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**Chapter 3. Evaluation of the existing flow condensation models**

With the advent of novel substitute refrigerants, the well-established semi-analytical correlations for flow condensation heat transfer are challenged by the different thermos-physical properties and failed to predict the new applications accurately. Working under high reduced pressure conditions, CO_{2} together with some substitute refrigerants, such as R404a and R410a, are known as “high-pressure” fluids. One significant feature of these refrigerants is that the vapour densities are higher than those of conventional refrigerants, such as R134a and R22, under equivalent working conditions. The different thermophysical properties lead to the different heat transfer characteristics and also calls into question the validity of applying the heat transfer and pressure drop models developed for traditional refrigerants to the novel refrigerants. This chapter compares the predictions of the existing flow regime transition criteria, flow condensation heat transfer and pressure drop models with the relevant experimental data available in the open literature, to identify the necessity for the development of a specialised flow condensation model for CO_{2}.

**Flow regime prediction for CO**_{2}** in-tube flow condensation**

To find a suitable flow regime transition predictor for CO_{2} in-tube flow condensation, the Soliman modified Froude number Fr_{so}, and the dimensionless vapour velocity J_{G}, proposed by Cavallini et al.[35], are evaluated by the observed flow regime points by Jang and Hrnjak in the coordinate of mass flux versus vapour quality, as shown in Figure 3.1 and 3.2.

Dobson et al.[26] verified Soliman’s Froude number against the flow regime observations of refrigerants R-134a, R22,and 60/40 and 50/50 blends of R-32 and R125 in horizontal tubes with inner diameters of 3.14mm, 4.57mm, and 7.04mm, respectively. Soliman’s transition criteria agreed well with Dobson’s experimental observations based on a comparison between the predicted and experimental effects of mass flux, tube diameter and saturation pressure on flow regime transition. Dobson et al.[36] proposed that Fr_{so}=18 was the value for transition from annular to wavy flow for the refrigerants R12 and R134a. In Figure 3.1, it can be seen that Soliman’s transition values of Fr_{so}=6 and Fr_{so}=14, are better fits for the effects of mass flux and vapour quality on the CO_{2} flow regime transition. The smaller value of Fr_{so}=14 compared to the original value of Fr_{so}=18 means that annular flow is sustained for longer with CO_{2} than is the case for R12 and R134a. The physical interpretation is that the required inertia force to overcome the increasing liquid gravity to form an annular flow is smaller for CO_{2} than for R12 and R134a under equivalent working conditions. The smaller inertia force of CO_{2} can be explained regarding the following comparison of the physical properties of the refrigerants. The dynamic viscosity of liquid CO_{2} at a saturation temperature of -15ºC is 62% and 75% of that of R12 and R134a at 35ºC, respectively. Therefore, to achieve the same superficial liquid Reynolds number, the lower viscosity of liquid CO_{2} requires a lower inertia force than is the case for R12 and R134a, which results in a lower value of Fr_{so}.

The dimensionless vapour velocity J_{G} was proposed as the parameter for annular-to-wavy flow transition by Breber et al.[37], Sardesai et al.[38] and Tandon et al.[39] based on flow regime observations of R12 and R22. It had a similar meaning to Soliman’s modified Froude number, in that for annular flow, J_{G} represented the magnitude of the vapour shear stress required to overcome the gravity force exerting on the liquid film. Cavallini et al.[35]summarised the flow transition criteria[37-39] and proposed J_{G} =2.5 as the transition from the annular-to-stratified flow. The Lockhart-Martinelli parameter X_{tt}=1.6 was used as the stratified-to-slug flow transition. This flow regime classification and the proposed flow condensation model by Cavallini accurately predicted the heat transfer and pressure drop of high-pressure working fluids.[35] Figure 3.2 shows Jang’s CO_{2} flow regime observation results with the flow transition parameters of J_{G} and X_{tt} proposed by Cavallini. It can be seen that a smaller value of J_{G} =2 is more appropriate than the original value of J_{G} =2.5 to predict the effects of mass flux and vapour quality on the annular-to-wavy flow transition, especially at high mass flux conditions. The dimensionless vapour mass velocity J_{G} is inversely proportional to the vapour density and the liquid-to-vapour density difference of working fluids. CO_{2} has a vapour density at the saturation temperature of -15ºC which is 143% and 120% of that of R12 and R22 at 30ºC respectively, with an equivalent liquid-to-vapour density difference. For the annular-to-wavy transition under the same mass flux and vapour quality conditions, the larger vapour densities of CO_{2} than those of R12 and R22 led to a relatively smaller J_{G} than the original value proposed by Cavallini.

One customised flow map for CO_{2} was proposed and developed by Cheng et al.[40] for flow boiling. The predicted flow patterns included fully-stratified flow (**S**), stratified-wavy flow (**SW**), intermittent flow (**I**), annular flow (**A**), mist flow (**M**) and bubbly flow (**B**) which were taken from the Wojtan-Ursenbacker-Thome flow boiling pattern map.[41] Transitions from intermittent flow to annular flow, and from annular flow to the dry out region were not based on visual observation but were fitted to the changes in experimental CO_{2} flow boiling heat transfer characteristics, such as, the drop in heat transfer coefficients with the appearance of annular flow which suppresses the nucleate boiling of intermittent flow, and the sharp drop of heat transfer coefficient which occurs with dry out. To evaluate the predictions of the Cheng et al. flow boiling map for CO_{2} flow condensation, the transition criteria are plotted in a mass flux-vapour quality diagram in Figure 3.3 with the observations of Jang and Hrnjak, expecting the dry out region, which does not occur for flow condensation. The SW-A transition for flow boiling is modified for flow condensation by extending the boundary line from the lowest point to the vapour quality of x=1, which represents the beginning of condensation. It can be seen that the border line of I-A can acceptably predict the transition from slug to wavy flows for flow condensation, but all wavy flow observation points are predicted as annular flow.

This is not surprising as the I-A transitions were defined by the decrease of nucleate boiling heat transfer coefficients for CO_{2} flow boiling by Cheng. For flow condensation in horizontal tubes, wavy flows account for a relatively high proportion in the whole condensation process, especially at the low mass flux conditions as shown in Table 2.2. The heat transfer mechanism for wavy flows is dependent on the interaction of the convective condensation heat transfer of annular flows and the dominant film condensation of stratified flows, and should be accounted for in a flow condensation model. Therefore, it can be concluded that the Cheng et al. flow map is not adequate for application to the case of CO_{2} flow condensation due to a lack of prediction accuracy for wavy flows.

**Evaluation of existing two-phase frictional pressure drop models**

It is desirable to minimise the energy required to operate heat exchangers in a refrigeration system.[4] Ideally condensing and evaporating heat exchangers should exhibit high heat transfer effectiveness with a low-pressure drop. Therefore, for the design of condensers, the ability to accurately predict pressure drop is as important as the prediction of heat transfer.

For the modelling of the two-phase pressure drop, the one-dimensional flow analysis implies that the pressure drop inside horizontal tubes for two-phase flows includes the pressure drop component caused by the phase change under diabatic conditions and the frictional pressure drop component. Thus, the frictional pressure drop for two-phase flow needs to be measured under adiabatic conditions so that the phase change effect is eliminated. Measurements of the frictional pressure drop of CO_{2} two-phase flow inside smooth tubes were conducted by the authors[7, 8, 13, 42] listed in Table 3.1, and the pressure drop data from these references were summarised to create a databank. In Kang’s experimental studies, the pressure drop data with condensation occurring were used to evaluate the frictional pressure drop models, and this might be the reason that the pressure drop data in these references tend to be under-predicted by the models which were developed for calculating the frictional pressure drop. As the quality change and the heat flux information was not given, the CO_{2} condensation pressure drop data in Kang’s study are not used to evaluate the frictional pressure drop models.

For CO_{2} frictional pressure drop in smooth tubes, the datasets of Zilly et al.[7], Jang and Hrnjak[8], and Park and Hrnjak[42] are used to evaluate the frictional pressure drop models of Cavallini et al.[35], Friedel[43] and Muller-Steinhagen and Heck[44]. Cavallini modified the Friedel model by correlating the constant and power numbers to the “high pressure” refrigerant experimental pressure drop data and the resulted new frictional pressure drop model was implemented into an annular flow heat transfer correlation[35]. The pressure drop model proposed by Muller-Steinhagen and Heck showed the best predictions for 788 pressure drop data points of five refrigerants irrespective of flow regimes. It gave the best prediction for the annular flow pressure drops of these refrigerants when compared to the other six pressure drop calculation methods in the study of Ould Didi et al.[45] In Park and Hrnjak[42]’s study on the CO_{2} frictional pressure drop, the Muller-Steinhagen and Heck model also performed better, with prediction errors of less than 20% compared to the other pressure drop models. The selected models for calculating the frictional pressure drop are listed in Table 3.2.

The results are plotted for comparison in Figure 3.4, and the statistics are listed in Table 3.3. It is shown that all of these models can predict the experimental data of CO_{2} frictional pressure drop with acceptable errors. To individually check the evaluations of the pressure drop models, comparisons between these models and all the data points in different flow regimes are also listed in Table 3.3. The classification of the data points is as per Jang’s observations since these studies used the same test rig as Jang’s. The results show that all the models make more accurate predictions of the pressure drop in wavy flows compared to those for stratified and annular flows. In Figure 3.4, it is shown that the Muller-Steinhagen & Heck correlation makes better predictions in small and medium pressure drop range, while the Cavallini model is more accurate for the high-pressure regions. The statistical results also show that the Muller-Steinhagen& Heck model predicts the CO_{2} frictional pressure drop in stratified wavy flows accurately while the Cavallini model has a slightly more accurate prediction for the data points in annular flow.

**Evaluation of existing flow condensation heat transfer models**

A number of widely used flow condensation models which were developed from experimental studies on other refrigerants, are the models proposed by Dobson and Chato[26], Cavallini et al.[27], Shah[28], Akers and Rosson[46], and Thome et al.[47] These models are listed in Table 3.4

**Discussions on the comparisons**

Based on the evaluation of the condensation models in the above section, it is noted that the experimental heat transfer data of CO_{2} flow condensation are predicted with significant errors using the selected models. The reason for these prediction errors can be traced back to the unique heat transfer properties of CO_{2} at high reduced pressure conditions. Since the existing condensation models were developed from the experimental data of traditional refrigerants, such as R134a, R22, R404a, and R410a, condensing at saturation temperatures typically ranging from 30 to 50°C. At low temperatures, CO_{2} has thermophysical properties substantially different from those of traditional refrigerants under their typical condensation temperatures.

In Figure 3.7, specific enthalpy of vaporization of CO_{2} and other traditional refrigerants are plotted as a function of saturation temperature from -30 to 60°C. It can be seen that the specific enthalpy of vaporization for CO_{2} at a saturation temperature of -15°C, is 170%, 160%, 220% and 170%, of that of R134a, R22, R404a and R410a at the condensation temperature of 40°C, respectively. The enthalpy of vaporisation is linked to the heat transfer coefficient of film condensation. For the same mass flow rate, a high enthalpy of vaporisation enhances the conductive heat flux through the condensate liquid film.

The thermal conductivity of liquid CO_{2} and other refrigerants at different saturation temperatures is depicted in Figure 3.8. As can be seen, the thermal conductivity of CO_{2} at -15°C is 170%, 160%, 200%, and 160%, of that of R134a, R22, R404a and R410a at 40°C, respectively. This feature of CO_{2} leads to a higher heat transfer rate through a liquid film than other refrigerants at typical operating conditions.

In Figure 3.9, the specific heat of different refrigerants at saturation temperatures ranging from -30°C to 60°C is plotted. It can be seen that the specific heat of liquid CO_{2} at -15°C is 150%, 170%, 130% and 120%, of that of R134a, R22, R404a and R410a at 40°C, respectively. The specific heat affects the film condensation process when the convective item of the energy equation is not negligible. It applies to condensation inside horizontal tubes as the condensate on the inner tube wall is subjected to a vertical gravity body force and a horizontal vapour shear stress. The high specific heat of CO_{2} enhances the condensation heat transfer under the small saturation-to-tube wall temperature difference condition.

**Table of Contents**

**Abstract **

**Acknowledgements **

**List of Figures **

**List of Tables **

**Nomenclature **

**Chapter 1. Introduction**

1.1 Carbon dioxide as a low-temperature refrigerant

1.2 The role of heat transfer in a CO2 subcritical refrigeration system

1.3 Research objectives

1.4 Thesis structure

**Chapter 2. CO2 in-tube flow condensation literature review**

2.1 One-dimensional flow model for in-tube two-phase flow

2.2 Flow regime transition for in-tube flow condensation

2.3 Disagreements in experimental results from different researchers

2.4 Chapter conclusions

**Chapter 3. Evaluation of the existing flow condensation models**

3.1 Flow regime prediction for CO2 in-tube flow condensation

3.2 Evaluation of existing two-phase frictional pressure drop models

3.3 Evaluation of existing flow condensation heat transfer models

3.4 Discussions on the comparisons

3.5 Chapter conclusions

**Chapter 4. A new model for CO2 flow condensation inside horizontal tubes**

4.1 Flow regime transition criteria for CO2 in-tube flow condensation

4.2 The main heat transfer mechanisms for in-tube flow condensation

4.3 Development of the correlation for stratified flows

4.4 Development of the correlation for annular flows

4.5 Comparison between the predictions by the model and experimental data

4.6 Chapter conclusions

**Chapter 5. The experimental test rig**

5.1 Test rig design and working principles

5.2 Measurement instrumentation

5.3 Validation of the test rig

5.4 Chapter conclusions

**Chapter 6. Experimental data reduction and results**

6.1 Data reduction

6.2 Prediction of the flow regime

6.3 Effect of mass flux and vapour quality

6.4 Effect of saturation temperature

6.5 Comparison between the experimental data under similar working conditions

6.6 Comparison between the predictions by the existing CO2 flow condensation models

6.7 Chapter conclusions

**Chapter 7. An improved model for CO2 flow condensation inside horizontal tubes **

7.1 Determination of experimental data points with high prediction errors

7.2 Prediction errors by the wavy flow correlation

7.3 Modification to the initial flow condensation model

7.4 Comparison between the updated model and the experimental data

7.5 Chapter conclusions

**Chapter 8. Conclusions **

**References**

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Flow condensation of CO2 in a horizontal tube at low temperatures