The effect of symmetrical perforated holes on the turbulent heat transfer in the static mixer with modified Kenics segments

https://doi.org/10.1016/j.ijheatmasstransfer.2016.03.110Get rights and content

Highlights

  • The model takes into account the coupled effect between fluid and segment wall.

  • The effects of Reynolds number and segment number on the heat transfer are evaluated.

  • In view of thermal performance factor, the perforated parameters are optimized.

  • The synergy between secondary flow and temperature field has been investigated.

Abstract

The numerical simulation on forced convective heat transfer of water in the modified Kenics static mixer (MKSM) was investigated by the three-dimensional turbulent and steady incompressible flow of computational fluid dynamics (CFD). The conservation equations were solved by using finite volume method (FVM) and the SIMPLEC algorithm scheme in ANSYS Fluent 16.1. The simulation results of Nusselt number and the friction factor in MKSM have a good agreement with the literature results. The effects of Reynolds number, perforated diameter, perforated spacing, and segment number on the heat transfer are evaluated in the range of Re = 2000–20,000 under uniform heat tube wall temperature conditions. The Nusselt number increases gradually with increasing Re. Furthermore, both the values and deviations of Nusselt number for different perforated diameter accord with an antisymmetrical tendency at the critical Re = 11,000. It could be seen that the Nusselt number and the friction factor are not sensitive to the increasing perforated spacing within a given perforated diameter. In view of thermal performance factor, the geometrical diameter and spacing of two symmetrical perforated holes are optimized. The MKSM with d/W = 0.3 and s/W = 0.6 have the best performance with the consideration of both heat transfer rate and friction loss compared to the others. Thermal performance factor decreases gradually with increasing Re which indicated that the modified Kenics segments are more effective for heat transfer in lower Re. The local and global synergies between secondary flow and temperature fields have been investigated through field synergy principle.

Introduction

Twisted tape swirl generators as a passive heat transfer enhancement device whose operation without any external power source have acquired extensive research on account of their superiority of simple configuration, ease of manufacture installation and steady performance [1]. The structure of twisted tapes can be obtained by distorting the plastic sheet or metal sheet in practical application [2]. Through employing twisted tapes in tube to produce swirls which can reinforce mainstream fluid to the boundary layer disturbance to thin the boundary layer thickness and enhance the mainstream fluid and boundary layer fluid mixing. Under the coupling effect between twisted tapes and the tube wall, the fluid can produce secondary flow which is perpendicular to the direction of mainstream. For turbulent heat transfer, the temperature drop is mainly occurred in the radial near the tube wall, the generation of secondary flow not only can improve heat transfer between mainstream fluid and boundary layer fluid, but also can conducive to fluid temperature homogenization in the mainstream zone, resulting in the wall temperature gradient increased so as to elevate the mixer’s heat transfer capability.

During the past decades, heat transfer enhancement by the enhanced tube inserted twisted tape has been investigated by many researchers. The enhanced tube inserted twisted tapes not only can partition and block the flow, but also reduce the hydraulic diameter, elongate the twisted flow path and generate a fin effect [3], [4]. All of them can lead to additional heat transfer improvements. Nevertheless, the thermal improvements are accompanied by increased pressure drop at the same time. Therefore, how to optimize the thermohydraulic performance of the tube fitted with twisted tapes has already received increasing attention [5], [6], [7], [8], [9]. Saha et al. [5] experimentally investigated the heat transfer and pressure drop characteristics of turbulent flow in a circular tube fitted with regularly spaced twisted tape connected with rod in the range of Re = 5000–43,000. It was shown that regularly spaced twisted tape elements did not perform better than full-length twisted tapes on the basis of both constant pumping power and constant heat duty. Later, Saha et al. [6] further investigated the effects of the width of tape elements and the diameter of connecting rod and phase-angle between successive tape elements on heat transfer and pressure drop characteristics. The results indicated that a narrower width of tape elements led to a worse thermohydraulic performance, while a thinner connecting rod resulted in a better one. The phase-angle was higher than zero only increased the tape-rod manufacturing complexity rather than yielding any better thermohydraulic performance. Eiamsa-ard et al. [7] experimentally investigated the convective heat transfer behaviors in a circular tube fitted with regularly spaced twisted tape in the range of Re = 2000–12,000, and they found that the Nusselt number and friction factor were both considerably decreased as compared with those of the tube fitted with a typical twisted tape (TTT). Chang et al. [8] experimentally studied compound heat transfer enhancement in a tube fitted with serrated twisted tape. Turbulent heat transfer augmentation attributed to the serrated twisted tape fell in the range of 250–480% of the plain tube level. That was about 1.25–1.67 times the heat transfer level in the tube fitted with typical twisted tape. Later, Chang et al. [9] conducted an experiment to study heat transfer and pressure drop in tube with a broken twisted tape insert which was newly invented without previous investigations available. Their experimental results indicated that the heat transfer coefficient, mean fanning friction factor and thermal performance factor of the broken twisted tape were augmented to 1.28–2.4, 2–4.7 and 0.99–1.8 times of those in the tube fitted with the typical twisted tape. The thermal performance factor of the broken twisted tapes with twist ratio of from 1.0 to 2.5 scored the highest than those of the tubes fitted with the typical and serrated twisted tapes in the range of Re = 1000–40,000.

Recently, some new types of twisted tapes were investigated by some researchers [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. Rahimi et al. [10] experimentally and numerically studied the heat transfer and friction factor characteristics of the tube equipped with perforated, notched and jagged twisted tapes, as compared with those of the typical twisted tape. The results revealed that the Nusselt number and thermal performance factor of the jagged insert were highest in the four kinds of twisted tape. The maximum of Nusselt number and thermal performance factor of the jagged insert were 1.31 times and 1.22 times of those obtained for the typical one. Within the range of Re from 2500 to 9500, Cui et al. [11] investigated the heat transfer characteristics and pressure drop of air flow in a circular tube fitted with edgefold twisted tape. The results demonstrated that the Nusselt number and friction factor of the tube with edgefold twisted tape inserts were 3.9–9.2% and 8.7–74% higher than those of typical twisted tape. They found that the gap width between tube and inserts has a significant influence on the heat transfer, while little influence on pressure drops. Murugesan et al. [12] proposed a twisted tape consisting of wire-nails which not only could induce common swirling flow, but also enhanced turbulence offered by the wire nails. Their investigation showed that Nusselt number, friction factor and thermal performance factor in a tube with twisted tape consisting of wire-nails were 1.08–1.31, 1.1–1.75 and 1.05–1.13 times of those in tube with typical twisted tape, respectively. Eiamsa-ard et al. [13] conducted an experimental investigation on thermohydraulic performance of laminar and turbulent flows in a tube equipped with peripherally-cut twisted tape. The results indicated that the heat transfer rate and friction factor in the tube equipped with the peripherally-cut twisted tapes were significantly higher than those of typical twisted tape and plain tube because of the higher turbulence intensity of fluid in the near wall region generated by the peripherally-cut twisted tape inserts, especially in the laminar flow regime. Murugesan et al. [14], [15] experimentally studied the effect of square-cut and v-cut twisted tape insert on heat transfer, friction factor and thermal performance factor characteristics in a circular tube. They found that the Nusselt number, friction factor and thermal performance factor of square-cut twisted tape were respectively, 1.03–1.14, 1.05–1.25 and 1.02–1.06 times of those in tube with typical twisted tape. Finally, they formulated empirical correlation to match with experimental data of Nusselt number and friction factor. Thianpong et al. [16] employed an experiment to investigate the heat transfer and friction factor in tube equipped with perforated twisted tape (PTT). The comparison results indicated that the maximum heat transfer was obtained by utilizing the tape with s/W = 0.4, d/W = 0.17 and y/W = 3, which was higher than those obtained from the plain tube with and without typical twisted tape by around 27.4% and 86.7%, respectively. Guo et al. [17] invented a center-cleared twisted tape which could reduce the upwind area blocking the flow in the tube while the disturbance of boundary layers was not weakened that much. The computation results revealed that the heat transfer and thermal performance factor of short-width twisted tapes were weakened by cutting off the tape edge, but the center-cleared twisted tape could improve heat transfer when it had a suitable central clearance ratio. Eiamsa-ard et al. [18] experimentally investigated the heat transfer, flow friction characteristics in a tube fitted with the oblique and straight delta-winglet twisted tape over the Re range of 3000–27,000. Their results displayed that the oblique delta-winglet twisted tape produced stronger disturbance and higher heat transfer coefficient compared with the straight delta-winglet twisted tape. On the basis of the delta-winglet study, Wongcharee and Eiamsa-ard [19] conducted an experiment using the twisted tape with alternate-axe and wing to investigate the effects on the thermal performance under turbulent flow condition. They found that the twisted tape consisted of both alternate-axe and trapezoidal wing offered the highest Nusselt number, friction factor as well as thermal performance factor through research. Recently, Eiamsa-ard et al. [20] studied the heat transfer, friction factor and thermal performance factor in a tube fitted with twin–winged twisted tape. The twin delta wings were made three different arrangements. The results showed that all twin–winged twisted tapes provided more superior thermal performance than the TTT. Among the three different arrangements, the twin delta-winged twisted tape in counterflow arrangement offered the best thermal performance factor of 1.26. Nanan et al. [21] investigated the heat transfer enhancement by using perforated helical twisted-tape (P-HTT) in tube. The subsistent holes could effectively reduce the body resistance when the fluid traversed the holes. Their experiment results revealed that the use of P-HTT led to the reduction of heat transfer and friction loss as compared with those of PTT. Apart from these mentioned above, P-HTT yield displayed lower thermal performance factor than the PTT due to a poorer tradeoff between the decreased heat transfer and friction loss.

The application of compound technologies has greatly improved the ability of heat transfer enhancement compared with single technologies [22], [23], [24], [25], [26]. Promvonge and Eiamsa-ard [22] experimentally investigated the thermal performance in a tube equipped with both conical-ring and twisted tape. The results indicated that this compound technique had showed better performance than using conical-ring alone. Promvonge [23] experimentally studied the heat transfer performance in a tube placed combined wire coil with twisted tape over the Re range of 3000–18,000. The results showed that the compound technology can obtain perfect heat transfer performance at lower Re for the lowest values of the coil spring pitch and twist ratio. Under the laminar flow condition, Saha et al. [24] experimentally investigated the heat transfer behaviors in a tube fitted with wire coil and center-cleared twisted tape. The experiment revealed that the thermal boundary layer separation and reattachment was more frequent than the hydrodynamic boundary layer. Therefore, the increase in heat transfer was more than the increase in pressure drop. Later, Eiamsa-ard et al. [25] investigated the effect of circular-ring and twisted tape on the thermohydraulic performance. They reported that the mean Nusselt number, friction factor and thermal performance factor in the tube equipped with compound components were 25.8%, 82.8% and 6.3% over the circular-ring alone. The maximum thermal performance factor of 1.42 was attained under Re = 6000, the circular-ring pitch ratio of 1.0 and the twisted tape twist ratio of 3.0. Rout and Saha [26] experimentally studied the heat transfer and pressure drop characteristics through a circular tube fitted with wire coil and helical screw-tape. Friction factor and Nusselt number data along with the correlations had been presented, which showed that the thermal boundary layer separation and reattachment was more frequent than the hydrodynamic boundary layer.

It should be noted that the fluid flow and heat transfer in a tube with staggered Kenics segments with central holes were investigated in the range of Reynolds numbers between 6000 and 28,000 by Lei et al. [27]. The modified Kenics segments are different from PTT and P-HTT [10], [16], [21]. It was found that the modified Kenics segments decreased the friction factor by 8.0–16.1% and enhanced the heat transfer by 34.1–46.8% in comparison with the TTT. To the best of our knowledge, the effect of perforated holes on the enhancement mechanism of turbulent flow and heat transfer still lack systematic study and discussion. It would be more interesting to investigate the enhancement characteristic and synergy degree of heat transfer in the tube with modified Kenics segments. Furthermore, it is necessary to optimize modified Kenics segments to enlarge thermo-hydraulic performance and improve the field synergy degree. An attractive option is numerically investigated the effects of Reynolds number, perforated diameter, perforated spacing, and segment number on Nusselt number, friction factor and thermal performance factor in the range of Re = 2000–20,000. The CFD model was validated by comparing the predicted numerical results against the thermal numerical data reported in the literature [27].

Section snippets

Physical model

The geometry of the static mixer with modified Kenics segments (MKSM) is depicted in Fig. 1. Two different geometric models are created. Compared the heat transfer and friction factor with numerical data available in the literature provided by Lei et al. [27], [28], the same geometry of the mixer is created: the length of one twist to the diameter of the twist is 2 and the intersection angle between the adjacent twisted tapes is φ = 30°, the modified insert has two holes with a pitch of 19 mm and

Governing equations and boundary conditions

The problem under consideration is assumed to be three-dimensional with constant fluid properties, incompressible and turbulent. The RNG k–ε turbulence model is applied to solve the numerical simulation of the enhanced tube which provides improved predictions of the near-wall flows and flows with high streamline curvature. Equations of continuity, momentum and energy for the fluid flow are given below in a tensor form [33],

Continuity equation:(ρvi)xi=0

Momentum equation:xj(ρvivj)=-pxi+xjμ

Effect of perforated diameter

The profiles of Nusselt number, friction factor and thermal performance factor with the increase of the ratio of perforated diameter to width d/W are respectively displayed in Fig. 5. It can be seen from Fig. 5a that two obvious maxima of Nusselt number are attained at d/W = 0.6 and d/W = 0.7. For the other d/W, the tendency of Nusselt number has a small increment for Re > 8000 and then slightly decrease for Re < 8000. That is to say, the largest Nusselt number is obtained at d/W = 0.6. The modified

Conclusions

The three-dimensional steady incompressible turbulent flow and forced convective heat transfer in the MKSM was investigated using ANSYS Fluent 16.1. The simulation results of Nusselt number and the friction factor in MKSM have a good agreement with the literature results. The effects of Reynolds number, perforated diameter, perforated spacing, and segment number on the heat transfer are evaluated in the range of Re = 2000–20,000 under uniform heat tube wall temperature conditions.

The Nusselt

Conflict of interest

None declared.

Acknowledgments

The authors acknowledge funding support for this research from the National Natural Science Foundation of China (21476142, 21306115, 21106086), the Program for Liaoning Excellent Talents in University (LR2015051), the Natural Science Foundation of Liaoning Science and Technology Bureau of China (2015020148), and Liaoning BaiQianWan Talents Program (2013921047). The valuable suggestions of the anonymous reviewer are greatly appreciated.

References (40)

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