Experimental study of turbulent flow heat transfer and pressure loss over surfaces with dense micro-depth dimples under viscous sublayer

Abstract

Presented are experimentally-measured heat transfer and pressure loss characteristics for dimpled surfaces, placed along one surface of a channel, with different ratios of dimple depth to channel height δ/H, and for Reynolds numbers ranging from 10,000 to 70,000. With the same relative dimple spacing to dimple print diameter, and the same ratio of dimple depth to dimple print diameter of δ/d = 0.20, experimental results for arrays of spherical indentation dimples with micro depths of δ = 0.6 and 1.0 mm (δ/H = 0.03 and 0.05) are compared with thermal characteristics for arrays of larger dimples with δ = 4.0 mm and δ/H = 0.20. Local surface heat transfer distributions are measured using transient liquid crystal thermography. Additional steady-state experiments are also employed to provide overall heat transfer enhancement and friction factor augmentation values. Results indicate that Nusselt number ratios and friction factor ratios of a turbulent flow in the channel are dependent upon the ratio of dimple micro depth to channel height, which are different findings from previous studies with larger-depth dimples in the cooling channels. As such, the present data for micro-depth dimples with ratios of dimple depth to channel height δ/H of 0.03 and 0.05 are firstly provided. The importance of a critical Reynolds number is demonstrated by the results, which is determined when the ratio of viscous sublayer layer thickness to the dimple depth is equal to unity, and has been ignored in the previous dimpled channel heat transfer design. Nusselt number enhancements for the micro dimples are generally lower at lower Reynolds numbers, but increase as the Reynolds number becomes larger and approaches the critical Reynolds number. Nusselt number enhancements are then approximately invariant with Reynolds number, when Reynolds number then exceeds the critical value.

Introduction

Improving the performance of turbine hot-section component thermal protection schemes, and the associated internal cooling technologies, is essential to increase the efficiency of gas turbine aero-engines and gas turbine utility power engines. Surface dimples, as an advanced cooling device, have been demonstrated to increase heat transfer, with minimal pressure loss augmentation, as a result of dimple geometric characteristics. As a result, the use of dimple arrays for surface heat transfer augmentation has attracted the attention of many researchers [1].

Consequently, many experimental and numerical studies have been conducted to investigate factors that affect the heat transfer augmentation performance of dimpled surfaces. Burgess et al. [2,3] present experimental results, which show the effects of the dimple depth on the heat transfer and flow resistance characteristics for deeper dimples, with the depth to print diameter ratios of 0.1, 0.2 and 0.3. They indicate that Nusselt numbers increase by 67%, as the dimple depth ratio increases from 0.1 to 0.3. Associated pressure losses also increase from 10 to 90%, since the deeper dimples produce stronger vortices, with more intense near-wall turbulent flow transport. Afanasyev et al. [4] and Rao et al. [5] show that shallow dimples, with a depth ratio of 0.067, provide associated surface heat transfer increases by 35–40%, without an appreciable increase of pressure loss penalty, and Rao et al. [5] indicated that the shallow dimples produce a horseshoe vortex within dimple leading edge regions, with locally enhanced turbulent mixing intensity and fluid momentum transport. Ligrani et al. [6] describe experimental results for turbulent flow and heat transfer characteristics of a channel with shallow dimples, such that δ/d = 0.1. They indicate that heat transfer magnitudes of such dimpled surfaces are insensitive to variations of inlet turbulence intensity level, and that globally averaged Nusselt number ratios are about 1.4, as friction factor ratios range from 1.28 to 1.57.

Using transient liquid crystal thermography, Chyu et al. [7] measure local heat transfer distributions of surfaces with arrays of spherical-indentation and tear-drop-shaped dimples, with a depth ratio of 0.29. Globally-averaged Nusselt number ratios for tear-drop-shaped dimples are about 2.5, which are higher than values for spherical-indentation dimples. Rao et al. [8] employ experimental and numerical approaches to investigate turbulent heat transfer and pressure loss characteristics of different dimple shapes with a depth ratio of 0.2. They show that dimple shape influences turbulent structural characteristics, and heat transfer enhancement magnitudes by appreciable amounts. Overall surface heat transfer enhancements for teardrop dimples are about 18% higher than for spherical dimples, with enhancements produced by elliptical dimples about 10% lower than values for spherical dimples. With a variety of experiments, Leontiev et al. [9] investigate heat transfer and viscous drag along surfaces with arrays of dimples with different shapes. They indicate that an oval-trench-shaped dimple reduces the extent of the flow separation region, which is ordinarily present within the upstream portion of each dimple indentation. Using a numerical prediction approach, Isaev et al. [10] also consider the oval-trench-shaped dimple, and show that a long spiral vortex, located within the trench region, is the principle source of surface heat transfer enhancement. Using TLC's (Transient Liquid Crystals) and TSP (Temperature Sensitive Paint) experimental procedures, Neil et al. [11] indicate that overall heat transfer enhancements of V-shaped dimples are similar in magnitude to enhancements produced by certain types of traditional rib turbulators. Brown et al. [12] show that strong counter-rotating vortices, formed as fluid is ejected from dimples, pull mainstream flow toward the wall, which gives important local heat transfer enhancements. Xie et al. [13] present results, which show that heat transfer is enhanced by increasing the indented cross-section area, perpendicular to the streamwise direction, because of an increase of the surface area associated with shear layer reattachment.

Afanasyev et al. [4] show that a more dense distribution of dimples, within a surface array, gives greater surface heat transfer enhancement magnitudes. Leontiev et al. [14] employ experimental procedures to investigate turbulent surface heat transfer and flow drag over the surfaces with δ/d = 0.13 dimples. They indicate that surface heat transfer values generally increase as dimple spacing density increases, regardless of whether the density increase is from smaller spacing in the streamwise or spanwise direction. An exception to this trend is present for dimple density values greater than 0.562, because surface heat transfer enhancement remains constant, but friction factors continue to increase, as spacing density increases further. Using experiments, Bunker et al. [15] consider the effects of dimple density on heat transfer and friction factors in circular tubes. They show that the density factor F variations from 0.3 to 0.5 have a significant effect on surface heat transfer augmentation magnitudes, with augmentation magnitudes approximately constant, as density factor F becomes larger than 0.5.

A number of investigations also show that dimple size has a significant effect on flow and surface heat transfer characteristics. Ligrani et al. [16] investigate dimple array flow structure, for a larger dimple with δ/d = 0.2, by utilizing smoke flow visualization. According to these investigators, the strengths of the primary and secondary vortex pairs become stronger, as the ratio of channel height to dimple diameter decreases from 1.0 to 0.25. According to Chyu et al. [7], surface heat transfer enhancements of dimples are insensitive to the ratio of channel height to dimple diameter, and to the magnitude of the Reynolds number, since the dimple-induced vortices only predominate within near-wall regions. Moon et al. [17] used a range of channel height to dimple diameter ratios H/d from 0.37 to 1.49, with a depth ratio of 0.19. They also indicate that Nusselt number ratios are approximately invariant with Reynolds number, and that neither Nusselt number ratios nor friction factors are altered by changes to the H/d, within the investigated ranges of H/d which are considered.

Such heat transfer characteristics of dimpled channels, which are independent of Reynolds number, are probably because dimple depth magnitudes are large relative to channel flow passage height. Note that maximum ratios of viscous sublayer thickness to dimple depth δ_v/δ_Dimple, for the Moon et al. [17] and Chyu et al. [7] investigations, are only 0.24 and 0.56, respectively, at the lowest Reynolds numbers considered. As a result, the viscous sublayer thickness is very small, relative to the dimple depth. By keeping the channel height constant and reducing the dimple diameter, Coy et al. [18] employ a dimpled channel with larger H/d ranging from 4.7 to 5.8. Under the condition of the same dimple depth ratio of about 0.2, results from Coy et al. [18] are consistent with data reported by Afanasyey et al. [4] and Bunker et al. [15], since all three investigations use similar H/d values greater than 4.5. Note that results from Coy et al. [18] are different from results obtained in investigations with smaller H/d between 0.37 and 1.49 [2,6,7,16,17]. Also, note that the δ/H value in the Coy et al. [18] experiments is very small, only 0.024–0.057, which is comparable to 0.0067 for Afanasyey et al. [4], and 0.053 to 0.11 for Bunker et al. [15]. Even though Coy et al. [18] claimed that the global heat transfer enhancement of the micro-depth dimples is independent of Reynolds numbers, however no specific data were provided in their publication to support that conclusion, which may be due to higher Reynolds numbers used in their experiments than the critical Reynolds numbers. Also, the experimental study of Coy et al. [18] did not show the influence of varying micro dimple depth on the heat transfer enhancement under different Reynolds numbers, when the ratio of dimple depth to diameter and keeps the same with constant spanwise and streamwise spacing ratios. Magnitudes of δ/H are 0.10–0.78 for the other studies are mentioned [2,6,7,16,17]. Such variations indicate that dimples with micro depths have a significant effect on surface heat transfer performance.

Table 1 shows a literature review summary of dimple heat transfer enhancement configurations. From this information, it is evident that a number of previous investigations are performed in channels with δ/H from 0.10 to 0.78, because the larger dimple depth with δ/H larger than 0.1 can provide considerable heat transfer enhancement capability.

The primary aim of the present investigation is consideration of the effects of dimples with micro depths on heat transfer and flow characteristics when relatively deep dimples of δ/d = 0.2 are used in the cooling channel. Of particular interest are arrangements wherein normalized dimple depth δ/H is less than 0.05, such that dimple depth magnitude is comparable to or less than the viscous sublayer thickness, which can be considered for cooling the thin wall of the gas turbine blades and micro energy conversion devices. Such configurations are important because thermal and flow performance characteristics are expected to be significantly different, compared with dimples with normalized dimple depth δ/H greater than 0.1. A secondary aim is to investigate the effects of Reynolds number on surface heat transfer characteristics within channels with micro-depth dimples. This goal is important because numerous previous investigations indicate that surface heat transfer augmentations, within dimpled channels, are invariant with Reynolds numbers. Different behavior is expected for dimples with micro depths. Considered are arrays of dimples with d = 3 mm (δ/H = 0.03), d = 5 mm (δ/H = 0.05), and d = 20 mm (δ/H = 0.2) for Reynolds numbers ranging from 10,000 to 70,000. To minimize the influences of dimple configuration, the spherical-indentation dimples within each array have the same depth ratio (δ/d = 0.2) and same spacing density along the test surface (F = 0.57).