Heat Transfer and Pressure Loss Measurements in a Turbulated High Aspect Ratio Channel With Large Reynolds Number Flows

The internal heat transfer experiments are designed to simulate combustor liner cooling in a gas turbine. The combustor is one of the hottest regions in a gas turbine and its walls must be cooled to avoid durability issue. Typical temperatures in the combustor core may exceed 2000 °C which is higher than the melting point of most metals. By utilizing advanced cooling concepts such as flow over turbulated surfaces, the combustor walls can be maintained within allowable thermal limits. The present study details the effect of a few typical turbulator geometries in a high aspect ratio channel. Several studies exist in open literatures that discuss the heat transfer enhancement obtained from turbulators such as ribs and dimples with various geometries.

A comprehensive literature review of the available internal cooling techniques used in the Gas Turbine industry has been summarized by Han et al. [1]. A few investigations on heat transfer in turbulated channels are discussed. Heat transfer in a channel from concave dimples and tear-drop shaped dimples (concavities) was studied by Chyu et al. [2]. Tear-drop shaped dimples gave slightly higher heat transfer than concave dimples with both dimple geometries giving much lower pressure drop as compared to rib turbulators. Effect of channel height on heat transfer and friction was studied by Moon et al. [3]. They found that heat transfer enhancement of about 2.1 times that of a smooth channel was observed for the dimple geometry tested. Mahmood et al. [4] studied the flow structure and the local heat transfer on a dimpled surface in a channel. Vortex pairs originating from flow within the dimples were found to augment heat transfer especially near the downstream rims of each dimple. Nine concave and cylindrical dimples with various diameters and depths were studied by Moon and Lau [5] for several Reynolds numbers in a square channel. Cylindrical dimples were found to give a higher heat transfer coefficient and a lower pressure drop than concave dimples with the same diameter and depth. Dimples were also studied by Griffith et al. [6] in a 4:1 aspect ratio rectangular channel. Data were presented by them for a stationary as well as rotating channel to simulate an internal passage of a rotating turbine blade. Effect of aspect ratio, temperature ratio and Reynolds number on heat transfer in a dimpled channel was investigated by Mahmood and Ligrani [7]. Comparison of Trip-Strip/Impingement/Dimple Cooling Concepts at High Reynolds Numbers (Re up to 360,000) was reported by Kim et al. [8]. Effect of dimple depth was investigated by Burgess et al. [9]. Deeper dimples were found to give higher heat transfer due to an increase in the strength of the vortical flow structures emerging from the dimples. Park et al. [10] reported the separate effects of Mach number and Reynolds number on jet array impingement heat transfer. They reported that heat transfer coefficients increased for jet Mach number beyond 0.2 up to 0.6 as compared with jet Mach number below 0.2 under the same jet Reynolds number condition. Esposito et al. [11] compared the extended port and corrugated wall jet impingement geometry for combustor liner backside cooling. Lauffer et al. [12] presented experimental and numerical results for a 6:1 aspect ratio channel machined with dimples on one of the wider walls similar to the present study. The geometry and definition of dimples used in their study are also similar to the present study. However, they presented data only on the narrow side walls of the channel. Heat transfer enhancement by impingement cooling in a combustor liner heat shield was reported by Lauffer et al. [13]. Experimental investigation on staggered impingement heat transfer on a rib roughened plate with different crossflow schemes was also reported by Xing and Weigand [14].

Heat transfer in a channel with ribbed walls has been investigated by several researchers and a few relevant studies are listed. Most of the available studies discuss ribbed channel heat transfer with ribs on two opposite walls of the channel. Han [15] correlated available data for angled rib turbulators based on the roughness function. Heat transfer enhancement in a square channel with parallel, crossed and V-shaped rib turbulators was studied by Han et al. [16]. Broken or discrete ribs were studied by Lau et al. [17] also in a square channel. V-shaped broken ribs were studied by Han and Zhang [18]. Both studies found that broken or discrete ribs gave higher heat transfer coefficients as compared to similar continuous ribs. Kukreja et al. [19] studied local heat/mass transfer distributions and pressure drop in a square channel with full and V-shaped rib turbulators. Zhang et al. [20] added grooves between ribs to gage their impact on heat transfer. Higher heat transfer was obtained using the rib and groove combination with minimal increase in friction. Heat transfer and pressure loss in a 2:1 aspect ratio channel at high Reynolds numbers were captured by Maurer et al. [21] using liquid crystal thermography and computational fluid dynamics (CFD). They used V-shaped ribs and found that heat transfer enhancement levels at Re > 200,000 tend to level off with enhancement levels of up to 2.5 at Re = 500,000. Wright et al. [22] studied the effect of angled, V-shaped and W-shaped rib turbulators in a 4:1 aspect ratio channel under rotating conditions. A majority of the above mentioned studies for rib turbulated channel heat transfer have been limited to rib blockage ratios of 0.1.

Several studies have been performed by Taslim et al. [23–27] to investigate the effect of ribs with large blockage ratios in square and rectangular channels. Blockage ratios up to 0.25 were tested by Taslim and Spring [23] with square and low aspect ratio ribs. Low aspect ratio ribs were found to give higher heat transfer. Angled, V-shaped and discrete ribs were also studied by Taslim et al. [24]. Effect of sharp-edged and round-cornered ribs was investigated by Korotky and Taslim [25] with sharp corners giving higher heat transfer. Taslim and Lengkong [26,27] measured heat transfer from 45 deg ribs in a square channel for three rib spacings and blockage ratios. The effect of sharp and round corners was also investigated. Best heat transfer was obtained for a rib-to-rib spacing and rib height ratio of 5. Local heat transfer measurements in a ribbed channel using the Infrared technique were performed by Astarita and Cordone [28] for angled ribs.

The effect of number of ribbed walls in a square channel was investigated by Chandra and Cook [29]. Tests were performed from a single ribbed wall to all four ribbed walls. Heat transfer on the ribbed wall did not show a significant change in heat transfer enhancement with addition of ribs on other walls, whereas on the smooth surface, the heat transfer increased with more ribbed walls. Heat transfer enhancement for the ribbed surface showed a slight decreasing trend with lower number of ribbed walls. In another study by Chandra et al. [30], the effect of number of ribbed walls was studied in a rectangular channel. Similar trends were observed for the rectangular channel as the square channel. Heat transfer with only one ribbed wide wall was found to be better than the case where both short sides were rib roughened. Also, friction from two roughened wide walls was much higher than two roughened narrow walls. Taslim et al. [31] also measured heat transfer and friction in partially ribbed passages using the liquid crystal technique. Tests were conducted in a square as well as a trapezoidal channel. Partial ribs were found to significantly improve heat transfer as compared to full-length ribs. Recently, Maurer et al. [32] reported heat transfer and pressure losses of v- and w-shaped ribs at high Reynolds numbers. Zhou and Acharya [33] studied heat/mass transfer and flow structure for four dimple shapes in a square internal passage. Rallabandi et al. [34] reported heat transfer and pressure drop measurements for a square channel with 45 deg round edged ribs at high Reynolds numbers. Hagari et al. [35] investigated heat transfer and pressure losses of w-shaped small ribs at high Reynolds numbers for combustor liner. Murata et al. [36] studied heat transfer enhancement due to combination of dimples, protrusions, and ribs in narrow internal passage of gas turbine blade. Thorpe et al. [37] provided an investigation of an impingement/pin-fin cooling system for gas turbine engine combustor applications. Mhetras et al. [38] investigated impingement heat transfer from jet arrays on turbulated target walls at large Reynolds numbers.

Internal heat transfer measurements were performed in the present study in a high aspect ratio channel with turbulators on one of the wider walls. This simulates the typical design in a combustor liner where only the liner wall is exposed to high heat fluxes originating from the combustor gases. Four different turbulator geometries are tested including three types of dimple arrays and one ribbed array. The enhancement obtained from these geometries is compared against a smooth liner wall. Tests are carried out for very large Reynolds numbers up to 1.3 × 10⁶ to maximize heat removal from the hot liner wall. Most experimental data available in the literature extend only up to Reynolds numbers of ∼100,000 for turbulated channels. Inadequate information pertaining to heat transfer enhancement from these turbulators is available at such high Reynolds numbers. Thus, the primary motivation of this study is to investigate the heat transfer characteristics of typical turbulators at very high flow conditions. Measurements for heat transfer are made at steady state conditions using thermocouples to record temperature data.

Tests were performed in a rectangular channel with an aspect ratio of 6. Three walls of the channel were heated including one wide wall or the test wall and the two narrow side walls. This design models the combustor liner where the test wall acts as the interface between the hot combustion gases and the gas turbine outer casing. This interface or liner wall is cooled from the outside to prevent it from overheating. The heated area of the channel was 10.7 D_h long. In addition to this length, an entrance and exit short channel with a length of 2.13 D_h was provided to ensure that the flow entering and exiting the heated portion of the channel is not disturbed due to the effects of sudden contraction at inlet and expansion at exit, respectively, as shown in Fig. 1. A smooth, converging duct guides the flow to the channel entrance from a pipe to prevent the formation of a vena contracta downstream of the test section entrance. A smooth diverging duct is also placed at the channel exit to prevent the exiting flow from affecting the upstream fully developed channel flow at compressible, high Mach number flow conditions. Figure 1 shows the layout of the test facility. The inlet and exit converging ducts were made from 0.32 cm thick steel sheet metal. The channel walls were made from aluminum and were 1.59 cm thick. Aluminum was chosen as it has a relatively high thermal conductivity of 177 W/mK ensuring almost uniform wall temperatures.

Tests were performed for heat transfer and pressure losses for flow in a smooth channel initially to compare against existing empirical correlations. Four different geometries were tested on the test wall and compared against data for a smooth channel. The four geometries tested include two cases with spherical dimples, one case with cylindrical dimples and one case with discrete, angled ribs. Figure 2 shows all the three dimple geometries tested. The dimple depth was maintained constant for all three cases with dimpled channels such that the depth to channel height ratio (H/H_ch) was 0.063. For the first case (case 1), a staggered array of spherical dimples with a sphere diameter of 3.77 H, and spacing of 3.83 H was used. The diameter of the circle formed by the dimple imprint on the test wall was 3.33 H. Figure 3 shows the detailed layout of the dimples on the test wall. A total of 650 dimples were machined on the test wall. To get maximum dimple density on the test wall, the dimples were arranged in staggered fashion in the streamwise direction. Thus, a dimple in an adjacent, downstream row was arranged such that its center lay on the vertices of an equilateral triangle with a length of 3.83 H (for case 1) formed by it and two dimples in the previous row. In case 2, smaller spherical dimples were used with a spherical diameter of 2.57 H, and spacing of 3 H was used. A total of 1104 dimples were machined on the test wall. In case 3, cylindrical dimples with the same size, depth and spacing as case 1 were used. Print circle diameter for the cylindrical dimples was 3.33 H with a spacing of 3.83 H. A fillet radius of 0.23 H was provided on the dimple imprint edge for all dimpled cases to account for the edge defects frequently encountered while casting the combustor liner walls. The layout of the dimples on the test wall is shown in Fig. 4 

Figure 4 also shows the ribbed geometry pattern tested on the test wall (case 4). The test wall is divided into six rows of ribs placed in the streamwise direction. Each discrete rib in each streamwise row was placed at an angle of 45 deg and had a length to height ratio (l/e) of 12.35 with a rib height to channel height ratio (e/H_ch) of 0.11. The rib pitch to rib height ratio (P/e) was 10. Discrete ribs made from brass were provided only on the test wall while the side walls were maintained smooth similar to the dimpled cases. The ribs can be subjected to a large form drag at very high Reynolds numbers and hence were glued on the test wall using a strong adhesive epoxy (JB-Weld). Conductive epoxy was not used due to these high strength requirements for the glue. Epoxy thickness was measured to be less than 0.35 mm. However, conjugate CFD predictions performed to study the impact of using a nonconductive epoxy indicated that a ∼30–40% temperature drop was observed across the epoxy as compared to a no-epoxy case. However, the ribs cover only a small area (14%) of the entire test surface and the dominant mode of heat transfer was through turbulence generated by the ribs and not by conduction through the rib itself. The impact of using a nonconductive epoxy is thus considered to be small. The ribs in adjacent streamwise rows were staggered with respect to each other. The ribs were arranged in a V-shaped discrete rib pattern for the center two streamwise rows and the adjacent rows were then arranged in a parallel discrete rib pattern resulting in a \\\/// arrangement (discrete V-shaped ribs). Table 1 shows the area enhancement by the addition of turbulators on the test wall as compared to a smooth test wall. A ∼20% enhancement is observed by addition of spherical dimples while cylindrical dimples give the largest surface area exposed to the mainstream flow.

Heat transfer and pressure loss experiments were performed for six nominal Reynolds numbers of 100,000, 200,000, 500,000, 900,000, 1,100,000, and 1,300,000. The maximum flow rate in the channel depended on the overall pressure drop over the test section. Hence, tests for the highest Reynolds number of 1.3 × 10⁶ could not be performed for turbulators geometries such as ribs which cause high frictional losses. The average inlet flow velocity was determined by traversing a pitot-static tube through a 5 × 3 matrix of points, 0.5 D_h upstream of the heated walls. It was found that the average inlet velocity was equivalent to 0.96 times the centerline velocity at the channel inlet. Flow profile at the exit of the heated test section was also measured using a pitot-static tube traversed through the same 5 × 3 matrix of points, 0.16 D_h downstream of the heated test section. The inlet flow Mach numbers for Reynolds numbers of 100,000–500,000 were less than 0.2 resulting in an incompressible flow regime (Mach = 0.04–0.19). However, the inlet flow Mach numbers for Reynolds numbers of 900,000–1,300,000 were greater than 0.2 resulting in a compressible flow regime (Mach = 0.35–0.5). The highest Mach number at Re = 1.3 × 10⁶ was around 0.5.

The heaters were stuck on the outer surface of the channel walls using a high temperature adhesive. All four channel walls were covered with fiber-glass insulation 4 cm thick to minimize extraneous heat loss.

Wall temperature in the test wall and the side walls was measured using T-type thermocouples embedded into the walls at eight streamwise locations placed 1.32 D_h apart. For the smooth and ribbed channels, the test wall was instrumented with thermocouples placed at seven equally spaced streamwise locations against eight locations for the dimpled test wall. Each streamwise location was fitted with five thermocouples on the test wall and three thermocouples on one of the side walls. For the three dimpled test walls, the five thermocouples were located such that two thermocouples were at the base of the dimples, whereas the other three were located just below the rim formed between adjacent dimples (Fig. 3). Each streamwise location temperature was based on average value of five thermocouples on the test wall and three thermocouples on one of the side walls. Only one side wall was instrumented with thermocouples as the heat transfer coefficients for both narrow side walls was assumed to be symmetric and same. However, both the side walls were heated to ensure symmetric thermal boundary layer development in the channel. The thermocouples were placed in tiny holes drilled from the outer surface of the channel walls and spanwise grooves were cut into the walls to allow passage for the thermocouples wires. The thermocouples were connected to a Fluke data logger to record temperatures. The four walls of the channel were isolated from each other to prevent heat conduction errors by placing a 1.6 mm rubber gasket between their contact interfaces.

where q″ is the net convective heat flux from the surface after accounting for the heat loss through the insulation and through conduction in the test wall.

To account for variation in the thermophysical properties of air along the length of the channel (from convection textbook), Nu₀ was corrected by multiplying it with a factor of (T_b,i/T_w,i)^−0.55. All the thermophysical properties were evaluated at the mean film temperature ((T_w + T_b)/2). It should be noted that the above empirical correlation (Eq. (7)) is valid for a fully developed thermal boundary layer when all walls of the channel are heated. In the present study, only three walls of a four-sided channel were heated, the thermally entrance length might be shorter than the four wall heated channel.

Local heat transfer measurements were done for case 1 with large spherical dimples using the steady state, hue-detection based liquid crystal technique. Wide band (20 °C) liquid crystal paint was used with a color change (red) start temperature of 45 °C (R45C20W). This liquid crystal paint was sprayed on a stainless steel plate machined with dimples with a streamwise length of 1.07D_h and the same width as the channel. A layer of nonreflective black paint was sprayed on the stainless steel plate prior to painting with the liquid crystal paint to provide good color contrast. The upstream edge of the stainless steel plate was located at a distance of 7.3D_h from the inlet of the channel. The thermal conductivity of stainless steel is similar to the metal used to cast the combustor liner wall. Thus, the wall temperatures measured from the liquid crystal technique correspond to a conjugate heat transfer problem similar to actual combustor liner conditions as heat conduction will occur within the liner wall. To accommodate this plate in the test section, the dimpled aluminum test wall was cut to fit this plate in the channel. The stainless steel plate was isolated from the adjacent aluminum test walls using a 3.2 mm thick rubber gasket. The same heater and data reduction was used to calculate the heat transfer coefficient. The wall temperature from thermocouples in Eq. (4) was replaced with the local wall temperature measured by the liquid crystal paint. The liquid crystal paint was calibrated for hue and temperature under the same optical conditions. The opposite wide wall of the channel was replaced with a plexiglass wide wall to allow optical access to the coated surface.

Uncertainty calculations were performed based on a confidence level of 95% and were based on the uncertainty analysis method of Coleman and Steele [40]. Lower Reynolds numbers gave higher uncertainties in the heat transfer coefficients due to lower magnitudes. Highest relative uncertainties for Nu were around 11% for Re = 100,000. Relative uncertainties in flow measurement and friction factor measurement were around 6% and 7.5%, respectively.

Experiments were initially performed for a smooth channel to calibrate the test section. Tests were performed for the specified range of Reynolds numbers. Results for heat transfer against streamwise distance are presented in Fig. 5 for all Reynolds number for the wide as well as narrow side walls. It should be noted that fully developed turbulent flow occurs in a smooth channel after about x/D_h = 20. Thus, the flow at the exit of the smooth channel may not be fully developed at x_max/D_h = 9.4 resulting in heat transfer enhancements greater than 1. The heat transfer is highest near the entrance of the channel due to a smaller boundary layer thickness as progressively decreases along the streamwise direction. The decrease in heat transfer is more noticeable for the narrow side wall. Peak Nusselt number for the highest Reynolds number for the first upstream thermocouple location is as high as 2200.

In a high aspect ratio channel, the velocity profile along the shorter side attains the fully developed turbulent profile much more quickly than along the longer side. Along the center span of the wider test wall, the flow behavior resembles the flow between parallel plates. For this reason, the heat transfer enhancement on the wider test wall is close to 1 at x/D_h = 7 as the flow is near fully developed with an x/W_narrow = 18.3 at the channel exit. The fluid boundary layer for the wide as well as narrow wall develops simultaneously and the thickness should be identical for a particular streamwise location. However, the velocity profile along the longer side does not attain a fully developed parabolic form as x/W_wide = 3.05 at the channel exit. Along the narrow wall, corner vortices at the edges may cause a greater impact on its average heat transfer coefficient resulting in slightly higher heat transfer. It should be also noted that one wide wall adjoining the narrow side wall is heated, whereas the other wide wall is not. As a result, the thermal boundary layer profile may be skewed which may also explain the higher heat transfer coefficients on the narrow side wall as compared to the correlation. Also, this results in large heat losses to the adjoining unheated wall at steady state due to a large contact area (20% of surface area for each wall interface) even though a 1.6 mm rubber gasket is provided between them. Heat loss from the narrow side wall at low Re is as high as 35% of the heat input to it. The effect of corner vortices and skewed thermal boundary layer may explain heat transfer enhancements from the side wall. As the Reynolds number increases, the enhancement at x/D_h = 7 approaches 1.

Streamwise distributions for cases 1–4 are shown in Figs. 6, 7, 8, and 9, respectively, for both the test wall and the side wall. Heat transfer distributions for the test wall are high near the channel entrance and decrease downstream similar to the smooth channel. However, due to the added turbulence from the turbulators, this decrease is less dramatic. In general, lowest Nusselt numbers are observed for about x/D_h = 8. The Nusselt number streamwise trends on all dimpled test walls are similar. Cases 1 and 3 show similar heat transfer magnitudes. Both these cases have similar dimple dimensions and spacing with case 1 having spherical dimples and case 3 having cylindrical dimples. Thus, the heat transfer distribution is insensitive to dimple shape. Case 2 with smaller spherical dimples shows slightly higher heat transfer than cases 1 and 3. A higher dimple density on the test wall may result in higher turbulence from secondary flows which may explain the slightly higher heat transfer magnitudes. Large increase in surface area for cylindrical dimples in case 3 (Table 1) does not help in increasing heat transfer as compared to cases 1 and 2. Heat transfer for the \\\/// discrete V-shaped ribbed channel (case 4 in Fig. 9) is higher and more uniform than that for the dimpled channel cases. Stronger reattachment and secondary flows setup due to the discrete V-shaped ribs may cause the flow to become periodic earlier than the dimpled channels. Flow reattachment and secondary flows inside the dimples is typically milder than ribs and has been visualized by Mahmood et al. [4].

Heat transfer on the side walls is also depicted in Figs. 6, 7, 8, and 9 for cases 1–4, respectively. Heat transfer enhancement for x/D_h = 7 is as high as 1.4 for the cases 1, 2, and 3 (dimples) and 1.5 for the case 4 (ribs) for Re = 100,000. However, it should be noted that the enhancement over the smooth channel data in Fig. 5 is much less due to higher Nusselt numbers for the smooth side wall at low Re than those observed from fully developed turbulent flow correlations. If normalized with the smooth channel data in Fig. 5, maximum enhancement for the side wall for Re = 100,000 is around 1.25 for the dimpled cases and around 1.35 for the ribbed case. At high Reynolds numbers, the enhancement decreases. Enhancement levels for the side wall drop down to ∼1 for the highest Reynolds numbers for the dimpled cases while enhancement levels close to 1.2 still persist for the ribbed channel. The overall increase in turbulence in the channel due to the presence of turbulators may contribute to the increase in heat transfer on the side wall. Heat transfer for the last thermocouple location at x/D_h = 9.5 shows higher heat transfer than the previous locations for all cases for both the test and the side walls. This unusual behavior is probably due to larger uncertainty from heat conduction to the downstream unheated exit guide duct. Temperature measurements on the downstream exit guide duct indicated some heat up which might indicate some conduction losses through the flange attaching the test section and exit duct even though a rubber gasket (3.2 mm thick) was used between the flanges to prevent heat conduction. This heat up was probably not accounted in its entirety in the heat loss estimates.

Figures 10 and 11 show the fully developed Nusselt number and its enhancement for test and side walls, respectively. For the test wall, the streamwise location x/D_h ∼ 8 is considered as the fully developed flow region, whereas for the side wall, x/D_h ∼ 7 is considered as the fully developed flow region. The figures compare the heat transfer among all cases. At high Reynolds numbers, the Nusselt number trends for all turbulated cases appear to converge with each other. From Fig. 10, it can be discerned that ribbed channel provides higher heat transfer than dimpled channels. The heat transfer enhancement for the ribbed channel decreases from about 2.4 for Re = 103,000–1.7 for Re = 1,240,000. The dimpled channels (cases 1–3) show similar heat transfer. Heat transfer for case 2 with smaller dimples is slightly higher than cases 1 and 3 as observed earlier. For case 2, the heat transfer enhancement drop is lower than the ribbed channel with increasing Re and decreases from 1.9 for Re = 106,000–1.6 for Re = 1,490,000. Case 1 with large spherical dimples appears to give the lowest heat transfer enhancement among all turbulated geometries tested.

From Table 1, it can be observed that the area increase by the addition of turbulators ranges between 20% and 28% for cases 1, 2, and 4 while that for case 3 with cylindrical dimples is as high as 72%. From Fig. 10, it appears that the heat transfer enhancement level for case 3 is of comparable magnitude to the area enhancement, indicating that the cylindrical dimples may not increase the average heat transfer coefficients on the surface beyond those for a smooth surface. A nonuniform heat transfer coefficient distribution may exist in case 3. Some regions such as the cylindrical side face wall of the dimple may have lower heat transfer coefficients than a smooth surface due to flow recirculation, whereas other regions such as the dimple floor may see an enhancement due to reattachment of flow. Note that it may be true only for this particular cylindrical dimple geometry. It may not be applied for other cylindrical dimple geometries. However, for cases 1, 2, and 4, the heat transfer enhancement is larger than the area enhancement suggesting that the turbulators employed were successful in raising the average heat transfer coefficients on the surface over a smooth surface.

Similar observations can be made for heat transfer on the side wall shown in Fig. 11. However, the Nusselt number magnitudes are much lower. Higher heat transfer for the smooth channel as compared to the Dittus-Boelter correlation (Eq. (7)) for low Reynolds numbers can be clearly observed from this plot. The heat transfer enhancement decreases with increasing Reynolds numbers similar to the test wall results. For the ribbed channel, heat transfer enhancement decreases from 1.5 for Re = 103,000–1.22 for Re = 1,240,000. Nusselt number enhancement for the dimpled channel cases approaches unity with higher Reynolds numbers.

Figure 12 compares the friction factors and its enhancement as compared to a correlation for a smooth channel (Eq. (9)) for all cases. The friction factor is based on the pressure drop measured from x/D_h = 3.35 to x/D_h = 9.6. Friction factors for the smooth channel are quite low with values decreasing from 0.014 to 0.012 with increasing Reynolds numbers. The measured friction factors are very close to the calculated friction factors from Eq. (9) with enhancement magnitudes close to unity for all Re. As with the heat transfer distributions, friction factors for the dimpled channels are similar with magnitudes ranging between 0.03 and 0.06. In general, case 3 with cylindrical dimples shows lowest friction factors among all turbulated cases. This might be due to flow recirculation inside cylindrical dimples. Highest friction factors are observed for the ribbed channel with an average magnitude of about 0.1 and an enhancement of around 8. In general, friction factors for the ribbed channel are about 80–100% greater than the dimpled channels. A minor increasing trend is observed with increasing Reynolds numbers for all turbulated cases.

Figure 13 shows the comparison of the thermal performance [16–18] expressed as the ratio of the Nusselt number enhancement to friction enhancement ((Nu/Nu₀)/(f/f₀)^1/3). All four turbulated cases have been plotted along with the smooth channel. The smooth channel shows an expected thermal performance of ∼1 for all Reynolds numbers. However, the thermal performance of other configuration deteriorates rapidly as the Reynolds numbers increase. Best thermal performance is observed for case 2 with small spherical dimples. Thermal performance for case 4 with discrete ribs is lowest with a magnitude of 0.82 for Re ∼ 1.2 × 10⁶ even though heat transfer enhancement is found to be the best for this case. This is due to the very high pressure drop caused by the ribs. Consequently, high heat transfer geometries such as case 4 can only be applied in applications where excess pressure drop is available.

Local heat transfer measurements using liquid crystals were performed near the fully developed region for case 1 with large spherical dimples for three Reynolds numbers to provide a secondary confirmation of the measurements from thermocouples as well as provide insight on the local metal temperature distribution. Since the paint was applied to a conductive surface (stainless steel), it was expected that local secondary flow field impact from the dimple geometry on heat transfer will not be captured. The thermal conductivity of stainless steel is similar to the metal used to cast the combustor liner wall. Thus, the wall temperatures measured from the liquid crystal technique correspond to a conjugate heat transfer problem similar to actual combustor liner conditions as heat conduction will occur within the liner wall. Maximum uncertainty measurements for the temperature measurements from the liquid crystal technique are 10% at the lowest measured Re (213 k). Only a small region of the entire turbulated test plate was painted with liquid crystal paint. This region was located between x/D_h = 7.3 and 8.4 in a region where the flow is fully developed. The heat transfer distributions are depicted in Fig. 14. Heat transfer levels on the dimple rims are much higher than those inside the dimple cavity. The secondary flow vortices upon emerging from the dimple cavity reattach on the rim resulting in higher heat transfer coefficients. High heat transfer on the dimple rims was also observed by Mahmood and Ligrani [7]. However, the local heat transfer distribution pattern is different from that observed by Moon et al. [3] and Mahmood and Ligrani [7]. The local distribution is symmetric around each dimple in the present study, whereas high heat transfer coefficients were observed immediately downstream of the dimples by other researchers. The symmetric distribution may be due to heat conduction as a stainless steel plate was used as the test wall in the present study. Inside the dimple cavity, the base shows slightly higher heat transfer due to mainstream flow reattachment. The average Nusselt numbers obtained from the liquid crystal tests are within 8.5% of the fully developed magnitudes for the corresponding Reynolds numbers observed in case 1.

Experiments were performed to investigate the heat transfer and pressure loss behavior at very high Reynolds numbers. Effect of three dimple shapes and discrete ribs was examined on the heat transfer enhancement and pressure drop. The main conclusions that can be discerned from this study are summarized below.

1. (1)

   Heat transfer enhancement ratio continually decreases with increasing Reynolds numbers. Enhancement ratio for Re > 1 × 10⁶ is less than 2 times even for the ribbed channel. Average enhancement ratio for the dimpled channels is around 1.6 times at Re = 1.4 × 10⁶.

2. (2)

   Best heat transfer enhancement ratio is observed for case 4 with a ribbed channel. However, highest friction factor is also observed for this case.

3. (3)

   Heat transfer and friction factors for the dimpled channels (cases 1, 2, and 3) are similar for all three cases. Case 2 with smaller dimples gives slightly higher heat transfer and pressure drop among the three cases studied.

4. (4)

   Thermal performance approaches unity at very high Reynolds numbers. Best thermal performance among all cases is also observed for case 2 with small dimples.

5. (5)

   Heat transfer enhancement on the smooth side wall increases due to the presence of a turbulated test wall.

6. (6)

   Local and average heat transfer measurements show good agreement.

The content of this paper is copyrighted by Siemens Energy, Inc., and is licensed to ASME for publication and distribution only. Any inquiries regarding permission to use the content of this paper, in whole or in part, for any purpose must be addressed to Siemens Energy, Inc., directly.

This project was supported by Siemens AG, Germany (The project initiated by Roland Liebe in 2003). The authors would like to acknowledge Huitao Yang for his help during the project work.

Nomenclature

A =

area (m²)

c_p =

specific heat of air (J/(kg K))

D =

dimple print diameter

D_h =

hydraulic diameter of the channel

e =

rib height (m)

f =

friction factor

h =

regional heat transfer coefficient (W/(m² K))

H =

dimple depth (m)

H_ch =

channel height (m)

I_ph =

phase current supplied to the heaters (A)

k =

thermal conductivity (W/(m K))

l =

length of rib (m)

Nu =

Nusselt number

p =

pressure drop (N/m²)

P =

rib pitch (m)

Pr =

Prandtl Number

q″ =

heat flux (W/m²)

Re =

Reynolds number

T =

temperature (K)

T_w =

wall temperature at steady state (K)

T_aw =

adiabatic wall temperature at steady state (K)

T_corr =

delta temperature based on bulk temperature increase (K)

V_ph =

phase voltage across the heaters (V)

$V¯$ =

mean velocity (m/s)

x =

streamwise coordinate (m)

Greek Symbols

ρ =

density of air (kg/m³)

μ =

dynamic viscosity of air (kg/ms)

Subscripts

0 =

reference, fully developed turbulent flow in a smooth tube

b =

bulk mean

c =

cross-section in metal plate normal to flow

cond =

conduction

i =

streamwise location

loss =

loss to the surroundings through insulation

s =

surface

w =

wall