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. 2021 Oct 8;11(1):20068.
doi: 10.1038/s41598-021-99476-6.

Robust and universal predictive models for frictional pressure drop during two-phase flow in smooth helically coiled tube heat exchangers

M A Moradkhani  1 , Seyyed Hossein Hosseini  2 , M Mansouri  1 , G Ahmadi  3 , Mengjie Song  4
Affiliations

Robust and universal predictive models for frictional pressure drop during two-phase flow in smooth helically coiled tube heat exchangers

M A Moradkhani et al. Sci Rep. .

Abstract

There is a lack of well-verified models in the literature for the prediction of the frictional pressure drop (FPD) in the helically coiled tubes at different conditions/orientations. In this study, the robust and universal models for estimating two-phase FPD in smooth coiled tubes with different orientations were developed using several intelligent approaches. For this reason, a databank comprising 1267 experimental data samples was collected from 12 independent studies, which covers a broad range of fluids, tube diameters, coil diameters, coil axis inclinations, mass fluxes, saturation temperatures, and vapor qualities. The earlier models for straight and coiled tubes were examined using the collected database, which showed absolute average relative error (AARE) higher than 21%. The most relevant dimensionless groups were used as models' inputs, and the neural network approach of multilayer perceptron and radial basis functions (RBF) were developed based on the homogenous equilibrium method. Although both intelligent models exhibited excellent accuracy, the RBF model predicted the best results with AARE 4.73% for the testing process. In addition, an explicit FPD model was developed by the genetic programming (GP), which showed the AARE of 14.97% for all data points. Capabilities of the proposed models under different conditions were described and, the sensitivity analyses were performed.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
MLP network for used estimation of two-phase FPD in coiled tubes.
Figure 2
Figure 2
Flowchart of GP approach used for modeling of the two-phase FPD in coiled tubes.
Figure 3
Figure 3
Data distribution of gathered data for two-phase FPD in helical coiled tubes.
Figure 4
Figure 4
Comparison of the experimental FPD data with those estimated by the previous correlations.
Figure 5
Figure 5
Heatmap of Spearman’s correlation coefficient between different factors.
Figure 6
Figure 6
Comparison of the experimental FPD data with those estimated by the MLP (a) and RBF (b) models.
Figure 7
Figure 7
Comparison of the experimental FPD data with those estimated by GP model (Eq. (20)).
Figure 8
Figure 8
Effect of mass flux on the variation of two-phase FPD versus vapor quality. Comparisons of predictions of GP correlation (Eq. (20)) and RBF model with the corresponding experimental values.
Figure 9
Figure 9
Effect of saturation temperature on the variation of two-phase FPD versus vapor quality. Comparisons of predictions of GP correlation (Eq. (20)) and RBF model with the corresponding experimental values.
Figure 10
Figure 10
Effect coil to tube diameter ratio on the variation of two-phase FPD versus vapor quality. Comparisons of predictions of GP correlation (Eq. (20)) and RBF model with the corresponding experimental values.
Figure 11
Figure 11
Effect of working fluids on the variation of the two-phase FPD versus vapor quality. Comparisons of predictions of GP correlation (Eq. (20)) and RBF model with the corresponding experimental values,.
Figure 12
Figure 12
Comparing the importance of operating parameters in two-phase FPD.
See this image and copyright information in PMC

References

    1. Zhou G, Zhang Y. Performance of a split-type air conditioner matched with coiled adiabatic capillary tubes using HCFC22 and HC290. Appl. Energy. 2010;87:1522–1528. doi: 10.1016/j.apenergy.2009.10.005. - DOI
    1. Alimoradi A, Olfati M, Maghareh M. Numerical investigation of heat transfer intensification in shell and helically coiled finned tube heat exchangers and design optimization. Chem. Eng. Process. Process Intensif. 2017;121:125–143. doi: 10.1016/j.cep.2017.08.005. - DOI
    1. Kushwaha N, Kumawat TC, Nigam KDP, Kumar V. Heat transfer and fluid flow characteristics for Newtonian and non-Newtonian fluids in a tube-in-tube helical coil heat exchanger. Ind. Eng. Chem. Res. 2020;59:3972–3984. doi: 10.1021/acs.iecr.9b07044. - DOI
    1. Huang Z, Zou Y, Wei X, Ding J, Lu J. Mixed convection heat transfer of molten salt outside coiled tube. Int. Commun. Heat Mass Transf. 2021;120:105004. doi: 10.1016/j.icheatmasstransfer.2020.105004. - DOI
    1. Mandal SN, Das SK. Gas–liquid flow through helical coils in vertical orientation. Ind. Eng. Chem. Res. 2003;42:3487–3494. doi: 10.1021/ie0200656. - DOI