the leading edge of the dimple, it separates and provides very low heat transfer enhancement. At the trailing edge of the dimple, the flow reattaches and provides very high heat transfer enhancement. Most of the heat transfer enhancement happens outside of the dimple. These areas of increased heat transfer are caused by the vortices shed from the trailing edge of each dimple. At low Reynolds numbers, the heat transfer enhancement of the dimples is much larger than that of a smooth plate. With increasing Reynolds number, however, the overall heat transfer enhancement appears to converge, and the dependency on Reynolds number for heat transfer enhancement decreases. Recall that, for a smooth tube, as Reynolds number increases, overall heat transfer increases. Similarly, for the dimpled channel, with increasing Reynolds number the overall heat transfer increases, but the magnitude of the Nusselt number ratio decreases due to the increased heat transfer in a smooth tube.

Similar Nusselt number ratio trends are given in Figure 9 for δ/D = 0.15. Decreasing δ /D increases the flat surface between dimples could possibly maximize the area of high heat transfer between dimples and increase heat transfer over the plate. However, this is not the case; decreasing δ /D also decreases dimple depth, which decreases the strength of the vortices leaving the dimples and reduces overall Nusselt number ratios. However, here the highest Nusselt number ratio happens at a Reynolds number of 20,000. In addition, the overall Nusselt number ratios are significantly lower than those gathered for δ /D = 0.3.

Figure 10 illustrates Nusselt number ratios across the streamwise centerline of each set of dimples. For δ /D = 0.30 the largest Nusselt number ratio occurs at the trailing edge of each dimple; as seen in Figs. 8 and 9, overall heat transfer enhancement generally decreases with increasing Reynolds number. However, for δ /D = 0.30 it is appears that the centerline data may be converging around an average Nusselt number ratio of 1.5. If this is the case, as Reynolds number increases, the dependency of the Nusselt number ratio on the Reynolds decreases. For δ /D = 0.15, the Nusselt number ratio is more independent of the Reynolds number.

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C. Thermal Performance Comparisons

Figure 11 shows the friction factor values for each flow scenario and both dimple depth geometries. As the figure shows, there is a marginal increase in the friction factor ratio between the dimpled surface geometries of 15% to 30% and also between Reynolds numbers. For every flow scenario, the friction factor ratio remains less than approximately 1.4. This is considerably less than the friction factor ratios encountered in ribbed designs.

Figure 12 is the average of the Nusselt number ratios measured at each of the three spanwise regions of the thirteenth row of copper plates. This spanwise average is representative of thermally fully developed flow conditions, avoiding both entrance and exit effects. As can be seen in the figure, the Nusselt number ratio is relatively insensitive to variations in Reynolds number. This behavior contrasts that of a ribbed surface geometry, which is much more sensitive to Reynolds number variations.

The thermal performance values for each flow scenario are depicted in Fig. 13. At larger Reynolds numbers, the thermal performance of both dimpled surface geometries remains at a relatively constant value of about 1.5. This behavior also contrasts that of a ribbed surface geometry since the thermal performance of ribs at higher Reynolds numbers approaches a value of 1. Thus, while at lower Reynolds numbers the thermal performance is greater for ribs, at higher Reynolds numbers dimpled surfaces hold a distinct heat transfer advantage.

Figure 6. Regionally-averaged Nusselt Number Ratio Distributions for 30% Dimples

Figure 7. Regionally-averaged Nusselt Number Ratio Distributions for 15% Dimples.

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Figure 9: Detailed Nusselt Number Ratio Distributions for 15% Dimples.

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.5 1 1.5 2 2.5 3

Nu/Nuo

Figure 8: Detailed Nusselt Number Ratio Distributions for 30% Dimples.

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

x / Dh

z / W

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.5 1 1.5 2 2.5 3

Nu/Nuo

Re = 10,000

Re = 20,000 Re = 20,000

Re = 10,000

Re = 30,000

Re = 40,000 Re = 40,000

Re = 30,000

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Figure 13. Effect of Dimple Geometry on Overall Thermal Performance

V. Conclusion Heat transfer enhancement at varying dimple depths and

Reynolds numbers were experimentally investigated using both a traditional copper plate technique and a relatively new transient TSP technique. This study aimed to validate the TSP techqnique against the generally accepted copper plate technique. For both copper plate and TSP measurments, the average overall Nusselt number ratio for δ/D = 0.15 is less than that of δ/D = 0.30. This is due to the fact that the smaller dimple depths do not induce as strong vorticies as that of deeper dimples, which in turn causes less mixing and lower heat transfer. However, (as seen in Fig. 12) for the TSP technique, the average overall Nusselt

number ratio for both dimple depths is lower than that of the copper plate. More research must be done to verify that this TSP technique is accurate for determing heat transfer coefficients. The advantages of the TSP technique have been demonstrated, and if the causes of inaccuacies between TSP measurments and copper plate measurments can be isolated, this TSP technique would be a viable way to determine heat transfer enhancement.

Figure 10: Centerline Nusselt Number Ratios from TSP δ/D = 0.30 (left); δ/D = 0.15 (right)

0

0.5

1

1.5

2

2.5

3

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

Nu

/Nu

o

X/Dh

Re = 10000Re = 20000Re = 30000Re = 40000

0

0.5

1

1.5

2

2.5

3

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9

Nu

/Nu

o

x/Dh

Re = 10000Re = 20000Re = 30000Re = 40000

Figure 11. Effect of Dimple Geometry on Channel Friction Factor Ratios

Figure 12. Effect of Dimple Geometry on Average Heat Transfer Enhancement

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References 1Han, J.C., Dutta, S., and Ekkad, S.V., Gas Turbine Heat Transfer and Cooling Technology, 1st ed., Taylor and Francis, New

York, 2000, Chaps. 1, 6

2Wright, L.M. and Gohardani, A.S., "Effect of Turbulator Width and Spacing on the Thermal Performance of Angled Ribs in a Rectangular Channel (AR = 3:1)," ASME International Mechanical Engineering Congress and Exposition, ASME Paper No. IMECE2008-66842, Vol. 10, ASME, Boston, MA, 2008, pp. 1103 - 1113

3Chandra, P. R., Alexander, C. R., and Han, J. C., "Heat transfer and friction behaviors in rectangular channels with varying number of ribbed walls,' International Journal of Heat and Mass Transfer, Vol. 46, No. 3, 2003, pp. 481 – 495

4Moon, H. K., O'Connell, T., and Glezer, B., "Channel Height Effect on Heat Transfer and Friction in a Dimpled Passage,” J. Eng. Gas Turbines Power, Vol. 122, No. 2, 2000, pp. 307 - 314

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