Detailed heat transfer and fluid flow investigation in a rectangular duct with truncated prismatic ribs

Experimental Thermal and Fluid Science 96 (2018) 383–396

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Detailed heat transfer and fluid flow investigation in a rectangular duct with truncated prismatic ribs

T

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Naveen Sharma, Andallib Tariq , Manish Mishra AVTAR (Aerodynamics Visualization and Thermal Analysis Research) Lab, Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India

A R T I C LE I N FO

A B S T R A C T

Keywords: LCT PIV Truncated prismatic ribs Heat transfer Friction factor Flow field

The paper presents an experimental study of detailed heat transfer and flow field characteristics in a rectangular duct having different types of truncated prismatic ribs on the bottom surface. The truncated prismatic ribs are manufactured by tapering the square rib from both the sides up to the center to provide rib height at the ends of 0, 2, 4, 6 and 8 mm. Experimental heat transfer results using transient liquid crystal thermography (LCT) are reported along with the mean flow field results using particle image velocimetry (PIV) at a rib pitch-to-height ratio of 10. The heat transfer effectiveness of proposed rib configurations is evaluated by examining the surfaceand spanwise-averaged Nusselt number distribution. The effect of rib configurations on the flow parameters as well as on the heat transfer augmentation, with an emphasis to overall averaged augmentation Nusselt number, friction factor ratio, and performance index factors, are studied over a wide range of Reynolds number (9400–58,850). Most of the truncated prismatic ribs provide higher augmentation Nusselt number (about 25.15%) and lower pressure penalty (about 54.65%) than those with the square ribs. The truncated prismatic ribs provide better thermohydraulic performance than the square rib, however, these values are about 25–53% higher respectively at the lowest and the highest Reynolds number. Further, the aero-thermal characteristics are studied and documented in order to enhance the understanding and to correlate the flow dynamic mechanisms with the heat transfer augmentation from the fundamental perspective for all proposed rib configurations at a fixed Reynolds number of 42,500. The combined analysis of aerothermal characteristics puts in evidence the role of fluid dynamic factors i.e. flow features, mean velocities, and the turbulence intensity in the heat transfer augmentation.

1. Introduction A compact, reliable, economic and energy efficient heat exchanging system has played a major role in industrial applications related to heating and cooling of the thermal systems under consideration. One practical way of enhancing the thermal performance of heat exchanging system is by using convective systems and liquid coolants for heat transportation [1]. Nanofluids have recently seen as a promising option for thermal fluids which can be effectively used for heat transport. The nanofluids significantly improve the thermal performance of the heat exchange systems employed in different practical applications, for instance CPU cooler [1], annulus and plate heat exchanger [2,3], and heat sink microchannel [4,5]. Aliabadi et al. [6] reported that the heat transfer coefficient and pressure drop for the ribbed wavy heat sinks are 4–128% and 8–185% higher than those for the smooth wavy sinks, which can be further enhanced by using nanofluids instead of water. Another way of enhancing the convective heat transfer is by using

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rib arrays inside flow passages, which are often used in many industrial applications such as cooling of gas turbine blades, combustor liner cooling passages, rib roughened radiator tubes/ducts, solar collectors, compact heat exchangers, cooling of electronic components and nuclear reactor fuel elements [7–9]. In each of the applications, the design/ geometry of the rib turbulators varies, and might depends upon the nature of flow and configurational requirement. For instance, the radius of curvature of the rib in radiator tubes/ducts is high, and are of the same order of magnitude as the rib height due to manufacturing constraints; while in cooling of internal passages of gas turbine blades or combustors, sharp-cornered ribs (square/rectangle) are used in practice. In heat exchangers, vortex generators (square/rectangular, plain, louver, semi-dimple, winglet etc.) are most commonly employed, while the rounded ribs have special relevance in AGR fuel elements. In general, the spanwise vortices induced by the ribs break up the boundary layer and generate turbulence due to flow separation and flow reattachment in the inter-rib region. The high magnitude of the turbulent

Corresponding author. E-mail address: [email protected] (A. Tariq).

https://doi.org/10.1016/j.expthermflusci.2018.03.029 Received 24 February 2018; Received in revised form 24 March 2018; Accepted 25 March 2018 Available online 27 March 2018 0894-1777/ © 2018 Elsevier Inc. All rights reserved.

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Nomenclature

Tw TI TLC u, v , w

specific heat capacity, (kJ/kgK) Cp hydraulic diameter of the test section, (m) Dh e maximum rib height, (mm) rib height at the ends, (mm) ep f friction factor for ribbed duct fo friction factor for smooth duct convective heat transfer coefficient, (W/m2K) h HTC heat transfer coefficient thermal conductivity of Perspex substrate, (W/mK) k ka thermal conductivity of air, (W/mK) local Nusselt number of the surface with ribs, Nu = hDh / ka Nu Nu/ Nuo augmentation Nusselt number (Nu/ Nuo)a overall averaged augmentation Nusselt number Re Reynolds number based on hydraulic diameter, Re = Ur Dh / ν Ta air temperature, (K) initial wall temperature, (K) Ti

Uxy Uxz Ur x , y, z

wall surface temperature, (K) 2 2 + vrms turbulence intensity, TI = urms , (m/s) thermochromic liquid crystal time-averaged velocity component in x , y , and z direction, (m/s) mean velocity magnitude, Uxy = ( (u2 + v 2) ) , (m/s) mean velocity magnitude, Uxz = ( (u2 + w 2) ) , (m/s) average velocity at the inlet of the test section, (m/s) coordinate axis indicating streamwise direction, wall normal direction and spanwise direction, respectively

Greek letters

η1, η2 ρ ρa ν τ

performance index factor density of Perspex substrate, (kg/m3) density of air, (kg/m3) kinematic viscosity of the air, (m2/s) time, (s)

highest heat transfer augmentation and friction factor among the square, triangular, and trapezoidal-ribs with both decreasing height and increasing height in the flow direction and could be helpful in obviating the local hot-spots formation. Ali et al. [30] investigated the effect of changing the trapezoidal angle (5°, 10°, 15° and 20° of the trapezoidal rib with decreasing height in flow direction on flow structures, and its consequent effect on the heat transfer augmentation at Reynolds numbers of 9400, 27,120, 44,600 and 61,480 using PIV and LCT techniques. It has been observed that the size of secondary recirculation bubble diminishes at higher Re and higher trapezoidal angle, and thereby leading to the removal of hot spots in immediate downstream of the rib. Moon et al. [31] numerically studied sixteen rib configurations of different cross-sectional shape and found the boot-shaped rib turbulators provides the maximum heat transfer performance with comparable pressure penalty to that of the square rib. The authors also reported that the slope of the front surface of the rib as a critical factor for determining the heat transfer performance because it directly affects the size of the recirculating zone. Effect of three different rib geometries (semi-circular, rectangular and hybrids of the two) on heat transfer and flow friction characteristics have been investigated by Alfarawi et al. [32]. The flow velocity, the turbulent intensity as well as rib pitch to height ratio (p / e ) are significantly altered the heat transfer augmentation, thereby leading the maximum heat transfer at p / e = 6.6 for the hybrids ribs and at p / e = 13.3 for remaining configurations. Recently, Sharma et al. [33] studied the effects of varying pentagonal angle (5° to 20°) and rib pitch to height ratio (6–12) on the local heat transfer and friction factor characteristics inside a rectangular duct roughened with pentagonal ribs one principal wall. LCT has been used to measure surface temperature distribution and finally to demonstrate the local HTC over the ribbed surface at different Re (9400–58,850). At higher Re and pentagonal angle, a significant improvement in augmentation heat transfer immediately behind the pentagonal ribs has been observed and thereby leading to obviation of the hot spots. The literature confirms the three-dimensional nature of the flow field within the ribbed duct even for the simplest rib configuration due to manipulation of vortical structures in the inter-rib region [8–10,20–22]. The ribs having a variable cross-sectional area along the width span of the duct, like delta-wing vortex generator (VG)/profiled ribs, referred as three-dimensional ribs hereafter, have also been gained significant interest from the research community [34–39]. The threedimensional ribs are not only strongly disturbed the boundary layer by the associated secondary flow, but also generated longitudinal vortices which persist over longer stream-wise distances. Using LCT and LDV,

transport provides good mixing to improve heat-exchange and thereby resulting in an increase of convective heat transfer rate. But unfortunately, the rib turbulators also increase the pressure penalty/energy consumption and thereby affecting the overall thermo-hydraulic performance of the thermal system [8–10]. Therefore, it is important to find optimal rib configuration which will produce maximum heat transfer with minimum pressure drop. Numerous experimental and numerical studies have established the significant effect of channel, rib, and flow features on heat transfer and friction factor characteristics [8–16]. The locally deteriorated heat transfer immediately behind the ribs, where the possibility of hot spot formation is the highest, has been reported along with higher pressure drop [8–10,15]. These local hot spots in the inter-rib region have found to be detrimental to the material structure and resulting in thermal failure of the thermal systems (like gas turbine blade, combustor liner etc.). The ribbed duct flow is highly complex and unsteady; therefore, detailed spatial and temporal information is required to understand the flow physics and heat transfer mechanisms. Investigations with pointwise based measuring tools are unable to identify instantaneous flow structures and provide discrete regional averaged information due to their restricted spatial resolution by the size and nature of the probes [17–19]. In recent years, the progress in computational and hardware capabilities, mainly focussed towards advancement in optical techniques i.e. liquid crystal thermography (LCT), infrared thermography (IR), particle image velocimetry (PIV) etc., permit the researchers working in the pertinent area of rib roughened ducts to acquire high resolution temporal and spatial data of temperature and flow fields. Several researchers have implemented these sophisticated experimental optical diagnostics in order to study local heat transfer distribution and flow field characteristics inside ducts with ribs of rectangular/square cross-section [8–11,15,20–23]. However, some researchers provided permeability in the rib that allows the flow to go through the rib, and resulting in successful manipulation of the large-scale vortical structures inside the reattaching shear layer [24–28]. These investigations concluded that permeable-ribbed ducts have an advantage of higher local heat transfer coefficient immediately behind the rib resulting in the removal of hot spots, and lower pressure penalty when compared with the duct with solid ribs. Apart from providing permeability, attempts have also been made to alleviate the problems of low heat transfer, high-pressure drop and hot spots formation by modifying the geometry of rib cross-section [17,29–33]. Using LCT, Wang and Sunden [29] found that the trapezoidal ribs with decreasing height in the flow direction provide the 384

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visualization experiments. Recently, Singh et al. [38] examined the effect of ribs (45° angled, V-shaped, W-shaped, and M-shaped ribs), dimples (a depth-to-print diameter ratio of 0.3), and combinations of rib and dimple on the heat transfer distribution (using LCT) and pressure drop in a two-pass square duct. The results showed that 45° angled and V-shaped compound configurations produce the higher heat transfer augmentation and thermo-hydraulic performance. The pertinent literature elaborates the importance rib geometry modifications (2D and 3D rib turbulators) on the manipulation of flow structures, and thereby the heat transfer and friction factor characteristics inside ribbed passages. The rib turbulated flow is highly unstable with complex time dependence and strong non-linearity, therefore, demands for instantaneous as well as ensemble averaged flow field information for better understanding the flow physics. Further, the precise locations of the hot spots (region of high temperature or low heat transfer region) in the inter-rib region cannot be identified suitably by the averaged temperature or heat transfer information thereby highlighting the importance of surface temperature or heat transfer measurements. In general, the LCT and PIV techniques are capable to provide surface heat transfer patterns and instantaneous/ensemble flow field respectively; nevertheless, their application to study detailed heat transfer and fluid flow features associated with three-dimensional rib turbulators are still less.

Liou et al. [34] studied the local/average HTC and instantaneous/ensemble average flow field, respectively, for twelve different longitudinal VGs at a fixed Re of 12,000. The delta-wing I and 45° V-shaped (with tips facing upstream) configurations offered better thermal performance and also recognized the most significant fluid dynamic aspects, i.e. the strength of secondary flow, the convective mean velocity, and the turbulent kinetic energy, are mainly responsible for upsetting the heat transfer augmentation. Using 2-D PIV, Armellini et al. [35] observed high turbulence level in front of the turbulence promoters of various shapes (square, circular, triangular, and rhomboidal); and thereby boosting strong instability of the horseshoe vortex at the wall/obstacle junction that further contributes to enhancement in spanwise velocity components and leads to a three-dimensional mass recirculation behind the turbulence promoters. The effect of introducing ribs of different heights in the downstream region of an obstacle on heat transfer distribution has been investigated by Ghorbani-Tari et al. [36] using LCT. The local heat transfer characteristics in the upstream of the obstacle are observed nearly unaffected, while the downstream region of the obstacle is modified significantly by the insertion of rib turbulator. The high-resolution LCT measurements of Terzis et al. [37] showed that the local values of exponent m in the correlation Nu x ∼ Rem x can be used for better visualization of the flow topology as compared the oil-flow

Fig. 1. Schematic of experimental facility used for LCT and PIV measurements. 385

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the inter-rib region of an array of truncated prismatic ribs mounted on the bottom wall of the rectangular duct. The proposed truncated prismatic ribs are thought to be simpler and do facilitate the ease of suitability in implantation from manufacturing constraint. High-resolution flow field results have been captured by using PIV, and surface heat transfer distribution is measured by using LCT, while rib pitch-to-height ratio has been set at the typical value of 10 which is widely used and recommended in the pertinent literature. Four set of truncated rib configurations have been used during experiments and the effect of different truncated prismatic ribs on the heat transfer and flow field characteristics inside a rectangular duct have been studied to understand the correlation between the flow physics as well as the heat transfer variation in tandem. The liquid crystal thermography (LCT) is used to observe the local variation, spanwise variation, local maxima and minima, spanwise averaged, and regional averaged heat transfer characteristics in the whole inter-rib region. In addition, the pressure drop across the considered rib turbulators is measured to evaluate the friction factor, and to ascertain the overall thermohydraulic performance. The heat transfer and friction factor measurements are performed at four different Reynolds numbers (9400, 26,160, 42,500, and 58,850). However, in order to highlight the flow physics correlation with that of the heat transfer enhancement in the inter-rib of investigated 3-D ribs, the PIV results in terms of mean flow structures, mean velocity, and turbulence intensity distribution are examined and elucidated at a typical Reynolds number of 42,500. Lastly, the thermo-fluid performance analysis has been compared with the array of solid rib configurations, which makes the present analysis complete. These set of performance indexes obtained over a broader range of Reynolds number in turbulent regime can be helpful in developing the heat transfer and friction factor correlations, and thereby beneficial in terms of understanding the behaviour of individual or combinations of parameters independently. The present investigation provides a valuable benchmark database of reliable aero-thermal measurement for the designers/engineers working for the optimal rib geometry in various applications to validate their numerical codes and solutions.

Fig. 2. Different rib configurations with arrangement on the bottom wall.

Recently, the present authors [39] reported the detailed flow field information in the inter-rib region of truncated prismatic ribs using PIV for both laminar (Re = 9400) and turbulent (Re = 42,500) flow conditions at a fixed rib pitch to height ratio of 12. The distribution of mean velocities, vortex structures identifiers, instantaneous velocity vector and corresponding vorticity fields, fluctuation statistics, and the salient critical points, clearly demonstrated the highly unsteady 3-D nature of the flow, which contributes towards the rise of turbulence activity in the flow field. Further, the instantaneous flow characteristics revealed the presence of large-scale coherent vortices in the separated shear layer region, and the existence of periodical processes such as intermittent ejection of the recirculation zone into the main flow and motion of the reattachment point. The flow features were appeared to be quite interesting and promising from higher mixing and heat transfer augmentation perspective, and therefore the fundamental fluid flow measurement prompts to look for a detailed heat transfer investigation while keeping its application with any of the heat transfer devices into perspective. Furthermore, there exists the great interest of the scientific community towards carrying the systematic investigation to reveal the mechanism for the momentum and heat transfer process in order to look for an optimal rib configuration for effective cooling. Although limited, but recent era have witnessed the reporting of detailed measurements of flow and surface heat transfer measurements on the same channel configuration and with the same boundary conditions [24,27,30,39–43], which are essentially desired to understand the thermal effectiveness from a fundamental fluid flow perspective. Most of these investigations carry permeable rib configurations, and thus the detailed aero-thermal investigations behind ribs other than rectangular cross-section are quite restricted. In this regard, the present investigation carries a detailed heat transfer and fluid flow investigation within

2. Experimental setup and procedure The three-dimensional sketch of the experimental facility along with instrumentations used for heat transfer, pressure drop, and flow field measurements is presented in Fig. 1. The comprehensive detail of the facility has already been discussed in the literature [27,33,39]; however, for the sake of completeness, a brief description is presented here. The inlet section comprises of a settling chamber (including a honeycomb section and three fine anti-turbulence screens) and a 9:1 contraction cone. The Plexiglas test section has characterized a length of 1500 mm and an internal cross-section area of 160 mm × 40 mm. The test section is followed by a diffuser connected to a long circular pipe encompassing an orifice flow-meter, a control valve and a blower operating in suction mode. The operating speed of the blower is controlled by using a digital AC Frequency Inverter (Micro-master 440 drive, Make: Siemens) that is used to provide desired air flow rates. Three-dimensional rib turbulators, termed as truncated prismatic ribs hereafter, are made of Aluminium with dull black color spray coating (Fig. 2(a)). The truncated prismatic ribs are prepared by tapering the square rib of cross-section 8 × 8 mm2 from center of the length to both ends, providing the rib height at the ends (ep) equal to 0 mm (ep/ e = 0), 2 mm (ep/ e = 1/4) , 4 mm (ep/ e = 1/2) , 6 mm (ep/ e = 3/4) and 8 mm (ep/ e = 1, square rib), where e is the height at the center of the rib. The rib pitch to height ratio (p / e ) is kept to 10. The ribs are placed transversely (Fig. 2(b)) to the main flow direction on the top surface of the heating section, and the position of first rib is fixed at a distance of 240 mm away from the inlet of the test section. The heating section (length = 1120 mm, width = 184 mm) is comprised of sequential heater-foil arrangement along with the several 386

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7th order polynomial curve between hue and temperature, as found in Sharma et al. [33], is used to get the temperature distribution over the entire surface. The local temperature information at different times over entire surface extracted in terms of 1000 set of temperature matrices using calibration curve (7th order polynomial curve) is further processed to compute the distribution of HTC over the complete test surface. The steady-state HTC over a surface coated with TLC sheet having a low thermal conductivity, low thermal diffusivity material can be obtained from transient experiments by solving 1-D transient conduction equation with the assumption of semi-infinite solid [11,30]. Thus, at a prescribed initial surface temperature and convective boundary conditions (at x = 0, and τ = 0 ), the relationship can be expressed as

layers, the details of which are illustrated in Fig. 3. The heating section is carefully designed so as to satisfy the assumption of semi-infinite solid. The details about the confirmation of semi-infinite boundary condition for the actual measurement duration of 50 s can be found in Sharma et al. [33]. K-type thermocouples connected with the data acquisition system have been used to measure temperature all along the heating section as well as at inlet and outlet of the duct. Two rectangular slots with plug arrangement are made 1300 mm apart in the top Perspex wall along the axial centreline at upstream and downstream side of the test section for determining the pressure difference (ΔP ) and the average velocity (Ur ) , respectively. These measurements are performed using a digital Micro-manometer (FCO-12, Furness Controls), which has a maximum error of ± 1% of the fullscale values ( ± 199.9 mm H2O) at laboratory temperature.

Tw−Ti h2τ ⎞ τ ⎞ ⎛ = 1−exp ⎛⎜ ⎟ erfc h ⎜ ρC k ⎟ Ta−Ti p ⎝ ρCp k ⎠ ⎝ ⎠

2.1. Heat transfer measurement

(1)

Here τ is the total time at which the initial surface temperature (Ti ) (at any location (x ,y ) ) reduces to a final value (Tw ) due to the airflow at ambient temperature (Ta) over the test surface. h is the convective heat transfer coefficient. ρ and k are the density and the thermal conductivity respectively of the substrate. The heat transfer results are presented in terms of local Nusselt numbers (Nui ) which can be calculated as:

The temperature distribution on the smooth and ribbed ducts is mapped by the thermochromic liquid crystal sheet, R35C5W (0.2 mm thick) from Hallcrest. The image acquisition system associated with LCT measurements consists of a 3-CCD-based video camera coupled with a lens of 3 mm focal length, workstation inserted with a frame grabber, and halogen lamps (150 W and 300 W, two each). The RGB images displaying the color distribution on the liquid crystal sheet are captured at the rate of 20 Hz by using the 3-CCD camera, which is fixed above the ribbed surface providing a spatial resolution of 1.04 mm/pixel. In heat transfer investigations using LCT, it is important to discern the correct color-temperature relationship. Thus, before execution of the transient experiments, the liquid crystal sheet has been initially calibrated by an in-situ calibration under the laboratory lighting conditions; however, the detailed description has been reported in the literature [27,33]. The monotonic variation between Hue and temperature with a minimum level of variance corresponding to hue clearly indicates the aptness of hue as a measure of temperature. Therefore, a

Nui = hi Dh / ka

(2)

Using Nui values, the average Nusselt number (Nua) is estimated as follows: B

Nua =

∑ i

Nui B

(3)

where B is the number of pixels within the region of interest. The term overall averaged augmentation Nusselt number (Nu/ Nuo)a represents the averaged local Nu/ Nuo values in one inter-rib region just after

Fig. 3. Details of designed heating section: (a) assembled and (b) exploded view. 387

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the effect of 2-D conduction. From Eq. (1), it is clear that the local heat transfer coefficient can be expressed as a function of Tw, Ti, Tm, α, k , and τ . The errors in temperature measurement by LCT is due to the bandwidth, thickness and quality of liquid crystal coating, image processing techniques and the lighting angle, and their mutual effect is evaluated by performing a number of calibration experiments. Based on the calibration experiments, the uncertainty in temperature measurement (Tw and Ti ) using LCT is found to be within ± 0.2 oC . The uncertainty in ambient temperature (Ta) measurement using thermocouple is found to be within ± 0.5 °C. While the frame rate (20 Hz) of captured video leads to the uncertainty of ± 0.05 s in τ . Finally, according to the law of error propagation; the overall uncertainty for heat transfer coefficient measurement (h) are turned out to be within ± 4.8%, respectively, over the range of conditions under consideration. The overall uncertainty in the local heat transfer coefficient is spatially varied and is expected to be maximum near the stagnation point regions where the detection time of liquid crystals is either relatively short or relatively fast. This means that the regions of higher and lower HTCs are inherently prone to higher uncertainties compared to other regions, and the aforementioned uncertainty in heat transfer coefficient indicates the same. The uncertainty in local Nusselt number (pixel-wise Nusselt number) is estimated to be within ± 5%, where higher heat transfer coefficients are calculated with higher uncertainty. Further, the uncertainty in friction factor is due to the errors in micro-manometer reading, the thermal properties and in the duct dimensions, and is found to be within ± 3%. The detailed discussion on uncertainty analysis for heat transfer measurement has been reported in literature [33,41]. The resulting error in the PIV measurements, i.e. combination of bias and precision errors, is estimated by following the procedure presented by Prasad et al. [44] and by Forliti et al. [45]. The accuracy of the PIV measurement largely depends upon the imperfection of the apparatus, PIV image acquisition and processing parameters i.e. number of PIV image samples, magnification factor, displacement of particles in image pairs, time interval between successive images, and nature of the flow being measured. The overall uncertainty in the mean velocities at 95% confidence level is estimated to be 3.2% of the streamwise averaged mean velocity, as previously discussed in detail by the authors in [39,41].

attainment of heat transfer periodicity [33]. The measured pressure difference (ΔP ) between the inlet and the outlet of the test section is used to determine the frictional factor ( f ) in the cooling duct by applying Darcy’s formula as:

f=

2ΔP Dh ρa Ur2 L

(4)

The characteristics dimension is the hydraulic diameter in the calculation of Reynolds numbers, Nusselt numbers and friction factors. Based on the enhancement factor (Nu/ Nuo)a and the friction factor (f / fo ) , two performances parameters i.e. η1 and η2 for each tested rib configuration are evaluated based on the constant pumping power criteria [7,28,32,33].

η1 = (Nu/ Nuo)a /(f / fo )

(5)

η2 = (Nu/ Nuo)a /(f / fo )1/3

(6)

Generally, η compares heat transfer per unit pumping power for the test duct, with rib turbulators, with that for a smooth duct. Here, Nuo and fo are referred to the Nusselt number and the friction factor respectively of the smooth duct. 2.2. Flow field measurement The flow field measurements, using TSI make 2-D PIV system [27,30,39], are made in the same setup with an additional 5 mm thick Perspex sheet is fitted at top of the LCT coated surface. A customized seeding arrangement, primarily comprising of a six-jet atomizer in conjunction with the compressor, a seeding distribution box and three perforated copper tubes, is employed to generate the seeding particles (∼ 2–3 µm) from olive oil and to provide homogeneous seeding particles at the duct inlet. A Quantel double cavity, double frequency Q-switched Nd: YAG laser system is used to illuminate the flow field seeded by seeding particle. A standard AF Nikkor 35–70 mm 1:3.3–4.5 lens attached with PowerView™ Plus camera is used to capture the tracer particles. A synchronizer is used to synchronize the laser pulses and the camera. Moreover, a workstation fitted with a frame grabber and INSIGHT-4G™ software is employed for capturing, processing and analysis of the PIV images. The PIV measurements are made with the experimental conditions as mentioned in Table 1. The PIV camera and the laser sheet are perpendicular to each other for performing measurements in different x −y and x −z planes, at five different spanwise locations (z / e = − 6.25, − 3.125, 0, +3.125, +6.25) and at two different vertical stations ( y / e = 0.5 and 1.25), as shown in Fig. 4, providing a spatial resolution of ∼ 112.7 µm/pixel and ∼ 99.89 µm/pixel, respectively. The field of view of the camera is set approximately 192 × 40 mm in vertical (x −y ) and 88 × 160 mm in horizontal (x −z ) streamwise planes to catch the flow field behaviour in the inter-rib region. An FFT-based cross-correlation algorithm in conjunction with a 2-D Gaussian fit is used to detect the correlation peak points. In the present investigation, a series of 500 instantaneous velocity vectors are used to provide the time-averaged information of different flow quantities such as time-averaged streamlines, mean velocities, and turbulent kinetic energy distribution in each measurement plane. After processing, PIV results most often contain some spurious vectors (< 5%) having sudden irregularity in magnitude and direction, which are eliminated by local median filtering (3 × 3, kernel size) and substituted with modified vectors using a bilinear least square fit technique amongst the neighbouring vectors [20,25,27,30,39].

3. Results and discussion The effect of rib configurations on heat transfer enhancement has been studied by examining the surface- and spanwise-averaged heat transfer distribution and the overall averaged heat transfer augmentation. The performance index parameters i.e. overall averaged augmentation Nusselt number, friction factor ratio and the thermohydraulic performance factor have been evaluated and compared for various truncated prismatic ribs at different Reynolds number varying Table 1 Experimental parameters used for PIV measurements. Maximum flow velocity, (Ur )

10.4 m/s

Seeding particle Energy of each laser pulse Pulse duration Laser sheet thickness Magnification factor

Spherical olive oil particles 140 mJ 10 ns ∼0.8 mm ∼112.7 µm/pixel in x −y and ∼ 99.89 µm/pixel in x −z 25 µs 2048 × 2048 pixels 15 pairs/s 500 INSIGHT-4G™ FFT based cross-correlation method 16 × 16 pixels with 50% overlapping 3 × 3 points Gaussian fitting

Pulse separation time, (Δt ) PIV CCD camera resolution Frame rate Number of image pairs, (N ) Data processing software PIV interrogation algorithm Interrogation window size Sub–pixel analysis

2.3. Uncertainty analysis The overall uncertainty in convective heat transfer coefficient (h) measurement using LCT depends upon many factors such as uncertainties in the measurement of Reynolds number, surface temperature, duration of transient experiments, mainstream temperature, and 388

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profound effect of rib geometry and Reynolds number. The behaviour of Nu/ Nuo in the developing flow regions is considerably different (Figs. 5–8), however, a definite periodic pattern has been observed after x/e ≥ 60 for all rib configurations irrespective of Re, and indicating periodicity in Nu/ Nuo well after 7th rib. It is well established from the literature, that the flow separation takes place at the front edge of the square rib with a thick layer of free shearing layer [8–10,20,30,33,39]. Due to variation in truncated prismatic rib geometry, the point of flow separation gets changed, and thereby modifies the separated shear layer region in a different manner. The low heat transfer region (Nu/ Nuo < 1) present in the immediate downstream corner of the square rib has been diminishes with variation in ep/ e , thereby confirming the reduction in low-velocity stagnant region. The modification in rib geometry alters the secondary flow structures in the inter-rib region and their interaction with the core mainstream flow. The spatial distribution of Nu/ Nuo clearly indicates that strong Nusselt number areas are developed in the inter-rib regions, and this observation can be attributed to the flow reattachment. By contrast, regions with minimum Nusselt number augmentation does exist in immediate downstream rib region and can be correlated with that of the secondary recirculation bubble just behind the rib. However, a higher heat transfer zone is observed just before the next rib which can be linked to the vortical structures produced by the adverse pressure gradient. The distribution of augmentation Nusselt number in lateral direction seems to be axisymmetric; however, a significant variation in its magnitude has been observed which confirms the twodimensionality in the HTC distribution. This indicates that the modification in 3-D rib geometry has contributing towards the generation of spanwise vortical structures. Figs. 5–8 also show that the augmentation Nusselt number is a strong function of Reynolds number, which decreases with the increase in Reynolds number from 9400 to 58,850, however, this drop in magnitude is also distinctly different along the transverse and streamwise direction. Once the flow gets fully turbulent (Re ⩾ 42500) , the reduction in overall augmentation Nusselt number is comparatively lower for investigated three-dimensional ribs. At Re = 26,160, the augmentation Nusselt number is found to be superior in developing region (before attainment of periodicity) for all configurations (Fig. 6), which can be attributed to the transitional nature of the flow in the smooth duct. Further, it is found that square rib yields superior heat transfer enhancement at the lowest Reynolds number (Re = 9400), whereas most of the truncated prismatic ribs perform better at the higher Reynolds

Fig. 4. Vertical and horizontal measurement planes for PIV.

in between 9400 and 58,850. The mean velocities and turbulent kinetic energy distribution in the inter-rib region have been studied at a Reynolds number of 42,500 that help in understanding the driving mechanism responsible for better mixing. Further, the aero-thermal characteristics have been studied in order to correlate the flow dynamics with heat transfer augmentation from a fundamental perspective. The flow field and heat transfer characteristics have been presented alongside the normalized spatial coordinates (x / e, y / e, z / e ) ; where x , y , and z represent the measurements along the streamwise, wall-normal and spanwise direction, respectively, while e is the maximum rib height (Fig. 4). The nature of the incoming flow at different Reynolds numbers, i.e. 9400, 26,160, 42,500, and 58,850 has been verified by performing heat transfer and flow field measurements in the smooth duct. The heat transfer [33] and flow field [39] results indicate laminar flow at the lowest Re (Re = 9400), transitional nature at intermediate Re (Re = 26,160) and turbulent nature at higher Re (Re ≥ 42,500). The range of Reynolds number (9400–58,850) under consideration significantly covers different flow regime i.e. laminar, transitional and turbulent in the test section. In the present investigation, the ribs are periodically mounted on the principal wall; therefore, it is important to verify the place from where the flow patterns in ribbed duct become periodic. The details about periodicity attainment in the inter-rib region have reported by the authors in earlier publications [33,39,41]. The results confirmed the flow and heat transfer periodicity after 7th–8th rib region, thereby illustrating that the periodicity in flow leads to periodicity in heat transfer. It is important to mention that the area between a pair of rib turbulators (between 7th and 8th rib), just after the attainment of periodicity has been considered for calculation of overall averaged augmentation Nusselt number.

3.1. Local heat transfer characteristics The local augmentation Nusselt number (Nu/ Nuo) distribution for different truncated prismatic ribs at Reynolds numbers of 9400, 26,160, 42,500 and 58,850 are presented in Figs. 5–8, respectively. To find the improvement of heat transfer on the surfaces purely due to the turbulence generated by the introduction of three-dimensional ribs, the locations of the ribs on the studied surface in Figs. 5–8 are covered with grey boxes in order to neglect the heat transfer enhancement produced by the heat conduction of the ribs. The local distribution of augmentation Nusselt number provides significant information at each point that provides more flexibility to analyse the results in any direction (transverse and longitudinal), and also used to obtain the spanwise and regionally averaged Nusselt number distribution. The distinctly different distribution of Nu/ Nuo in the inter-rib region indicates the

Fig. 5. Augmentation Nusselt number distribution in the inter-rib region for different truncated prismatic ribs at Re = 9400. 389

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Fig. 6. Augmentation Nusselt number distribution in the inter-rib region for different truncated prismatic ribs at Re = 26,160.

Fig. 8. Augmentation Nusselt number distribution in the inter-rib region for different truncated prismatic ribs at Re = 58,850.

(Nu / Nuo ) are observed in the near downstream vicinity of the rib, up to ∼ 3e , for all truncated prismatic ribs (ep/ e = 0−3/4) as against the square ribs (Fig. 9). The high heat transfer zone just behind the truncated prismatic ribs could be helpful in eliminating the hot spots prevalent behind the square ribs. The location of the maximum Nu / Nuo is found to be shifting towards the downstream side of the rib, and thereby leading towards a significant reduction in reattachment length for truncated prismatic ribs than that of square rib. The shape of Nu / Nuo curves remains identical but becomes flatter with increasing Reynolds number. At Re = 58,850, the truncated prismatic ribs (1/4 ⩽ ep/ e ⩽ 3/4) produce higher Nu / Nuo in the entire inter-rib region than the square ribs. It is important to mention that the truncated prismatic rib with ep/ e = 3/4 provides higher Nu / Nuo values than other cases at a typical location of X∗ ∼ 3e for all the considered range of Reynolds number (Fig. 9(ii)). 3.2. Averaged heat transfer and friction factor Fig. 10 presents the variation of overall averaged augmentation Nusselt number, (Nu/ Nuo)a as a function of rib configuration i.e. ep/ e for different Reynolds numbers. As expected, it is observed that all the rib configurations have significant improvement in heat transfer augmentation ((Nu/ Nuo)a > 1) with respect to the smooth duct in the considered Reynolds number range. The trend of (Nu/ Nuo)a with ep/ e at Re = 9400 is entirely different than that at other Reynolds number, it monotonically increases (up to 22.54%) with an increase in ep/ e from 0 to 1. However, at higher Re, (Nu/ Nuo)a initially increases with increase in ep/ e , reaches a maximum value (at ep/ e = 3/4 for Re = 26,160–42,500, and at ep/ e = 1/2 for Re = 58,850) and then decreases with further increase in ep/ e . The values of (Nu/ Nuo)a for truncated prismatic ribs are inferior at the lowest Re (Re = 9400) and superior at the highest Re (Re = 58,850) than square rib (ep/ e = 1) . However, the (Nu/ Nuo)a values for truncated prismatic rib of ep/ e = 0 is always smaller than that of square rib for the complete investigated range of Re, but this difference is decreasing with increase in Reynolds number because of the attainment of fully turbulent flow condition in the smooth duct at Re≥42500 . As indicated in Fig. 10, the overall averaged augmentation Nusselt number for all the rib configurations are decreasing with increasing Reynolds number. It drops from 4.57 to 1.62 (64.55%), 4.68 to 2.06 (55.98%), 5.15 to 2.09 (59.41%), 5.40 to 2.04 (62.22%), and 5.6 to 1.67 (70.18%) as Re increases from 9400 to 58,850 for different truncated prismatic ribs having ep/ e of 0, 1/4, 1/2,

Fig. 7. Augmentation Nusselt number distribution in the inter-rib region for different truncated prismatic ribs at Re = 42,500.

number value (Re≥26160 ). Further inspection of Fig. 5 reveals that the Nu/ Nuo distribution seems to be uniformly distributed over each streamwise location (except in just downstream of the rib up to 1e), though a significant variation in spanwise direction has been observed at Re = 9400. However, the mapping of local augmentation Nusselt number clearly shows the footprints of flow separation, reattachment, flow recirculation and boundary layer redevelopment in the inter-rib modules for each configuration at Re≥26160 (Figs. 6–8). In order to understand the quantitative behaviour of local HTC distribution, the spanwise averaged augmentation Nusselt number (Nu / Nuo ) (i) in the inter-rib region between 7th and 9th rib, and (ii) at X∗ ∼ 3e for different truncated prismatic ribs for Reynolds numbers of 9400, 26,160, 42,500 and 58,850 is presented in Fig. 9. This summarizes the whole exhaustive experimental data and further reveals critical information about the variation of Nu / Nuo with ep/ e and Re ; and also about the variation of reattachment length. Comparatively higher values of spanwise-averaged augmentation Nusselt number 390

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Fig. 9. Comparison of spanwise averaged augmentation Nusselt number distribution (Nu / Nuo ) (i) in the inter rib region between 7th and 9th rib and (ii) at X∗ ∼ 3e for different truncated prismatic ribs at (a) Re = 9400, (b) Re = 26,160, (c) Re = 42,500 and (d) Re = 58,850.

3/4 and 1, respectively. This provides a clear confirmation that the heat transfer augmentation is strongly dependent on the rib geometry and Reynolds number. The maximum improvement in heat transfer performance in terms of overall augmentation Nusselt number is around 25.15% for truncated prismatic rib with ep/ e = 1/4 (Re = 58,850) when compared with the square ribbed duct. The effect of the truncated prismatic ribs and Reynolds number on pressure penalty in terms of friction factor ratio (f / fo ) is clearly observed Fig. 11. The ribbed duct has higher friction factors than the smooth ones. In the given Reynolds number range, the friction factor ratio decreases with a decrease in ep/ e from 1 to 0. The decrease in ep/ e

leads to lower blockage ratio, and therefore the pressure drop is reduced. The maximum reduction in friction factor ratio is around 54.65% for truncated prismatic rib with ep/ e = 0 , when compared with the square ribbed duct. The friction factor ratio is the highest at Re = 58,850, the lowest at Re = 9400 and comparable for Re of 26,160 and 42,500 for all the investigated configurations. Overall, it can be concluded that the truncated prismatic ribs perform better than the square ribs in terms of heat transfer augmentation, associated with the decrease in flow resistance.

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lower Re show higher values of thermohydraulic performance (η2 ) than the cases with higher Reynolds numbers. This indicates that the pressure drop penalty dominates more than the increased heat transfer benefit, at the higher Reynolds numbers. In order to understand the flow mechanism responsible for heat transfer augmentation, the detailed flow field characteristics in the inter-rib region between 7th rib and 8th rib are discussed and presented along with the heat transfer features in the following sections, at a typical Reynolds number of 42,500. 3.4. Flow characteristics, normalized velocity fields and turbulence intensity The information regarding movement of tracer particles in the flow domain is obtained from the time-averaged streamline topology. The distribution of normalized average velocity (Uxz / Ur = (u2 + w 2)1/2 / Ur ) along with the definable flow patterns for different truncated prismatic ribs at y / e = 0.5 and 0.125 are plotted in Fig. 13(a) and (b), respectively. The flow patterns show symmetry along z / e = 0 for all the rib configurations and consequently seem to be responsible for the axisymmetric distribution of Nusselt number augmentation, as evident from Fig. 7. In the lower horizontal streamwise plane (y / e = 0.5) , a very low-velocity region behind the rib separating primary recirculation bubble and the curved free shear layer is clearly observed for all truncated prismatic (Fig. 13(a)) ribs. In this region, the streamline bifurcates conveying a portion of fluid upstream and shedding residual fraction downstream. A node-saddle pattern is observed corresponding to reattachment line. The existence of a node-saddle downstream the rib confirms three-dimensionality and unsteady nature of the flow because of larger deviation in magnitude of ∂w / ∂z [39]. The spread of

Fig. 10. Overall averaged augmentation Nusselt number at different Reynolds numbers from 9400 to 58,850 for all investigated rib configurations.

Fig. 11. Friction factor ratio at different Reynolds numbers from 9400 to 58,850 for all investigated rib configurations.

3.3. Overall thermal performance evaluation The performance index parameters, η1 (Eq. (5)) and η2 (Eq. (6)) combining the heat transfer and flow resistance are presented together in Fig. 12. The performance parameter, η1 curves tend to decrease with increasing ep/ e from 1/4 to 1, which is further decreased with increasing Reynolds number. The qualitative trend for the truncated prismatic ribs, as shown in Fig. 12(a), did not change with the Reynolds number. However, the values of η1 is almost comparable to truncated prismatic ribs of ep/ e = 0 and 1/4, except at the lowest Re (Re = 9400). As a result of having the lower f / fo , ribs with ep/ e = 0 and 1/4 provide the higher values of η1 at most of the Re. Although having the excellent heat transfer performance, ribs with ep/ e ≥ 1/2 have performed badly concerning the value of η1 because of the larger values of f / fo . From Fig. 12(b), it is clearly seen that most of the truncated prismatic ribs provide η2 > 1, thereby confirming that the performance-enhancing feature is better than that of the smooth duct, and therefore suitably recommended to use for improved performance in different heat exchange systems. The comparable values of η2 are provided by truncated prismatic ribs having ep/ e ≤ 3/4 at Re = 9400, however, these values are about 18–25% better than the square rib. At Re≥26160 , the truncated prismatic ribs of ep/ e in between 1/4 and 3/4 provide better thermohydraulic performance, η2 than the other configurations, and this is attributed to the high heat transfer augmentation as well as low flow resistance. It is interesting to observe that the ribbed ducts with

Fig. 12. Comparison of the thermal performance factors: (a) η1 = (Nu/ Nuo)/(f / fo ) and (b) η2 = (Nu/ Nuo)/(f / fo )1/3 at different Re for different rib configurations. 392

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Fig. 13. Time-averaged velocity fields (Uxz / Ur ) with streamlines for different truncated prismatic ribs in x −z plane of (a) y / e = 0.5 and (b) y / e = 1.25 at Re = 42,500.

corner eddies in the downstream corner region of the square rib and lateral walls are clearly predictable from the streamline patterns. As expected, these corner eddies completely fade away with a decrease in ep/ e . Interestingly, the maximum values of Uxz / Ur for square ribs are observed neither along the symmetry line nor along the lateral walls but in regions −6 < z / e < −3 and 3 < z / e < 6 for x −z plane located at y / e= 0.5 and 0.125. However, higher values of Uxz / Ur for truncated prismatic ribs (ep/ e ⩽ 3/4) are found nearer to lateral walls and its spread increases and shift towards the leeward side of the rib with the reduction in ep/ e from 1 to 0 (Fig. 13). The spanwise variation in the size of recirculation bubble, and thereby the reattachment length for the square rib, is almost unchanged, while for others configurations it is significantly changed with ep/ e (Fig. 13). Therefore, the PIV measurements in x −y plane at five different spanwise locations (z / e = − 6.25, − 3.125, 0, +3.125, +6.25) have been made in order to verify and understand the impact of truncated prismatic ribs on the flow field characteristics in the inter-rib region. The normalized average velocity field with respect to the flow direction (x / e ) in vertical planes located at different spanwise stations

negative velocity region becomes broader with an increase in ep/ e i.e. the highest for square rib, thereby indicating the distinctly different size of recirculation bubble for different configurations, and leading to variation in the position of maximum heat transfer region, as witnessed from Fig. 9. As expected, the streamlines closer to lateral walls are unaffected by the presence of rib turbulators having ep/ e of 0, 1/4, and 1/2 because of the measurement plane higher than the rib height at the ends. However, the streamline patterns for 3-D ribs having ep/ e > 1/2 revealed that the mainstream flow is deviated towards the line of symmetry because of small lateral pressure gradient and turns in front of the successive rib towards the lateral side walls. It is also relevant to mention that the spanwise extent of primary recirculation region that limits the spanwise extent of reattachment line, is lowest for ribs with ep/ e = 0 , and highest corresponding to rib with ep/ e = 1, as expected. However, a distinct behaviour corresponding to square rib is clearly observed in the vicinity of the lateral walls, where the reattachment point appears at far downstream region compared to that at the center of the duct. Casarsa and Arts [10] combined this observation with the deviation of sidewall boundary layer forced by rib turbulators. In addition, the existence of 393

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an effort has been made to understand the flow physics with the heat transfer distribution, by superimposing the turbulence intensity 2 2 (TI / Ur = urms + vrms / Ur ) and streamlines on the local Nusselt number distribution (as shown in Fig. 16). Generally, the periodic flow acceleration and separation processes in the inter-rib region are responsible for the generation of turbulence. The truncated prismatic ribs provide strong swirling motion in the inter-rib region, as observed from [39], and therefore, higher turbulence intensity. Fig. 16 shows the distribution of normalized turbulence intensity, which is found to be superior within the mixing layer region than that of the free stream and the near wall region. It typically increases with increase in y / e , reaches to the maximum at y / e ∼ 1 and then decreases to the corresponding free stream values. The magnitude and spread of turbulent intensity in vertical symmetry plane increase with increasing ep/ e . However, the region of higher turbulence intensity shifts towards the rear face of the rib when moves in spanwise direction for the truncated prismatic ribs of 1/4 ≤ ep/ e ≤ 3/4 , due to the variation of rib height along the width of the duct. Near the bottom wall high values of the turbulence activity are

and its corresponding streamline topology for different truncated prismatic ribs of ep/ e ≤ 3/4 are compared in Fig. 14. The size of primary recirculation bubble diminishes when moving away from the center of the duct (z / e = 0) in spanwise direction. By inspecting Figs. 13 and 14 altogether, a good agreement between the flow field information in horizontal and vertical streamwise planes is clearly observed, confirming the significant variation in the size of primary recirculation bubble, and thereby the reattachment length along the spanwise direction. In this work, the reattachment point is identified from time-averaged streamlines patterns, where the entrained flow strikes normally on the ribbed wall and splits along the solid surface, and from the contour plots of the time-averaged streamwise velocity component, where the near wall u− velocity changes its sign in x − axis, as described in Sharma et al. [39]. At reattachment point, the reattaching flow divides into two parts, one part of the reattachment flow flows back in the low-pressure region existing in the downstream of the rib, thereby forming a secondary vortex that could explain the mechanism of lower heat transfer just behind the rib. The other part of the reattaching flow moves past the following rib, where a high-pressure region is produced in front of the rib resulting in flow separation. An exhaustive summary of the reattachment length corresponding to different truncated prismatic ribs at rib pitch to height ratio of 10 at different z / e locations has been presented in Table 2. For truncated prismatic ribs, the reattachment lengths initially decrease with an increase in ep/ e , reach to the minimum at ep/ e = 1/2 and then increase with further increase in ep/ e towards the vertical symmetry plane. For other vertical planes in the spanwise direction, the values of reattachment are less than that of the square rib and increase with the increase in ep/ e . Fig. 14 also reveals that the flow structures, mainly separation bubble, and secondary recirculation bubble, that are clearly identified in the vertical symmetry plane (z / e = 0) seldom appear in planes nearer to the lateral wall (z / e = ± 6.25) . The magnitude of Uxy / Ur considerably diverges from the minimum at the duct center/rib center (z / e = 0) and increases as it moves towards the side walls (z / e = ± 6.25) . The lowvelocity region shrinks towards the wall when moved in the spanwise direction of the duct for all the rib configurations. The normalized time-averaged wall normal component of velocity (v / Ur ) field as presented in Fig. 15 for truncated prismatic ribs show a strong positive peak of v -velocity around the top upstream corner of the rib signifying the separation of flow for all the ribs. The v -velocity distribution is positive over top and ahead of the ribs leading to an upward deflection of the shearing layer. The streamwise extent (x / e ) of the positive v -velocity distribution just ahead of the ribs seems to be a function of rib geometries, and seem to be unaffected for different truncated prismatic ribs. The entangled region of negative average wallnormal velocity distribution in the downstream of rib shows significant dependency on ep/ e . It spreads gradually to a larger extent in upstream and downstream of the reattachment point with increasing ep/ e . The negative v / Ur distribution, within and above the reattaching shearing layer indicates the dominance of downwash motion of the fluid i.e. the entrained mainstream fluid moving towards the ribbed wall. The negative v / Ur velocity region corresponding to the downward motion of the entrained mainstream fluid significantly increases as moved away from the line of symmetry towards the sidewalls, and this is more pronounced at a higher value of ep/ e . The negative v / Ur velocity region shifts towards the downstream side of the rib and indicates the reduction in reattachment length in the spanwise direction, which correlate well with the high heat transfer region away from the center line (Fig. 7). The pertinent literature [10,25,27,41–43] establishes the importance of turbulence intensity/kinetics in understanding the flow mixing, and its subsequent effect on surface heat transfer enhancement. It had been observed that the turbulent kinetic energy increases from the near wall region [25,27,41,42], and there exist a direct correlation with the surface heat transfer enhancement [10,41–43]. In this regard,

Fig. 14. Comparison of normalized average velocity (Uxy / Ur ) fields superposed with streamlines for different truncated prismatic ribs in x −y planes at Re = 42,500. 394

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Table 2 Reattachment length based on PIV measurement for different truncated prismatic ribs at Re = 42,500. Truncated prismatic ribs

Reattachment length (Xr )

z /e = 0

z / e = ±3.125

z / e = ±6.25

ep/ e = 0

3.9e

2.5e

1.35e

ep/ e = 1/4

3.3e

2.4e

1.72e

ep/ e = 1/2

3.3e

2.38e

2.16e

ep/ e = 3/4

3.49e

3.1e

2.89e

ep/ e = 1

3.72e

–

–

Fig. 16. Distribution of the normalized turbulence intensity fields with streamlines superposed on local Nusselt number (Nu) distribution for different truncated prismatic ribs in x −y planes at Re = 42,500.

which lead to high turbulence intensity and thereby leading to improvement in heat transfer. Conclusively, the aerodynamic fields results and heat transfer information clearly demonstrates that the reduction in low velocity region (by reduction in size of recirculation bubble), increase in negative extent of wall-normal velocity (by increase in downwash motion of the core fluid) and also enhancement of turbulence activity in near ribbed wall region (higher wall normal component of turbulence intensity) leads to higher heat transfer performance. 4. Concluding remarks

Fig. 15. Comparison of normalized v− component of velocity (v / Ur ) fields for different truncated prismatic ribs in x −y planes at Re = 42,500.

The effect of different truncated prismatic ribs (ep/ e = 0, 1/4, 1/2, 3/4 and 1) on the flow mechanism, and consequential heat transfer characteristics has been investigated. From these results, the following main conclusions are drawn:

found around the reattachment point (also see Table 2) and a small region in front of the rib, thereby leading to higher Nusselt number values in these regions (refer Fig. 9). However, their magnitude is generally weaker in spanwise direction because of the lateral wall boundary layer effect and leads to low value of Nusselt number. The interaction of vortical structures in the wall-bounded regions induces flow mechanisms i.e. ejection, sweep, and out-, and inward events

1. The local heat transfer distribution is found to be axisymmetric and shows 2-dimensionality in heat transfer distribution for all rib configurations. The mapping of augmentation Nusselt number

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2.

3.

4.

5.

indicates the footprints of reattachment, separations and recirculation bubble in terms of spatial HTC distribution, except at Re = 9400. Among the studied rib configurations, truncated prismatic rib with ep/ e = 1/4 yields the highest overall averaged augmentation Nusselt number, about 25.15% higher than those with the square ribs at Re = 58,850. Truncated prismatic rib with ep/ e = 0 provides a better performance in friction factor ratio, about 54.65% lower than those with the square ribs. At different Reynolds number, the truncated prismatic ribs (ep/ e ≤ 3/4 perform better than the square ribs due to prominent performance in friction factor as well as heat transfer, thereby indicating the usefulness of proposed rib configurations for heat transfer in different applications like gas turbine blade cooling, combustor liner cooling with lower energy consumption. The truncated prismatic ribs have altered the shape of the flow structures shape, thereby modifying the primary recirculation bubble region and compressed its area, while the corner vortices, i.e. secondary recirculation bubble and separation vortex are completely diminished in spanwise direction for truncated prismatic having ep/ e < 3/4 . Overall, it can be concluded that the truncated prismatic ribs enhance the heat transfer in the vicinity of the rib, and therefore, can be seen as the potential benefit in terms of obviating the hotspots formation. The production of vortical coherent structures and their interaction effectively contribute towards the intensification of turbulence activity in the flow field and thereby higher mixing and heat transfer enhancement. With the change in rib geometry, the region of higher turbulence intensity shifts towards the rear face of the rib when moves in the spanwise direction for the truncated prismatic ribs of 1/4 ≤ ep/ e ≤ 3/4 .

[12]

[13]

[14]

[15]

[16] [17] [18]

[19] [20] [21] [22] [23] [24] [25] [26]

[27]

[28]

Acknowledgements [29]

The author acknowledges the financial support of the Ministry of Human Resource and Development (MHRD), India for initiating this research activity in Mechanical & Industrial Engineering Department at Indian Institute of Technology Roorkee, India. Further authors wish to extend sincere thanks and acknowledge the support of Gas Turbine Research Establishment (GTRE), India for providing the financial assistance in order to improve the laboratories at IIT Roorkee, India.

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