In this model (Feentra et al., 2000), predicted velocity ratio of the phases is given by

S = 1+25.7(Ri x Cap)0-5 (P/D)-1 (46)

Where Cap is the capillary number and Ri is the Richardson number

3.3.4 Comparison of void fraction models

The HEM greatly over-predicts the actual gamma densitometer void fraction measurement and the prediction of void fraction model by Feenstra et al., is superior to that of other models. It also agrees with data in literature for air-water over a wide range of mass flux and array geometry (Feentra et al., 2000). The main problem with using the HEM is that it assumes zero velocity ratios between the gas and liquid phases. This assumption is not valid in the case of vertical upward flow, because of significant buoyancy effects.

3.4 Dynamic parameters

3.4.1 Hydrodynamic mass

Hydrodynamic mass mh is defined as the equivalent external mass of fluid vibrating with the tube. It is related to the tube natural frequency f in two-phase mixture as discussed in (Carlucci & Brown, 1997) and is given below:

mh = mtKf / f )2 -1] (47)

where mt is the mass of tube alone and f is the natural frequency in air.

Hydrodynamic mass depends on the pitch-to-diameter ratio of the tube, and is given by (Pettigrew et al., 1989)

(48)

where p is the two-phase mixture density.

De / d = (0.96 + 0.5P / d)P / d, for a triangular bundle. (49a)

De / d = (1.07 + 0.56P / d)P / d, for a square bundle. (49b)

where De is equivalent diameter to model confinement due to the surrounding tubes as given by (Rogers et al., 1984).

Early air-water studies (Carlucci, 1980) showed that added mass decreases with the void fraction as shown in Figure 19. It is also less than (1 — a), where a is the void fraction. This deviation from expected (1 — a) line is caused by the air bubble concentrate at the flow passage center. Surprisingly added mass has attracted very little attention of researchers which is a potential avenue for future researches.

£ 0.8

S

ІЛ ІЛ

rc E

Void fraction %

Fig. 19. Added mass as a function of void fraction (Carlucci, 1980).