Evaluation of heat transfer correlations for two-phase flow boiling in twisted tapes inserted tubes

Many experimental researches were conducted in the twisted tapes inserted tubes, and many correlations were proposed and evaluated. However, most of the evaluations were based on specific experimental data, and the number of correlations evaluated was limited in each paper. This paper conducted a review of correlations and experimental investigations of the two-phase flow boiling heat transfer coefficient for twisted tapes inserted tubes, the key forms of the 5 correlations were reviewed, and the prediction accuracy of the 5 correlations was evaluated against the 508 published experimental data. This paper proposed a new correlation which has a MAD of 17.2%, 10.2% lower than the best existing correlation.


Introduction
The high heat transfer efficiency and miniaturization requirements of heat exchangers have promoted the development of flow boiling in intensified heat transfer tubes.The twisted tape is widely used in passive enhanced heat exchange equipment because the twisted tape is easy to install and remove, it can be used directly in a new exchange equipment or reinserted into an old one.Due to the complexity of the internal mechanism, the current models for predicting the heat transfer coefficient of flow boiling are generally limited.Therefore, in this paper, the prediction method of boiling heat transfer coefficient in the interpolated torsion belt tube is studied, to more accurately predict the boiling heat transfer coefficient and friction pressure drop, and provide a reference for the design of heat exchanger.

Theory of enhanced heat transfer
The twisted tape is mainly to form the vortex flow of the tube-side fluids to enhance the heat transfer so that the fluid flow velocity near the boundary layer increases.Meanwhile, the mutual mixing of the two-phase fluids is accelerated.The existence of interpolation in the tube will cause flow blockage, flow redistribution and induce secondary flow.Due to the flow blockage, the free flow area is reduced, so that the influence of viscosity in the flow process is reduced.The existence of secondary flow leads to the generation of eddy current, and the efficiency of fluid mixing is accelerated, which increases the temperature gradient and enhances the heat exchange [1] .Under the same experimental conditions, the difference in the two-phase flow boiling heat transfer coefficient between the tube interpolated twist strap and the smooth tube is mainly affected by the torsion rate y.

Review of the existing empirical correlations
There are 5 existing empirical correlations for calculating h for two-phase flow boiling in the tube interpolated twist strap are briefly reviewed in this paper.The key forms of these correlations are briefly summarized in Table 1.

Evaluation of the existing empirical correlations
508 experimental data collected from 5 publicly published thesis which covered 3 kinds of refrigerants was compiled here in Table 2.The details of each data source are summarized in Table 2. Some key parameters of the database are as follows: Quality x = 0-1; heat flux q =5-20 kW/m 2 ; mass flux G =75-389 kg/m 2 s; saturation pressure Psat: 239-489 kPa; diameter di: 0-16 mm; torsion rate y: 3-14; twist tape thickness e: 0.1-0.5 mm.

∋ ( ∋ ( ∋(
∋ ( ∋ ( ∋( where y(i)pred and y(i)exp is the predicted value of point i, and y(i)exp is the experimental value of the point i, and N is the number of the total data points.
where MAD means the mean absolute relative deviation and MRD means the mean relative deviation.For better studying the heat transfer characteristics of flow boiling in the interpolated twisted belt tubes and to study the applicability of 5 existing empirical correlations.This paper selects several representative experimental data to observe the changes in the two-phase flow boiling heat transfer coefficient with dryness and torsion of twisted belts and to analyze the prediction follow-up of the correlations.As can be seen from Table 3 and Figures 1-3: a.As can be seen from Table 3, the correlation with the highest prediction accuracy is Mogaji et al. [5], which has a MAD of 27.4%, and N30 of 63.3%, followed by Kanizawa et al. [6], whose prediction MAD is 32.8%, and the prediction MAD of the other models is greater than 40%.Different correlations have different prediction effects on different working fluids.For example, the predicted values of R113 and R134a working fluids in Kanizawa et al. [6] are lower than the experimental values, while the predicted values of Mogaji et al. [5] are relatively uniformly distributed around the experimental values for all working fluids.b.Generally speaking, the smaller the inserted twisted tape torsion rate y is, the greater the heat transfer coefficient is, because the smaller the torsion rate y of the twisted tape is, the stronger the disturbance to the flow is, and the centrifugal force near the wall increases, which in turn enhances the heat exchange.Under different experimental conditions, the changing trend of heat transfer coefficient with dryness is varying, and the change of two-phase flow boiling coefficient of heat transfer with dryness has a great relationship with the flow pattern.In the case of intermittent and annular flow patterns, as shown in Figure 1a, generally as dryness increases the two-phase flow boiling coefficient of heat transfer increases, and this trend is more obvious in the case of small dryness, and with the increase of dryness, there will be dryness in the tube, and then the two-phase flow boiling coefficient of heat transfer will decrease.and in the stratified flow, as shown in Figure 3a, the two-phase flow boiling coefficient of heat transfer does not change significantly with the dryness over the whole dryness range.c.From Figure 1b, Figure 2b, Figure 3a, and Figure 3b, it can be seen that Mogaji et al. [5] have the best prediction performance, and Akhavan-Behabadi et al. [4] have unsatisfactory prediction results.The prediction and follow-up of the Kedzierski and Kim [3] models may even contradict the experimental results.d.On the whole, Mogaji et al. [5] have the best prediction accuracy and predictability with dryness, and it is recommended to give priority to them in engineering.Correlation formulas with better accuracy and a more concise form of prediction effect need to be proposed.

New proposed correlation
Based on 508 experimental data mentioned in Table 3 shows the predicted MAD and MRD of the new model for the whole database and the predicted MAD and MRD of the new correlation for different refrigerants, and Figure 4a and Figure 4a show the prediction performance of the new correlation based on the 508 experimental data mentioned in Table 2. From Table 3, Figure 4a, and Figure 4a, the new correlation has a small prediction error value for the experimental data, and the prediction MAD of the new correlation for the whole database is 17.2%, and the MRD is 0.1%.
Most of the prediction values (Figure 4b) are in the error band of 30%, and the predicted values are more evenly distributed on both sides of the experimental values over the entire dryness range (Figure 4a).This indicates that the new model has a good prediction effect on all data in the whole dryness range, and the prediction error of the new correlation for different working fluids has some deviations, the prediction error of R113 and R134a is small, and the prediction error of R12 is the largest.

Conclusion
A survey of two-phase flowing correlations of heat transfer in twisted tape inserted tubes was carried out.There are 5 classical correlations for the prediction of heat transfer in twisted tape inserted tubes are reviewed, and 508 experimental data are collected.the following conclusions can be seen: a.The correlation with the highest prediction accuracy was Mogaji et al. [5], which had a MAD of 27.4% and N30 of 63.3%.b.The torsion rate y of the inserted twist tape affects the two-phase flow boiling heat transfer coefficient, generally speaking, the heat transfer coefficient increases with the decrease of the torsion rate y of the interpolated twist tape.c.The changing trend of heat transfer coefficient with dryness is different in different experimental conditions, and the change of heat transfer coefficient with dryness has a great relationship with the flow pattern.d.This paper proposed a new correlation which has a MAD of 17.2%, 10.2% lower than the best existing correlation.

Figure 4 .
Figure 4. Comparison of the new correlation with the entire data.

Table 2 .
The available experimental data.correlationsforcalculatinghfor two-phase flow boiling in the tube interpolated twist strap are evaluated based on 508 experimental data mentioned in Table2.The prediction of these correlations is summarized in Table3.

Table 3 .
MAD and MRD of correlations.