Numerical analysis on heat transfer flow structure and exergy loss of combined truncated and circula

Abstract

Keywords: Computational Fluid Dynamics; Heat Transfer; Ribbed Cooling; Exergy Loss; Nusselt Number; Friction Factor

Introduction

Turbulators are being used to enhance the heat transfer performance of coolant in the channels. An increase in the demand for higher efficiency of gas turbines requires elevated gas inlet temperature which subsequently necessitates effective cooling of turbine blades. In order to withstand such an extreme thermal load on the blades an effective internal cooling technique needs to be

developed. Internal cooling methods predominate the external cooling as it avoids the blending of gas and air enhancing the aerodynamic performance of the turbines. The commonly used internal cooling methods for turbine blades are jet impingement, rib turbulators and pin fins. Experimental and numerical studies have been performed to investigate the heat transfer performance of rib turbulators. An experimental study by Chandra et al. [1] examined heat transfer and friction behavior in a flow channel

*Corresponding author. *E-mail address: illyasmech4@gmail.com This paper was recommended for publication in revised form by Regional Editor Md Hasanuzzaman Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

with a varying number of transverse ribs. They reported that the thermal performance associated with friction increases with number of ribs and developed the correlations to predict the heat transfer and friction factor as a function of Re and aspect ratio. Gao and Sunden [2] employed PIV technique to present the flow characteristics of the rectangular channel provided with staggered, inline and cross ribs. The results showed the strong effect of inclined ribs on the flow behavior in the development of secondary flows. Lu and Jiang [3] performed experimental and numerical investigations on a flow channel containing angled rib turbulators. The authors reported that the SST k-ω turbulence model is superior in the prediction of turbulent heat transfer over the RNG k-ε model. Chang et al. [4] examined a rectangular channel with Vshaped ribs on its performance indexed by (HTE) heat transfer enhancement ratio (Nuavg/Nu∞) for forward and backward flows (Re = 1000-30000). They obtained the Nuavg/Nu∞ ratio = 6.8 for forward flows at Re = 30000 which they claimed that the highest among the available heat transfer enhancement (HTE) devices. Choudhury and Das [5] studied the viscoelastic effect of hydrodynamic flow over a porous plate. They derived approximate velocity, temperature fields and rate of heat transfer using perturbation technique. Choi et al. [6] presented a compound cooling technique with dimple and angled ribs on rectangular channels. The experimental results provided insight into the role of rib-induced secondary flow in the local Nu distribution. Mohammed et al. [7] investigated heat transfer and flow characteristics of vertical duct using nanofluids inducing mixed convection. They reported decrease in skin fiction coefficient with increase in Re and Pr. Xie et al. [8] carried out a numerical study on heat and transfer flow characteristics of a square duct with mid truncated ribs with varying angular positions for the Re range of 10000 – 50000. They reported that the presence of truncated rib develops secondary flow causing intense magnitudes of stream wise vorticity over the channel corner. Their results revealed that reduction in recirculating flow and the presence of large-scale stream-wise velocities enhances heat transfer. They concluded that 135° mid truncated rib provides higher heat transfer and 90° rib position offers relatively less pressure drop. An experimental study by Yaghmourali et al. [9] developed a thermal calorimetric flow meter with suspended cantilever structure. They reported presence of convection effect on the both sides of the active area due to suspended structure and lower velocity boundary layer thickness of the cantilever which enhances the sensitivity of the sensor. Singh et al. [10] compared the inline and staggered cross pattern ribs on their heat transfer and fluid flow characteristics (Re = 30000 - 60000). They reported that the rib-induced secondary flows increased the near-wall shear stress directly, which improved heat transfer on the end walls with rib turbulators. However, the staggered and inline pattern induce an increase in near-wall shear stress

and the nature of the turbulence mixing caused by the two counter-rotating vortex pairs was different. Their study reveals that heat transfer enhancement of inline and staggered configurations are however similar the friction factor of inline arrangement is relatively lower. Wang et al. [11] numerically investigated heat transfer and flow characteristics of the wavy rib by varying the geometric parameters. They reported that rib height, radius and angle have a greater influence on heat transfer and flow structure while rib thickness is having little influence. Heat transfer performance and pressure consequences are positively correlated with rib height and angle while it is negatively correlated with radius. Numerical studies on heat transfer enhancement [12-15] with trapezoidal and cylindrical duct configurations were also carried out. The study investigated the thermo physical properties and thermal performance of nanofluids. Bahiraei et al. [16, 17] employed nanofluids for the exergy and entropy generation analysis in the study related to solar thermal applications and heat transfer enhancement techniques. Jing et al. [18] performed a numerical study on trapezoidal channel with slot and dimples. They analyzed the effect of dimple arrangement, rotation number (0 - 0.8) and channel orientation (0°- 60°) on flow and heat transfer characteristics under stationary and rotating states of the channel. They reported that rotation number has stronger influence compared to channel orientation on heat and flow characteristics and 108% improvement in Nu is achieved by increasing the rotation number. Heat transfer augmentation studies [19-21] were performed on the heat transfer devices using nanofluids. Bahiraei and Mazaheri [22] investigated the hydrothermal and irreversibility characteristics of grapheme based nanofluid with spiral heat sink. They reported diminishing temperature gradient with higher particle concentration leading to smaller irreversibility. Lee and Shih [23] numerically analyzed the effect of heat load (3.2 – 582 kW/m2) on flow and heat transfer in cooling duct with staggered array of pin fins. They reported density and velocity variation in the boundary layer development due to heat load variation. They concluded heat transfer-induced changes in the flow field were found to allow Nu to be nearly constant in the post-entrance region even though Re is decreasing along the duct and to significantly slow the rate at which row-averaged Nu increases along the duct in the entrance region. Wei et al. [24] carried out comprehensive review on heat transfer characteristics in the trailing region of gas turbines. They reviewed the heat transfer characteristics of cooling method by using pin fin, latticework duct, dimple/ protrusion and film cooling. They reported that the however pin fin enhances the heat transfer in the trialing edge, the latticework duct has relatively high heat transfer ability compared to pin fin duct. They concluded that the protrusions/ dimples can improve heat transfer with low pressure loss. However, the heat transfer performance is less than that of a latticework duct or a pin fin duct. The

dimple/protrusion should therefore be paired with another cooling system. Luo et al. [25] experimentally analyzed thermal-hydraulic performance of a two pass duct with delta winglet vortex generator for its varying aspect ratio (length/height) and attack angle (30° - 90°). They reported 24% increase in thermal-hydraulic performance of the duct fitted with turbulator compared with smooth duct. They obtained highest thermal-hydraulic performance with low pressure drop with turbulator fitted with aspect ratio of 2 and 45° attack angle. Kumar et al. [26-28] performed heat transfer and exergy analysis of solar air heating system coated with nano particles. Their comprehensive study compared the heat transfer performance smooth and rough absorber plate with grapheme nanoparticles coating. Bahiraei et al. [29] used a spiral rib in a triple tube heat exchanger to study the irreversibility characterisitics of nanofluids. They reported decrease in entropy generation and exergy destruction by the decrease in rib pitch ratio. The studies [30, 31] emphasized heat transfer enhancement using PCM and nanofluids. Al-Dulaimi et al. [32] analyzed the heat transfer characteristics of a square channel with a vortex generator of varying attack angle (0°, 30° and 45°), block ratio (0.1,

Physical And Computational Models

The middle part of the turbine blade is generally cooled by internal ribbed passages. To simplify the computation, a ribbed flow channel with a square section is employed to simulate the mid part of the turbine blade passage with internal ribs. The height and width of the ribbed duct are 40 mm with a length of 500 mm. Truncated rectangular and circular ribs are provided on the flow passage as shown in Figure 1.The physical parameters considered for the duct and the rib are based on the studies conducted by Xie et al. [8] and Xie et al. [33] and Wang and Sunden [34] as shown in Table 1. The nomenclature of the flow channel and the rib are shown in Figure 2.The pitch distance selected for the truncated rib is 13% of the duct length Xie et al. [33] and the pitch distance for the circular rib is half of the pitch distance of the truncated rib. The length of the rib is selected considering the reattachment length varied between 4 to 7 times of the rib height Xie et al. [33].The rib height to hydraulic diameter ratio is (h/Dh) is fixed as 0.125 according to Wang and Sunden [34]. In the present study, a three-dimensional steady system is developed for a flow channel with a rib turbulator thereby focusing on flow dynamics and heat transfer intended to describe the effect of ribs on the flow field. Numerical analysis is performed using CFX. The simulation is performed based on the governing equations of fluid flow namely continuity, momentum and energy equations plus appropriate turbulence model as a closure. The flow channel consists of

three sections. The middle section consist of ribs arrangement and is provided with a heat source. The front and rear sections are provided with no ribs to obtain steady and fully developed flow to ensure computational accuracy. The geometric configurations of the flow channel are shown in Figure 1. The fluid is considered as air and supplied at a temperature of 303 K. The inlet boundary condition is provided with uniform velocity corresponding to the Re. The outlet condition is assigned with an average pressure of 1 bar. The bottom surface and confined surfaces (top and side walls) are provided with constant heat flux and adiabatic wall boundary conditions respectively.

In the present study, the Reynolds Averaged Navier Stokes (RANS) computations were carried out which requires solving of time-averaged governing equations. The velocity field in this method is divided into mean velocity and fluctuating velocity so that . The time-averaged Navier-Stokes equations contains Reynolds stress as an additional term. Also the time-averaged energy equation is having turbulent heat flux as an additional term. To close the system of equations, these additional terms must be modelled. The time averaged governing equations for mass, momentum, and energy conservation can be expressed as [35]

Table 1. Geometric parameters of the ribbed duct Geometric Parameter

Table 2. Turbulence models and other parameters in select numerical analysis on Ribbed duct Literature

The additional term in equation (2) is Reynolds and in (3) is turbulent heat flux stress tensor . In the present study, the eddy viscosity hypothesis is used to model the Reynolds stress as

(4) Where, μt denotes eddy viscosity and δij refers to Kronecker delta, δij = 1 if i = j and δij = 0 if i ≠ j. and turbulent heat flux is modeled as (5) Where, Prt is a turbulent Prandtl number. SST k-ω model equation can be written as [41]

While k, ω, v, Pk denote the turbulent kinetic energy, turbulent frequency, kinematic viscosity and production rate of turbulence respectively whereas σ3, β3, σω2, σω3, σk3 are model constants. SST k-ω model over predicts the eddy viscosity as it does not include the transport of turbulent shear stress. A limiter to the formulation of eddy viscosity ensures the proper transport behavior as follows

Table 3. (a) Comparative results of Nu and friction factor for different turbulence models (b) Quantitative results for Nu distribution in Figure 4 (a)

BSL Earsm

Figure. 3 (a), (b) and (c) Computational grid showing fine mesh near the truncated and circular ribs for 90° rib angle.

(9) where S denotes an invariant measure of strain rate, c1=

Results And Discussion

Stream and Velocity Fields The streamline flow along the duct for various rib angles is shown in Figure 6. It can be seen that the streamline for all the rib arrangements reveals the flow separation zones associated with rectangular and circular ribs. The secondary flow originates from the side wall just behind the rectangular ribs and moves inwards towards the center line of the duct as shown in Figure 6. The induced secondary flows enhance turbulence in the vicinity of the rib resulting in increased heat transfer as it is seen in Nu distribution in Figure8. It is seen that the symmetric flow pattern as well as recirculation zone appearing along the stream-wise direction for rib angles 15°, 30° and 45° (Figure 6 a, b, c) with increasing size of recirculation zone with increasing angle between 15° and 45° (Figure 6 a, c). The induced secondary flow due to symmetric larger recirculation zones has relatively significant interaction over the bulk flow with enhanced mixing causing a peak Nu in the span-wise direction for 30° and 45° as shown in Figure 6 b, c. While a larger recirculation zone appearing at the upper region behind the rectangular rib directs most of the flow stream to the lower part of the circular rib (towards the side wall) for the rib angle of 60° (Figure 6 d) whereas the flow stream is directed upper part of the circular rib due to

Figure 6. Flow streamlines along stream wise direction in the 5th and 6th row of ribs for rib angles 15° - 90° at Re = 12000. (a) 15° (b) 30° (c) 45° (d) 60° (e) 75° (f) 90°.

Figure 7. Velocity variation along streamwise direction for rib angles 15°- 90° at Re = 12000 (a) 15° (b) 30° (c) 45° (d) 60° (e) 75° (f) 90°. a larger recirculation zone at the lower part behind the rib angle of 75° (Figure 6 e). On relative comparison of heat transfer enhancement in this region (side walls of the circular rib), it is seen that the Nu has significantly increased for the rib angle of 60° and 75° as shown in Figure 8 d, e

compared with the other rib arrangements. Thus with the 60° and 75° rib arrangements the heat transfer rate is relatively better than other arrangements. The flow approaching the circular rib spreads out and moves around causing a boundary layer separation. On separation the wake is

formed in the separated flow region behind the circular rib as shown in Figure 6. It is observed that the position of the wake region is highly dependent on the separation point over the circular rib as the wake moves away radially from the axis of the duct for rib angles of 60°, 75° and 90° (Figure 6 d, e, f). The presence of the wake behind the circular rib causing turbulent eddy motion and vortex formation resulting in an increased heat transfer rate as higher Nu is observed as shown in Figure 7 for all cases. Figure 7 shows mean velocity variation for the various rib arrangements. The velocity field behind the rib near the wall reduces significantly with the presence of recirculation zones. This lower velocity zone seen as maximum for the 90° (Figure 7 f) rib angle implying a larger recirculation zone just past the rib. As the flow progressed further past the circular rib the nature of secondary flow induced at the side walls are different with those found for the rectangular rib as it is seen in stream line flow in the Figure6. As it is seen that the lower velocity field appears at the wake region and it intensifies for the rib angles of 60°, 75° and 90° (Figure 7 d, e, f) along the flow direction. While the flow separation is minimal at the lower part as observed in streamline flow in Figure6 between the rectangular and circular ribs resulting in increased velocity in that region for 15° and 30° (Figure 7 a, b) angles whereas 60°, 75° and 90° (Figure 7 d, e, f) cases exhibiting intense flow separation at the downstream of rectangular rib causing a reduced velocity field. When the fluid moves over the circular rib beyond the stagnation point it accelerates first over the front portion

and decelerates as it passes round the rear portion due to an adverse pressure gradient resulting in flow reversal and separation as shown in Figure 7. It can be seen that the flow deceleration is relatively higher for 60° and 75° (Figure 7 e, f) rib arrangements resulting in the intense wake region. Nu Field Figure 8 shows the Nu distribution between Rib 5 and

6. While the overall heat transfer is low and a local peak

appears at the rib area for 15° and 30° (Figure 8 a, b) whereas non-uniform heat transfer appears at either side of the rib for 75° and 90° (Figure 8 e, f) cases. The heat transfer has a marginal increase along the stream wise direction for the cases 15° and 30° (Figure 8 a, b) and the influence of rib at downstream is marginal. On contrary, the heat transfer increases as the high Nu area appears at downstream for the cases 45° and 60° (Figure 8 c, d). The enhanced heat transfer appears as the Nu increases along the flow direction for 45° (Figure 8 c). The lower heat transfer is observed in the region between the two consecutive ribs. This is fact is due to redeveloped boundary layer past the rib region. The flow separates and reattaches at the downstream of the rib forming a recirculating region also shown in Figure 5 resulting in increased Nu. as shown in Figure 8 and its intensity is high for 45° and 60° (Figure 8 c, d) cases. The flow separation and reattachment are due to an adverse pressure gradient caused by the next rib as shown by Wang and Sunden [34]. The flow separation downstream of the rib causing a reduction in Nu

Figure 8. Nu number distribution along stream wise direction for rib angles 15°- 90° at Re = 12000 15° (b) 30° (c) 45° (d) 60° (e) 75° (f) 90°

exhibits symmetry about the flow axis for 15°, 30°, 45° and 90° cases (Figure 8 a, b, c and f). Nu decreases and reaches its minimum in the middle part of the channel for 90° (Figure 9 f) and a marginal rise for 75° (Figure 9 e) rib arrangement. This shows that heat transfer augmentation is weakened in the middle part of the channel for 75° and 90° (Figure 9 e, f) rib angles. The lower Nu at the middle part than those observed near the side wall, probably due to intensified secondary flow at the side walls than at the middle region as observed by Wang and­­­ Sunden [34] in his study for a square duct with continuous ribs. The Nu peak is relatively higher in the middle part of the duct for 15°, 30° and 45° (Figure 9 a, b, c) rib angles while this peak is not found in the other cases. The normalized

Nu number variation along span-wise direction for various rib angle positions is shown in Figure 9 a, b. The Nu number has a peak in the center part of the duct along the span wise direction. The normalized Nu number increases along the span-wise direction at each z/B location towards the channel center line and reaches a maximum for the rib angles between 15° and 60° (Figure 9 a, d). The increase in Nu is attributed to the enhanced turbulence associated with decreased mean velocity along the spanwise direction. A trend analysis (second order polynomial) for the increase in normalized Nu number for 15° and 60° rib angles towards center line in span wise direction is shown in Figure 10. This further implies that turbulence behavior has strong influence on the heat transfer in span wise direction. Whereas this trend is contrary as the This increase in Nu

(b) Figure 9. Nu variation along span wise direction at Re = 12000 (a) Upstream of 4th Rib (b) Downstream of 4th Rib

Figure 10. Polynomial trend analysis for the increase in Nu for 15° and 60° rib angles in spanwise direction.

is attributed to the presence of the wake region just behind the cylindrical rib as it is seen in streamline plot (Figure 6) where the high turbulence prevails. However, the Nu peak is marginally lowered the heat transfer uniformity has increased along spanwise direction for the rib angle of 60° as shown in Figure 9 d. As the flow progressed further past the truncated rib the resulting turbulent mixing with the interaction of bulk flow influences the heat transfer characteristics in the span wise direction as shown in Figure 9 b. As it is seen that the Nu distribution in the middle part of the duct is varying compared with those upstream of rectangular ribs (Figure 9 a). The Nu peak for the rib angle 30° and 45° at downstream of the rib (Figure 9 a) reaches their maxima compared to the rib upstream (Figure 8 b). This fact is due to the formation of symmetric secondary recirculation zones at near wall in the vicinity of the rib as observed in streamline (Figure 6) resulting in increased Nu. While the increase in Nu number is observed in the middle part of duct for the rib angles of 15°, 30°,45° and 60° as shown in Figure 9 b compared to the rib upstream (Figure 9 a) the variation is marginal for the rib angle of 75° and 90° positions. However the increase in Nu is significant at the side walls for 75° and 90° rib angles as shown in Figure 9b. Vorticity and turbulence kinetic energy fields Figure 11 shows the vorticity in the span wise direction. The existence of intense vorticity is apparent in the flow stream at the vicinity of the rib as well as side walls due to velocity gradients causing shear layer at jet edges. The development of such vortices towards the side wall of the duct which are coherent in nature for rib angle 15°, 30° and 45° (Figure 11 a, b, c) enhancing turbulence thereby increasing the heat transfer rate near the ribs. While relatively larger vortices on one side of the duct for the rib angle 60°, 75° and 90° (Figure 9 d, e, f) affecting the uniformity of vorticity distribution along span-wise direction as shown in Figure 11 e, d and f. The weak vortices are observed in the

middle part of the duct spread out in the span wise direction for rib angle of 75° and 90° as shown in Figure 11 e, f. Whereas with increasing z/B distance from the middle of the duct the shear layer develops outward resulting in an increase in vorticity for rib angles 75° and 90° (Figure 11 e, f). On the other hand, the existence of two shear layers one in the inner and another in the outer region of the flow causes strong vortices and leaves behind a weak vorticity zone between these two regions for rib angles between 15°, 30° and 45° as shown in Figure 11 a, b, c. Figure 10 shows the intensity of turbulence for the various rib arrangements. It is seen that the turbulence originates from both corners of the side wall with nearly equal intensity and travels inwards towards the channel center line for 15°, 30° and 45° rib angles (Figure 12 a, b, c). The turbulent fluctuations are primarily due to the flow reversal causing the secondary vortices which developed behind the rectangular ribs. The secondary vortices formed in the shearing layer of flow may get through into the boundary layer and offer mixing of fluids of differing temperature as well as kinetic energy causing a local rise in heat transfer as they disperse downstream according to Zuckerman and Lior [45]. The turbulent flow structures in large scale as observed for the rib angles of 60°, 75° and 90° (Figure 12 d, e, f) originating from one side wall have marked effect on the heat transfer. However they extend more towards on wall side for 75° and 90° (Figure 12 e, f) cases whereas the turbulence spreading is towards the center of the duct for 60° (Figure 12 d) rib angle and with nearly equal intensity for 15°, 30° and 45° (Figure 12 a, b, c) rib arrangements as reported earlier. This equal intensity of turbulent flow structure leads to uniform heat transfer towards the middle part of the duct. Thermal performance and Exergy loss Figure 13 shows the normalized Nu variation for the Re range between 12000 and 43000. Nu decreases gradually with an increase in Re which is consistent with the results

Figure 11. Vorticity distribution (ωDh/U) along spanwise direction for rib angles 15°- 90° at Re = 12000 (a) 15° (b) 30° (c) 45° (d) 60° (e) 75° (f) 90° of Wang and Sunden [34] and Tanda [46]. It can be seen that the Nu is relatively higher for 60° rib angle showing heat transfer enhancement at lower Re followed by 75° position. The Nu for 30° rib angle is marginally lower than 15° and 45° rib positions at lower Re. Figure 14 shows the normalized friction factor (f/f0) for the various rib angles. However higher heat transfer obtained from turbulence enhancement usually causes a higher pressure drop, the (f/f0) trend is different from the normalized Nu distribution. While 15°

rib angle shows relatively lower pressure drop at all ranges of Re, the 90° rib arrangement exhibits a higher pressure drop. Though the pressure drop for the 75° rib position is lower than the 90° rib position at a lower range of Re number its magnitude reaches close to the 90°. While the thermal-hydraulic performance shown in Figure15 is relatively lower for the 90° rib angle, it is higher for the 60° case at a lower Re and marginally reduces with increasing in Re compared with the 15° arrangement. The exergy losses represent difference between the maximum available energy

Figure 12. Intensity of turbulence along span wise direction for rib angles 15°- 90° at Re = 12000 (a) 15° (b) 30° (c) 45° (d) 60° (e) 75° (f) 90° and actual energy. The exergy loss for varying Re and rib angles are shown in Figure 16. The trend shows that exergy loss increases with increases in Re which is an agreement with studies of Elwekeel et al. [47] and Kottayat et al. [48]. The exergy loss for 60° rib angle is relatively higher compared with other rib angles and followed by 75° rib arrangement. The increase in exergy loss for the 60° and 75° angles

is 51.3% and 46.1% respectively when the Re is increased from 23000 to 33000 and it is 47.1% and 45.6% respectively when it is increased from 33000 to 43000. The exergy loss is maximum for the 60° rib arrangement for the Re of 23000, 33000 and 43000. The average heat transfer rate is relatively higher in the case of 60° rib angle as observed in Figure 7 which incurs more exergy loss compared to other rib angles.

Figure 13. Normalized Nu for rib angles of 15°- 90° at Re = 12000 - 43000

Comparison with Previous Studies The present average Nu ratio (Nu/Nu0) for the rib angles of 15° - 90° is compared in Figure 17 a with the average friction factor ratio (f/f0). The highest Nu enhancement is given by 60° continuous ribs and delta backward ribs employed by Han and Park [49] and Han et al. [51]. It is observed that the magnitudes of such enhancement are significantly influenced when a particular rib configuration is provided with varying rib height, pitch, relative spacing and blockage. The results for 30° and 60° rib angles are reasonable with the results of Han and Park [49] and the 90° rib angle is comparable with Han and Park [49] and Han et al. [50]. The performance factor Nu/Nu0/f/f0 as it varies with f/fo are compared in Figure 17 b. The values of Nu/Nu0/f/f0 are varying between 0.68 – 1.1 for the rib angles of 15° - 90°. As such the present values show reasonable performance relative to previous studies [48-50]. The scatter plot of showing the deviation is shown in Figure 18.

Conclusions And Recommendations

Figure 14. Normalized friction factor for rib angles of 15°90° at Re = 12000 - 43000

Figure 15. Thermal hydralulic performance for rib angles of 15°- 90° at Re = 12000 – 43000.

The heat transfer and flow characteristics of ribbed wall duct were numerically studied. The results were predicted with SST k-ω turbulence model with Re number varying between 12000 and 43000. The important conclusions of the present study are as follows: • The key findings on the flow field reveal that the turbulent flow structures in large scale developed on the wall side enhance the uniformity of Nu distribution with reduced magnitude for 60° rib angle. Besides the symmetric secondary flows originated behind the rib which is relatively larger in size causing peak Nu on the mid-section of the duct for 30° and 45° rib angles. • The presence of wake region behind the cylindrical rib causing peak Nu in the middle part of the duct for 15° (Nu/Nuo = 2.45), 30° (Nu/Nuo = 2.6) and 45° (Nu = 2.57) rib angles. The enhanced turbulence associated with decreased mean velocity along the span wise direction increases the normalized Nu at each z/B location towards channel center line and reaches maximum for the rib angles between 15° and 60°. • The position of wake region is highly dependent on separation point over the circular rib as wake moves away radially from the axis of the duct for rib angles of 60°, 75° and 90°. The flow deceleration is relatively higher for 60° and 75° rib arrangements resulting in intense wake region. The turbulent flow structures in large scale originates from side wall have marked effect on the heat transfer for the rib angles of 60°, 75° and 90° and with nearly with equal intensity for 15°, 30° and 45°. • The thermal hydraulic performance factor relatively higher for 60° rib angle at lower Re = 12000 and it marginally increases with increase in Re for 15° rib angle. • The exergy analysis reveals that the exergy loss is relatively higher for 60° and 75° rib angles for Re = 12000 and the variation is marginal among the rib positions at lower

Figure 16. Exergy loss for rib angles of 15° - 90° at Re = 12000- 43000.

Figure 17. Thermal performance of rib angle of all cases with comparision of results obtained in previous studies (a) Nu/ Nuo as dependendent upon f/fo (b) Nu/Nuo/ f/fo as dependent upon f/fo.

Figure 18. Scatter plot showing the deviation of Nu/Nuo as dependent upon f/fo.

Re. The increase in exergy loss for the 60° and 75° angles is 51.3% and 46.1% respectively when the Re is increased from 23000 to 33000 and it is 47.1% and 45.6% respectively when it is increased from 33000 to 43000. Some recommendations for future research work are as follows, • The present numerical study on heat transfer and flow can be further extended for rotating channel with varying heat input. • The numerical analysis can be carried out for understanding flow physics of two pass channel featuring truncated and circular ribs. • Experimental optimization is required to find the geometric parameters of the ribs leading to enhanced thermal hydraulic performance

Nomenclature

Width of the duct , m Hydraulic Diameter, m Diameter of circular rib, m Height of the duct, m Height of the rectangular rib, m Length of the rectangular rib, m Exergy rate, kW friction factor friction factor for a smooth duct Thermal conductivity of air, W/m K Length of the duct, m Nusselt number Nusselt number for a smooth duct Pressure drop, N/m2 pitch distance, m Heat transfer, kW Heat flux, W/m2 Reynolds number

Temperature of air, K Temperature of wall, K Velocity, m/s Density of air, kg/m3 Vorticity, s-1

Acknowledgement

The authors would like to gratefully acknowledge the support provided by B S Abdur Rahman Crescent Institute of Science and Technology during the course of this research.

Authorship Contributions

Conceptualization, Methodology, Resources, Formal analysis and investigation – S.Mohamed Illyas, V.Kumaresan and A. Muthu Manokar. Writing, review and editing – S.Mohamed Illyas, V.Kumaresan and A. Muthu Manokar.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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