# Two-phase flow regimes for forced convective condensation

Convective condensation in tubes occurs in the condensers of air-conditioning systems and refrigerators. Depending on the tube’s geometric configuration, condensation within can be classified as condensation in vertical or horizontal tubes. Condensation in a vertical tube is relatively simple, because gravity acts parallel to the flow direction and, consequently, an annular liquid film forms on the inner surface of the tube. Therefore, the flow pattern for condensation in a vertical tube is limited to annular flow, and an analytical solution can easily be obtained. Condensation in a horizontal tube, on the other hand, is much more complicated, because gravity acts perpendicularly to the flow direction and various flow patterns are possible. When condensation occurs in a horizontal tube, different flow regimes are observed at different positions along its length. Two possible sequences of flow regimes for convective condensation in a horizontal tube are possible, depending on the mass flow rate (Hewitt, 1998).

Figure 1: Flow patterns for condensation inside horizontal tubes.

Figure 1 (a) shows the sequence of flow regimes that arise during condensation in a horizontal circular tube with higher mass flow rate. Superheated vapor enters the horizontal tube, which has a temperature below the saturation temperature of the vapor. The flow at this point in the tube is single-phase vapor flow, since no condensation occurs near the inlet. After the vapor cools and becomes saturated, condensation starts to occur on the inner wall of the tube. The flow pattern at the beginning of condensation is annular, because the velocity of the vapor is much higher than that of the condensate. The dominant force in the annular flow regime is shear stress at the liquid-vapor interface, with gravity playing a less important role. As condensation continues, the velocity of the vapor phase decreases and the dominant force shifts from shear force at the interface to gravitational force. Liquid accumulates at the bottom of the tube, while condensation takes place mainly at the top portion of the tube where the liquid film is thin. The void fraction in the tube decreases as the vapor condenses downstream, and the flow patterns change to slug and plug flows. The size of the vapor plugs further decreases downstream, and the two-phase flow enters a brief bubbly flow regime before the completion of condensation. Near the outlet of the horizontal tube, the quality reduces to zero and the flow in the tube becomes single-phase liquid flow.

Figure 2: Flow pattern map for condensation in a horizontal tube.

The sequence of flow regimes for convective condensation in a horizontal tube at a lower mass flow rate is shown in Fig. 1(b). Superheated vapor enters the tube and the flow is single-phase vapor near the inlet, as in the high mass flow rate case. Another similarity is that the flow regime is annular flow at the commencement of condensation. As condensation continues, the condensate at the top portion of the tube flows to the bottom portion due to gravitational force. Since the mass flow rate is not high enough to produce slug or plug flow, two-phase flow in the horizontal tube enters a stratified flow regime where liquid flows in the bottom portion of the tube and vapor flows in the top portion. Unlike the case of high flow rate, the vapor at lower flow rate never completely condenses. Breber et al. (1980) used an extensive collection of data from the literature to demonstrate that the flow pattern of Taitel and Dukler (1976) is applicable to condensation in horizontal tubes. Experimental data from more than 700 condensation flow regime observations in the literature, including water, R-12 and R-113, inner-tube diameters of 4.8 to 50.8 mm, and a wide range of operating parameters, were used for the comparison. With the exception of data from the smallest inner-diameter tube (4.8 mm), agreement was good with the flow regime transition boundaries as predicted by Taitel and Dukler.

A flow map for condensation in a horizontal tube was suggested by Tandon et al. (1982) and is shown in Fig.2. The dimensionless vapor velocity is defined as

$j_{v}^{*}=\frac{x\dot{{m}''}}{\sqrt{gD{{\rho }_{v}}({{\rho }_{\ell }}-{{\rho }_{v}})}}\qquad\qquad(1)$

where D is the diameter of the tube. The abscissa is the relative cross-sectional area of the tube occupied by the liquid and vapor, ${{A}_{\ell }}/{{A}_{v}}=(1-\varepsilon )/\varepsilon$. The flow regimes shown in Fig. 2 can be summarized in Table 1. The most frequently occurring flow regimes for condensation in a horizontal tube are the annular-dispersed flow and the stratified flow. The dispersed-annular flow can also occur in condensation in a vertical tube if the vapor velocity is high enough to allow the effect of gravity to disregarded.

Table 1: Flow regimes of convective condensation in a horizontal tube.

 $(1- \varepsilon )/ \varepsilon$ $j_{v}^{*}$ Flow regimes $(1- \varepsilon )/ \varepsilon \le 0.5$ $j_{v}^{*} \le 1$ Stratified flow $1 \le j_{v}^{*} \le 6$ Annular-dispersed flow $j_{v}^{*}>6$ Spray flow $(1- \varepsilon )/ \varepsilon >0.5$ $j_{v}^{*} \le 0.01$ Slug flow $0.01 \le j_{v}^{*} \le 0.5$ Semi-annular flow $j_{v}^{*}>0.5$ Bubbly flow

## References

Breber, G., Palen, J.W., and Taborek, J., 1980, “Prediction of Horizontal Tubeside Condensation of Pure Components Using Flow Regime Criteria,” ASME Journal of Heat Transfer, Vol. 102, pp. 471-476.

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Hewitt, G.F., 1998, “Multiphase Fluid Flow and Pressure Drop,” Heat Exchanger Design Handbook, Vol. 2, Begell House, New York, NY.

Taitel, Y., and Dukler, A.E., 1976, “A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow,” AIChE Journal, Vol. 22, pp. 47- 55.

Tandon, T.N., Varma, H.K., and Gupta, C.P., 1982, “A New Flow Regime Map for Condensation inside Horizontal Tubes,” ASME Journal of Heat Transfer, Vol. 104, pp. 763-768.