NUMERICAL PREDICTIONS ON FLOW AND HEAT TRANSFER IN HEAT EXCHANGER TUBE EQUIPPED WITH VARIOUS FLOW ATTACK ANGLES OF INCLINED-WAVY SURFACE

Numerical analysis on flow configuration, heat transfer behavior and thermal performance in the heat exchanger tube equipped with various flow attack angles of the inclined wavy surface are presented. The laminar flow (Re = 100 – 1200) and turbulent flow (Re = 3000 – 10000) are considered for the present investigation. The flow attack angles of the inclined wavy surface are varied as 15 – 60. The finite volume method with SIMPLE algorithm is selected to evaluate the current problem. The numerical results are reported in terms of flow and heat transfer mechanisms. The performance evaluations in forms of the Nusselt number ratio (Nu/Nu0), friction factor ratio (f/f0) and thermal enhancement factor (TEF) are also concluded. As the results, the vortex flow, impinging flow and thermal boundary layer disturbance are detected when inserted the inclined wavy surface in the heat exchanger tube. These behaviors effect for the augmentation of the heat transfer rate, pressure loss and thermal performance. The optimum flow attack angle of the inclined wavy surface for the laminar and turbulent flows are also concluded.


INTRODUCTION 1
The development of the heat exchanger in various industries is very important for the energy saving process. The thermal performance improvement in the heat exchanger can do by various methods. The insertion of the vortex generator or turbulator in the heat exchanger or tube/channel heat exchanger is one of the methods to enhance heat transfer rate and thermal performance. The generator can produce the vortex flow and impinging flow, which disturbs the thermal boundary layer on the heat transfer surface. The type, shape, dimension, arrangement, etc., of the vortex generators effect for the flow structure and heat transfer behavior. The examples for the investigations on heat transfer enhancement in the heat exchangers with various types of the vortex generators are performed as follows. Menasria et al. (2017) investigated the turbulent flow and heat transfer in a solar heater channel with rectangular baffle. The Reynolds number, blockage ratio and pitch ratio were varied. They reported that the blockage ratio of 0.7 with the pitch spacing ratio of 2 gives the highest thermo-hydraulic performance factor around 0.875. The augmentations on heat transfer and friction factor are around 2.16 and 15.95 times above the smooth channel, respectively. Alam and Kim (2016) numerically studied thermal performance in a solar air heater duct with semi ellipse shaped obstacles. The influences of the flow attack angle (30 o -90 o ), arrangement (inline and staggered) and Reynolds number (6000 -18,000) on heat transfer and friction loss were presented. They concluded that the flow attack angle of 75 o performs the greatest heat transfer rate. They also stated that the maximum heat transfer rate and friction factor are around 2.05 and 6.93, respectively for staggered arrangement, while around 1.73 and 6.12, respectively, for inline arrangement. Chai et al. (2016a) presented laminar flow and thermo-hydraulic performance in a microchannel heat sink with fan shaped ribs. They reported that the average Nuseelt number increases around 6 -101% and the total thermal resistance decreases around 3 -40% for the aligned fan-shaped ribs, while the average Nusselt number enhances around 4 -103% and total thermal resistance reduces around 2 -42% for the offset fan-shaped ribs when compared with the smooth channel. Rajaseenivasan et al. (2015) compared between circular and V-shaped tabulators on heat transfer and pressure loss in a solar air heater channel. Chai et al. (2016b) numerically investigated on convective heat transfer in a microchannel heat sink with offset ribs for laminar flow regime (190 ≤ Re ≤ 838). They summarized that the Nusselt number and friction factor are around 1.42 -1.95 and 1.93 -4.57 times above the smooth channel, respectively, while the performance evaluation criteria is around 1.02 -1.48. Zhan and Park (2016) presented the effects of plate angle on flow bifurcations and heat transfer characteristics in a channel with inclined plates. The flow configuration and heat transfer characteristic with different angle of the inclined plate were concluded. Sabzpooshani et al. (2014) reported the exergetic performance evaluation of a single pass baffled solar air heater. They found that the addition of the fin and baffle can lead to noticeable enhancement of the exergy efficiency. Hong et al. (2017) studied the heat transfer and flow structure in a wavy corrugated tube for Re = 7500 -20,000. They showed that the wavy configuration can help to improve heat transfer rate and thermal performance when compared with the smooth tube. They also reported that the greatest performance evaluation criterion for the wavy corrugated tube is around 1.56.

Frontiers in Heat and Mass Transfer
Available at www.ThermalFluidsCentral.org Frontiers in Heat and Mass Transfer (FHMT), 11, 10 (2018) DOI: 10.5098/hmt.11.10 Global Digital Central ISSN: 2151-8629 Sawhney et al. (2017 experimentally investigated the pressure loss, heat transfer configuration and thermal performance in a solar air heater with wavy delta winglet. The number of wave (3, 5 and 7), Reynolds number (4000 -17,300), arrangement (inline and staggered) and relative longitudinal pitch (3, 4, 5 and 6) were varied. They reported that the maximum Nusselt number is around 223% over the flat plate with the friction loss around 10.3 times above the base case. They also stated that the optimum thermo-hydraulic performance is found to be around 2.09. Li et al. (2016) numerically reported the laminar flow and heat transfer in a microchannel heat sink with triangular cavities and rectangular ribs for Re = 173 -635. The influences of relative rib width and relative cavity width on the flow structure and performance were investigated. Shirvan et al. (2017) summarized the effects of wavy surface on natural convection heat transfer in a cosine corrugated square cavity filled with nanofluid. Xu et al. (2015) experimentally investigated on thermal performance enhancement in a wavy finned flat tube heat exchanger for the Reynolds number in the range 1340 -13,476. They stated that the Nusselt numbers of discontinuous type, staggered type and vortex-generator type are increased by 11.29%, 28.61% and 56.46% on average, and the friction factors are increased by 3.23%, 66.26% and 48.58% on average, respectively. Xiao et al. (2017) studied the augmentations on heat transfer and performance in a wavy finned flat tube by water spray cooling for Re = 210 -680. They claimed that the Nusselt numbers of three water flow rates are increased by 48 -68% on average when compared to the case without spray. Du et al. (2014) performed the investigations on heat transfer augmentation in a wavy finned flat tube with punched longitudinal vortex generators.
The flow attack angle of the delta winglet vortex generators was considered. They claimed that the optimum performance evaluation criterion is detected at the flow attack angle of 25 o around 1.23. Khan et al. (2015) studied thermal performance of 3D wavy channel based printed circuit heat exchanger. They stated that the wavy surface of the channel can improve the heat transfer rate and thermal performance higher than the plain channel.
In the present work, the combinations of the inclined baffle and wavy surface called "inclined wavy surface" are presented. The inclined wavy surface is equipped in the heat exchanger tube to change the flow structure. The presumption for the present research, the inclined wavy surface can create the flow, which disturbs the thermal boundary layer on the heat transfer surface. The disturbance of the thermal boundary layer is the reason for heat transfer and thermal performance augmentations. The influences of the flow attack angle for the inclined wavy surface on heat transfer, pressure loss and thermal performance are considered. The investigations are done on both laminar and turbulent flows with the Reynolds number in range 100 -1200 and 3000 -10,000, respectively.

BOUNDARY CONDITION AND ASSUMPTION
The assumptions for the present investigation are as follows; 1. The flow and heat transfer are steady in three dimensions. 2. The test fluid is air at 300K with the Prandtl number around 0.707.
3. The air is set as incompressible fluid on both laminar and turbulent flows. 4. The thermal properties of the air assume to be constant at the average bulk mean temperature. 5. The forced convective heat transfer is considered, while the natural convection and radiation are ignored. 6. The body force and viscous dissipation are uncounted.
The boundary conditions for the computational domain on both laminar and turbulent flow are concluded as Table. 1

MATHEMATICAL FOUNDATION
The heat exchanger tube equipped with the inclined wavy surface is governed by the continuity, the Navier-Stokes equations and the energy equation.
For laminar flow, the energy equation is discretized by the SOU scheme, while the governing equations are discretized by power law scheme. All governing equations are discretized with the SOU numerical scheme for the turbulent flow. The current investigation is resolved by finite volume method with SIMPLE algorithm. The solutions are measured to be converged when the normalized residual values are less than 10 −5 for all variables, but less than 10 −9 only for the energy equation.
The realizable k- turbulent model is selected for the turbulent part: and: the constant values are as follows: The main parameters are Reynolds number, friction factor, local Nusselt number, average Nusselt number and thermal enhancement factor.
The Reynolds number is calculated as: The friction factor, f, is measured by pressure drop, p, across the periodic module, L: The local heat transfer is written as: The average Nusselt number can be obtained by: The Thermal enhancement factor (TEF) is calculated by the augmentations on both heat transfer and friction factor at similar pumping power: The Nu 0 and f 0 are the Nusselt number and friction factor for the smooth circular tube (Cengel and Ghajar (2015)), respectively. Figs. 2 and 3 report the verifications of the smooth tube for laminar and turbulent flows, respectively. The differences of the Nusselt number and friction factor between the correlation values and present values are around ±0.03% and ±0.05%, respectively, for laminar flow and around ±5% and ±11%, respectively, for turbulent flow. As the results above, it can be concluded that the numerical model of the heat exchanger tube with wavy surface has reliability to predict flow and heat transfer mechanisms.

NUMERICAL RESULT
The numerical results are separated into two parts; laminar and turbulent flows. The flow configuration, heat transfer behavior and thermal performance evaluation are stated in each part. The content for the numerical result is illustrated as follows; o    surface in the heat exchanger tube gives the Nusselt number around 2 -9 times above the smooth tube with no generators. The addition of the inclined wavy surface in the heat exchanger tube not only increases in heat transfer rate, but also augments pressure loss. The present of the inclined wavy surface in the heat exchanger tube provides higher friction loss than the smooth circular tube in all cases (f/f 0 > 1). As the figure, the pressure loss increases when enhancing the Reynolds number. The maximum and minimum values of the f/f 0 are found at the flow attack angles of 60 o and 15 o , respectively. In the range studies, the present of the inclined wavy surface in the test section is around 7 -65 times higher than the smooth tube with no generator. In addition, the low flow attack angle can help to reduce the friction loss in the heat exchanger.
Almost cases, the installation of the inclined wavy surface in the heat exchanger tube enhances the thermal performance higher than the smooth tube (TEF > 1). Considering at Re = 1200, the lowest TEF is The relations of the Nu/Nu 0 , f/f 0 and TEF with the flow attack angle for the heat exchanger tube inserted with the inclined wavy surface are depicted as Figs. 10a, b and c, respectively. As seen in the figures, it can be concluded that the suggested flow attack angle for the inclined wavy surface of the circular tube heat exchanger is around 30 o -40 o due to these flow attack angles give high heat transfer rate and thermal performance.

Flow and heat transfer behavior
The  2 iso-surface, tangential velocity vector and longitudinal vortex flow are plotted for the heat exchanger tube inserted with the inclined wavy surface at turbulent regime to describe the flow mechanism in the test tube. Figs. 11a

Performance analysis
The performance evaluations in the heat exchanger tube equipped with the inclined wavy surface at various flow attack angles are reported in terms of the Nusselt number ratio (Nu/Nu 0 ), friction factor ratio (f/f 0 ) and thermal enhancement factor (TEF) similarly as the laminar regime.
The relations of the Nu/Nu 0 , f/f 0 and TEF with the Reynolds number at various flow attack angles of the inclined wavy surface are depicted as Figs. 17a, b and c, respectively. In general, the Nu/Nu 0 decreases when increasing the Reynolds number for all flow attack angles. The insertion of the inclined wavy surface in the heat exchanger tube performs higher heat transfer rate than the smooth circular tube for all cases (Nu/Nu 0 > 1). The peak of heat transfer rate is detected for the flow attack angles in the range 45 o -60 o , while the reverse trend is found at the inclined wavy surface with the flow attack angle of 15 o . The augmentation on heat transfer rate depends on the strength of the vortex flow and impinging flow. The high flow attack angle can perform the strong vortex flow and impinging flow in the test section. In the range studies, the Nusselt number is around 3.0 -6.7 times above the smooth tube when inserts the inclined wavy surface in the heat exchanger tube.
The insertion of the inclined wavy surface in the tube leads to augment pressure loss across the test section. The present of the inclined wavy surface in the heat exchanger tube gives higher friction loss than the smooth tube in all cases (f/f 0 > 1). As seen, the f/f 0 slightly increases when enhancing the Reynolds number for all flow attack angles. The maximum and minimum friction factor values are found at the flow attack angle of 60 o and 15 o , respectively. For the present-study condition, the friction factor is around 15 -80 times over the smooth tube. In addition, the low flow attack angle of the inclined wavy surface can help to reduce the pressure loss in the test tube.
Due to the insertion of the inclined wavy surface in the heat exchanger tube leads to the augmentations on both heat transfer rate and friction loss, therefore the thermal enhancement factor is selected to decide the performance in the test section. Generally, the TEF decrease when augmenting the Reynolds number for all flow attack angles. The optimum TEF is detected for the flow attack angle in the range 20 o -30 o . The TEF is found to be maximum at the flow attack angle of 30 o and Re = 3000 around 1.9. In the range studies, the TEF is around 0.9 -1.9 depends on the flow attack angle and Reynolds number. The relations of the Nu/Nu 0 , f/f 0 and TEF with the flow attack angle for the heat exchanger tube inserted with the inclined wavy surface at various Reynolds numbers are plotted as Figs. 18a, b and   The insertion of the inclined wavy surface in the heat exchanger tube changes the flow structure and heat transfer behavior for both laminar and turbulent flows. The vortex flow, impinging flow and thermal boundary layer disturbance are detected when inserting the inclined wavy surface in the heat exchanger tube. These behaviors lead to higher heat transfer rate and thermal performance.
The flow and heat transfer patterns for the laminar and turbulent flows are found closely, but the strength of the flow is not equal.
The suggested attack angle for the laminar region is around 30 o -40 o , while around 20 o -30 o for the turbulent flow when considered at the thermal enhancement factor.