# Internal Flow Analysis of a Heat Transfer Enhanced Tube with a Segmented Twisted Tape Insert

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}/m

^{3}in particular structure configurations [9], it has been employed as a pipe insert to increase the effective surface in the heat exchanger. However, it is generally recommended for low-Reynolds-number fluids, as its high thermal performance is often offset by high head loss [10,11,12]. Besides, uncontrollable size and diameter largely depend on the manufacturing process, which makes it hard to build solid theory. Lacroix et al. estimated the pressure drop of pipes using a simplified model for a cubic unit cell but with a good agreement with experimental results [13]. With the advantage of 3D printing (3DP), the periodic cellular structure is regarded as a promising insert to enhance the heat transfer performance by two-fold advantages, such as large surface area and low-pressure drop. Busse et al. designed periodic open cellular structures (POCS) and carried out a comparative analysis with the randomly packed bed, open-cell foam and honeycomb [14]. They studied material, morphology and wall coupling of POCS, and the result showed that POCS outperform others, particularly at a low flow rate. In reference to stochastic open-cell foams, another octet truss lattice (OTL) structure with a 12 node connection was proposed by Chaudhari et al. [15]. They investigated the effect of porosity on thermal conductivity, permeability, inertial coefficient, friction factor and Nusselt number, and a correlation was also established. The experimental investigation proved that OTL is a possible alternative in heat exchanger/sink in consideration of low pressure drop.

## 2. Geometric Model

## 3. Numerical Method

_{t}in Equation (5) can be obtained in Equation (6).

^{3}, specific heat 4182 J/(kg·K), thermal conductivity 0.601 W/(m·K) and dynamic viscosity 1.003 mPa·s. To inspect the pressure distribution, the pressure–velocity coupling algorithm SIMPLE is selected. A second-order scheme is utilised in pressure, momentum, turbulent terms and energy, while a least-squares cell based spatial discretization is used in the gradient. The turbulent intensity is kept at 5% at the inlet while the hydraulic diameter is fixed at 10 mm. The residual constitutes one of the important parts in numerical simulation, and a tight convergence level at 10

^{−6}is selected.

## 4. Results and Discussion

#### 4.1. Temperature and Velocity Field

#### 4.2. Local Heat Transfer Coefficient

_{x}through the cross-section of the fluid domain was calculated according to Equation (10) and the h

_{x}over average value of the plain tube h

_{0}was plotted in Figure 6, Figure 7 and Figure 8.

_{x}/h

_{0}experienced a sharp increase near 100 mm, where the segmented twisted tape is inserted. However, contrary to expectations, the Reynolds number seemed not to have a strong influence on the convective heat transfer coefficient. However, little different was observed in cases with the same P/D and formed three distinctive group at different length ratios. The best performance observed in cases whose P/D equalled 2.0 in every L/P and Re meant that the effect of the twist ratio (P/D) surpassed the effect of the Reynolds number and dominated the overall range. The small discrepancy within a group may be explained by the following: The Reynolds number is calculated according to the condition at the inlet and may deviate from the actual fluid state in the local turbulent region. Thus, the acutely turbulent flow near the vortex generator could not be reflected accurately.

_{x}/h

_{0}reached a plateau and lasted until the end of the tape; then, a gradual decrease was observed. Smaller L/P at fixed P/D was witnessed by the earlier drop in the local heat transfer heat coefficient after the tape region, which could be read from the change of black dotted data points; even they experienced the same trend at first in accordance with the other twos. This difference can be explained by the early stoppage of the fierce turbulence region caused by twisted tape. In the following process, the tubes with longer tape generally had better performance, which meant the longer tape had positive impacts on heat transfer performance.

_{x}/h

_{0,}which caused the largest difference of about 0.2. However, the effect of the twist ratio still surpassed this effect, so it is safe to conclude that the twist ratio played a dominant role in heat transfer enhancement. One reason is that deviation around the h

_{x}/h

_{0}was observed within a common range from 100 mm to 110 mm, in which all the different twisted tapes existed. Another is that after the common range, the deviation in all subplots could still be observed with the smallest twist ratio (P/D = 2.0) remaining the largest.

#### 4.3. Overall Heat Transfer Coefficient

_{0}varied from 1.125 to 1.235, indicating the enhancement of segmented twisted tape in heat transfer. Displayed in different colours, three distinct zones in different twist ratios (P/D) were observed, which means that a small twist ratio and large length ratio of inserted tape had positive impacts on the heat transfer enhancement. The quantitative results showed that the highest enhancement of mean heat transfer rate could reach up to 23.5% when P/D = 2.0 and L/P = 0.7. For specific cases with the fixed twist ratio, the longer the twisted tape was, the bigger the Nu number was. This could be attributed to the fact that tape with a small twist ratio generated a strong swirl flow, causing a thinner thermal or hydrodynamic boundary layer and promoting heat exchange with the tube wall. Besides, the long smooth surface of twisted tapes contributed to the growth of swirl flow; thus, energy could be transferred fast and effectively across the boundary layer.

## 5. Conclusions

- (1)
- Segmented twisted tapes can disturb the growth of developed flow and generate a vortex, thus increasing local heat transfer coefficient h
_{x}/h_{0}up to 2.8. - (2)
- Twist ratio P/D plays a more critical role in local heat transfer enhancement over length ratio L/P, and a smaller P/D usually has a better performance.
- (3)
- Twisted tapes with P/D = 2.0 and L/P = 0.3 yield the highest heat transfer rate and performance evaluation factor.
- (4)
- In comparison with the smooth tube, the largest enhancement of heat transfer performance in terms of Nu can reach up to 23.5%, but along with a more than doubled friction factor at 2.35.
- (5)
- It seems that a bigger pressure loss is the cost when achieving entirely better heat transfer performance for segmented twisted tape inserts.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

## Nomenclature

A_{x} | cross section area of fluid at location x, m^{2} |

C_{μ} | turbulence model constant |

D | inner tube diameter, mm |

E | total energy, J |

f | friction factor |

h | convective heat transfer coefficient, W m^{−2} K^{−1} |

h_{x} | local convective heat transfer coefficient at the length of x mm, W m^{−2} K^{−1} |

k | turbulent kinetic energy |

L | tape length, mm |

Nu | Nusselt number |

Nu_{0} | Nusselt number in plain tube |

P | pitch of twisted tape, mm |

p | static pressure, Pa |

Q | total heat transfer, W |

q_{m} | mass flow, kg·s^{−1} |

Re | Reynolds number |

S | tube length |

T | temperature, K |

T_{w} | wall temperature |

$\overline{T}$ | average temperature of fluid, K |

u | mean velocity, m s^{−1} |

u_{i} | velocity components, m s^{−1} |

${{u}_{i}}^{\prime}$ | fluctuation velocity components, m s^{−1} |

## Greek symbols

δ_{ij} | Kronecker delta |

ε | turbulent dissipation rate, m^{2} s^{−3} |

λ | thermal conductivity, W m^{−1} K^{−1} |

λ_{eff} | effective thermal conductivity, W m^{−1} K^{−1} |

μ | kinematic viscosity, kg s^{−1} m^{−1} |

μ_{t} | eddy viscosity, kg s^{−1} m^{−1} |

η | performance evaluation factor |

ρ | density, kg m^{−3} |

## References

- Kumar, P.; Judd, R.L. Heat transfer with coiled wire turbulence promoters. Can. J. Chem. Eng.
**1970**, 48, 378–383. [Google Scholar] [CrossRef] - Pak, B.C.; Cho, Y.I. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp. Heat Transf.
**1998**, 11, 151–170. [Google Scholar] [CrossRef] - Xuan, Y.; Li, Q. Heat transfer enhancement of nanofluids. Int. J. Heat Fluid Flow
**2000**, 21, 58–64. [Google Scholar] [CrossRef] - Pavel, B.I.; Mohamad, A.A. An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media. Int. J. Heat Mass Transf.
**2004**, 47, 4939–4952. [Google Scholar] [CrossRef] - Qian, J.-Y.; Li, X.-J.; Wu, Z.; Jin, Z.-J.; Sunden, B. A comprehensive review on liquid–liquid two-phase flow in microchannel: Flow pattern and mass transfer. Microfluid. Nanofluid.
**2019**, 23, 207. [Google Scholar] [CrossRef] - Qian, J.-y.; Wu, Z. Heat transfer analysis on dimple geometries and arrangements in dimple jacketed heat exchanger. Int. J. Numer. Methods Heat Fluid Flow
**2019**, 29, 2775–2791. [Google Scholar] [CrossRef] - Xue, Y.; Ge, Z.; Du, X.; Yang, L. On the Heat Transfer Enhancement of Plate Fin Heat Exchanger. Energies
**2018**, 11, 1398. [Google Scholar] [CrossRef] [Green Version] - Bayram, H.; Sevilgen, G. Numerical Investigation of the Effect of Variable Baffle Spacing on the Thermal Performance of a Shell and Tube Heat Exchanger. Energies
**2017**, 10, 1156. [Google Scholar] [CrossRef] [Green Version] - ERG. Duocel Aluminum Foam Data Sheet. In ERG Material and Aerospace; ERG: Oakland, CA, USA, 1999. [Google Scholar]
- Webb, R.L. Enhancement of single-phase heat transfer. In Handbook of Single-Phase Convective Heat Transfer; John Wiley & Sons, Inc.: New York, NY, USA, 1987. [Google Scholar]
- Kays, W.M.; London, A.L.; Eckert, E.R.G. Compact heat exchangers. ASME J. Appl. Mech.
**1960**, 27, 377. [Google Scholar] [CrossRef] [Green Version] - Boomsma, K.; Poulikakos, D.; Zwick, F. Metal foams as compact high performance heat exchangers. Mech. Mater.
**2003**, 35, 1161–1176. [Google Scholar] [CrossRef] - Lacroix, M.; Nguyen, P.; Schweich, D.; Pham Huu, C.; Savin-Poncet, S.; Edouard, D. Pressure drop measurements and modeling on SiC foams. Chem. Eng. Sci.
**2007**, 62, 3259–3267. [Google Scholar] [CrossRef] - Busse, C.; Freund, H.; Schwieger, W. Intensification of heat transfer in catalytic reactors by additively manufactured periodic open cellular structures (POCS). Chem. Eng. Process. Process Intensif.
**2018**, 124, 199–214. [Google Scholar] [CrossRef] - Chaudhari, A.; Ekade, P.; Krishnan, S. Experimental investigation of heat transfer and fluid flow in octet-truss lattice geometry. Int. J. Therm. Sci.
**2019**, 143, 64–75. [Google Scholar] [CrossRef] - Fan, J.F.; Ding, W.K.; Zhang, J.F.; He, Y.L.; Tao, W.Q. A performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving. Int. J. Heat Mass Transf.
**2009**, 52, 33–44. [Google Scholar] [CrossRef] - Ji, W.-T.; Jacobi, A.M.; He, Y.-L.; Tao, W.-Q. Summary and evaluation on single-phase heat transfer enhancement techniques of liquid laminar and turbulent pipe flow. Int. J. Heat Mass Transf.
**2015**, 88, 735–754. [Google Scholar] [CrossRef] - Bergles, A.E.; Morton, H.L. Survey and Evaluation of Techniques to Augment Convexction Heat Exchanger; MIT Dept. of Mechanical Engineering: Cambridge, MA, USA, 1965. [Google Scholar]
- Wijayanta, A.T.; Aziz, M.; Kariya, K.; Miyara, A. Numerical Study of Heat Transfer Enhancement of Internal Flow Using Double-Sided Delta-Winglet Tape Insert. Energies
**2018**, 11, 3170. [Google Scholar] [CrossRef] [Green Version] - Wijayanta, A.; Pranowo; Mirmanto; Kristiawan, B.; Aziz, M. Internal Flow in an Enhanced Tube Having Square-cut Twisted Tape Insert. Energies
**2019**, 12, 306. [Google Scholar] [CrossRef] [Green Version] - Chang, S.W.; Jan, Y.J.; Liou, J.S. Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape. Int. J. Therm. Sci.
**2007**, 46, 506–518. [Google Scholar] [CrossRef] - Chang, S.W.; Yu, K.-W.; Lu, M.H. Heat Transfers in Tubes Fitted with Single, Twin, and Triple Twisted Tapes. Exp. Heat Transf.
**2005**, 18, 279–294. [Google Scholar] [CrossRef] - Wongcharee, K.; Eiamsa-ard, S. Heat transfer enhancement by twisted tapes with alternate-axes and triangular, rectangular and trapezoidal wings. Chem. Eng. Process. Process Intensif.
**2011**, 50, 211–219. [Google Scholar] [CrossRef] - Thianpong, C.; Eiamsa-ard, P.; Promvonge, P.; Eiamsa-ard, S. Effect of perforated twisted-tapes with parallel wings on heat transfer enhancement in a heat exchanger tube. Energy Procedia
**2012**, 14, 1117–1123. [Google Scholar] [CrossRef] [Green Version] - Hasanpour, A.; Farhadi, M.; Sedighi, K. Intensification of heat exchangers performance by modified and optimized twisted tapes. Chem. Eng. Process. Process Intensif.
**2017**, 120, 276–285. [Google Scholar] [CrossRef] - Manglik, R.M.; Bergles, A.E. Heat Transfer and Pressure Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes_Part II—Transition and Turbulent Flows. J. Heat Transf.
**1993**, 115, 890–896. [Google Scholar] [CrossRef] - Hong, S.W.; Bergles, A.E. Augmentation of Laminar Flow Heat Transfer in Tubes by Means of Twisted-Tape Inserts. J. Heat Transf.
**1976**, 98, 251–256. [Google Scholar] [CrossRef] - Saha, S.K.; Gaitonde, U.N.; Date, A.W. Heat transfer and pressure drop characteristics of laminar flow in a circular tube fitted with regularly spaced twisted-tape elements. Exp. Therm. Fluid Sci.
**1989**, 2, 310–322. [Google Scholar] [CrossRef] - Eiamsa-ard, S.; Thianpong, C.; Promvonge, P. Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements. Int. Commun. Heat Mass Transf.
**2006**, 33, 1225–1233. [Google Scholar] [CrossRef] - Zimparov, V. Enhancement of heat transfer by a combination of threestart spirally corrugated tubes with a twisted tape. Heat Mass Transf.
**2001**, 44, 551–574. [Google Scholar] [CrossRef] - AI-Fahed, S.; Chakroun, W. Effect of tube-tape clearance on heat transfer for fully developed turbulent flow in a horizontal isothermal tube. Int. J. Heat Fluid Flow
**1996**, 17, 173–178. [Google Scholar] [CrossRef] - Hansjosten, E.; Wenka, A.; Hensel, A.; Benzinger, W.; Klumpp, M.; Dittmeyer, R. Custom-designed 3D-printed metallic fluid guiding elements for enhanced heat transfer at low pressure drop. Chem. Eng. Process. Process Intensif.
**2018**, 130, 119–126. [Google Scholar] [CrossRef] - Femmer, T.; Kuehne, A.J.C.; Wessling, M. Estimation of the structure dependent performance of 3-D rapid prototyped membranes. Chem. Eng. J.
**2015**, 273, 438–445. [Google Scholar] [CrossRef] - Martinez, L.I. Investigation of CFD Conjugate Heat Transfer Simulation Methods for Engine Components at SCANIA CV AB. 2017. Available online: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-138758 (accessed on 31 December 2019).
- Balafas, G. Polyhedral Mesh Generation for CFD-Analysis of Complex Structures. Master’s Thesis, Technische Universität München, München, Germany, 2014. [Google Scholar]
- Peric, M.; Ferguson, S. The Advantage of Polyhedral Meshes. Available online: http://www.cd-adapco.com/press_room/-dynamics/24/testVspoly.html (accessed on 21 October 2019).
- Ghadirijafarbeigloo, S.; Zamzamian, A.H.; Yaghoubi, M. 3-D Numerical simulation of heat transfer and turbulent flow in a receiver tube of solar parabolic trough concentrator with louvered twisted-tape inserts. Energy Procedia
**2014**, 49, 373–380. [Google Scholar] [CrossRef] [Green Version] - Eiamsa-ard, S.; Wongcharee, K.; Sripattanapipat, S. 3-D Numerical simulation of swirling flow and convective heat transfer in a circular tube induced by means of loose-fit twisted tapes. Int. Commun. Heat Mass Transf.
**2009**, 36, 947–955. [Google Scholar] [CrossRef] - He, C.H.; Feng, X. Principles of Chemical Engineering; Science Press: Beijing, China, 2007. [Google Scholar]
- Yang, C.; Chen, M.-R.; Qian, J.-Y.; Wu, Z.; Jin, Z.-J.; Sunden, B. Heat transfer study of a hybrid smooth and spirally corrugated tube. Heat Transf. Eng.
**2019**, 1–13. [Google Scholar] [CrossRef] [Green Version]

**Figure 4.**Temperature field comparison between the research object and the smooth tube at different locations. Tube with tape: (

**a**) x = 108 mm, (

**b**) x = 118 mm, (

**c**) x = 138 mm, (

**d**) x = 168 mm, (

**e**) x = 218 mm, (

**f**) x = 418 mm. Smooth tube: (

**g**) x = 108 mm, (

**h**) x = 168 mm, (

**i**) x = 218 mm, (

**j**) x = 418 mm.

**Figure 5.**Contour plot of streamline at different attack angles (x-direction, counter clockwise): (

**a**) 0°, (

**b**) 45°, (

**c**) 90°, (

**d**) 135°.

**Figure 6.**Local convective heat transfer coefficient along the tube: (

**a**) L/P = 0.3, (

**b**) L/P = 0.5, (

**c**) L/P = 0.7.

**Figure 7.**Relationship between heat transfer coefficient and length ratio along the tube: (

**a**) P/D = 2.0, (

**b**) P/D = 3.3, (

**c**) P/D = 4.6.

**Figure 8.**Relationship between heat transfer coefficient and twist ratio along the tube: (

**a**) L/P = 0.3, (

**b**) L/P = 0.5, (

**c**) L/P = 0.7.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, G.; Yang, C.; Zhang, J.; Zong, H.; Xu, B.; Qian, J.-y.
Internal Flow Analysis of a Heat Transfer Enhanced Tube with a Segmented Twisted Tape Insert. *Energies* **2020**, *13*, 207.
https://doi.org/10.3390/en13010207

**AMA Style**

Liu G, Yang C, Zhang J, Zong H, Xu B, Qian J-y.
Internal Flow Analysis of a Heat Transfer Enhanced Tube with a Segmented Twisted Tape Insert. *Energies*. 2020; 13(1):207.
https://doi.org/10.3390/en13010207

**Chicago/Turabian Style**

Liu, Gan, Chen Yang, Junhui Zhang, Huaizhi Zong, Bing Xu, and Jin-yuan Qian.
2020. "Internal Flow Analysis of a Heat Transfer Enhanced Tube with a Segmented Twisted Tape Insert" *Energies* 13, no. 1: 207.
https://doi.org/10.3390/en13010207