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Numerical investigation and multi-criteria optimization of the thermal–hydraulic characteristics of turbulent flow in conical tubes fitted with twisted tape insert

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Abstract

The ever-growing interest in developing compact and more effective heat exchangers necessitates the investigation of combined passive solutions. Despite the diverse related literature, there are no studies on smooth conical tubes (convergent and divergent tubes) fitted with twisted tape inserts. This study analyzes and optimizes the absolute and relative thermal and hydraulic performances of tube heat exchangers, with and without twisted tape inserts, based on Nusselt number and friction factor, by adjusting the tube’s diameter ratio and the operational Reynolds number. A consolidated framework of computational fluid dynamics simulations, data-driven multilayered perceptron-based modeling, and gradient-free genetic dual-objective optimization is employed. The results showed that conventional straight tubes are the most favorable in terms of hydraulic performance, with a maximum friction factor of only 0.042. Convergent tubes are the most effective in terms of thermal performance, with Nusselt numbers up to 475.9. Divergent tubes do not show potentials for heat transfer enhancement unless equipped with a tape insert. Twisted tapes effectively improve the thermal performances of all system configurations but also drastically increase the friction factor. Compared to a baseline design of an empty straight tube, the thermal performance can be improved by up to 74.8%. Almost all Pareto frontier solutions belonged to convergent tubes of different configurations. The selected moderate non-dominated solution (assuming equal importance of thermal and hydraulic performances) corresponds to a Nusselt number of 402.9 and a friction factor of 0.130 for a tape-fitted convergent tube with a diameter ratio of 0.445, operating at a Reynolds number of 39,854. In terms of relative performance, the moderate solution corresponds to a Nusselt number ratio of 1.535 and a friction factor ratio of 6.157 using a tape-fitted convergent tube with a diameter ratio of 0.385, operating at a Reynolds number of 31,254. Overall, convergent tubes are recommended as a simple way for boosting the heat transfer rate and the proposed models can be used as flexible tools for selecting the operating conditions based on the designer’s preference.

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Authors and Affiliations

  1. Mechanical Power Engineering Department, Faculty of Engineering, Cairo University, Giza, 12613, Giza, Egypt

    Muhammed A. Hassan & Mahmoud A. Kassem

  2. Mechanical Engineering Department, Faculty of Engineering, Fayoum University, El-Fayoum, 63514, Egypt

    Amr Kaood

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  1. Muhammed A. Hassan
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  2. Mahmoud A. Kassem
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Contributions

MAH was involved in conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, writing—original draft, writing—review and editing, and supervision. MAK was involved in writing—review and editing and resources. AK was involved in conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, and writing—review and editing.

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Correspondence to Muhammed A. Hassan or Amr Kaood.

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Appendices

Appendix 1: Correlations used for model validation

Sieder and Tate [47]:

$$\text{Nu} = 0.027{ }\text{Re}^{4/5} \text{Pr}^{1/3} \left( {\frac{\mu }{{\mu_{\text{w}} }}} \right)^{0.14} ;0.7 \le \text{Pr} \le 16700;\quad \text{Re} \ge 10^{4} { }$$
(38)

Dittus-Boelter [46]:

$$\text{Nu} = 0.023{ }\text{Re}^{0.23} \text{Pr}^{0.4} \left( {\frac{\mu }{{\mu_{\text{w}} }}} \right)^{0.14} ;\quad 0.6 \le \text{Pr} \le 160;\quad \text{Re} \ge 10^{4} { }$$
(39)

Gnielinski [48]:

$$\text{Nu} = 0.012{ }\left( {\text{Re}^{0.87} - 280} \right)\text{Pr}^{0.4} ;\quad 1.5 \le \text{Pr} \le 500;\quad 3000 \le \text{Re} \le 10^{5} { }$$
(40)

Filonenko [50]:

$$f = { }\left( {1.82{ }\log \text{Re} - 1.64} \right)^{ - 2} ;\quad 2300 < \text{Re} < 10^{6} { }$$
(41)

Petukhov [49]:

$$f = { }\left( {0.79{ }\ln \text{Re} - 1.64} \right)^{ - 2} ;\quad 3000 < \text{Re} < 5 \times 10^{6} { }$$
(42)

Blasius [51]:

$$f = { }0.316{\text{ Re}}^{ - 0.25} ;\quad {\text{Re}} \ge 2 \times { }10^{4} { }$$
(43)

Appendix 2: Full set of simulation results

The full set of simulation results and the regression coefficients of the RSM models are available in the electronic annex attached to the article’s online version.

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Hassan, M.A., Kassem, M.A. & Kaood, A. Numerical investigation and multi-criteria optimization of the thermal–hydraulic characteristics of turbulent flow in conical tubes fitted with twisted tape insert. J Therm Anal Calorim 147, 6847–6868 (2022). https://doi.org/10.1007/s10973-021-10998-7

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