Results and Discussion

Radial Profiles of Two-Phase Flow Properties

The radial profiles of void fraction, interfacial area concentration, liquid velocity, and turbulence intensity are shown in Fig. 11.4. The horizontal axis is the radial position from the pipe center to the pipe wall, and the vertical axis is the measured data. The void fraction increases along the flow direction, mainly as a result of the static pressure change. The void fraction profile at z/D ¼ 3.2 seems to be uniform and shows a flat shape. As increasing z/D, the void fraction profile changes to core peak because the large bubble moves to the core region. The interfacial area

Fig. 11.3 Experimental setup for lead–bismuth-eutectic (LBE) two-phase flow measurement

concentration also increases as increasing z/D, as shown in Fig. 11.4b. The axial liquid velocity profiles are shown in Fig. 11.4c. The dashed lines are the calculated value of seventh power law, as follows:

where Umax is the measured velocity at the pipe center. The measured liquid velocity profile at z/D ¼ 32.4 has a core peak, although the profiles at z/D ¼ 3.2 and 17.6 have a wall peak. Thus, the liquid velocity profiles were also developed axially and the gas–liquid interfacial drag force caused by the rising bubbles might act on the liquid phase. The turbulence intensity profiles in the liquid metal two-phase flow have a wall peak and they increase with the increase of z/D. These profiles have a shape similar to that in an air–water two-phase flow. However, the nondimensional turbulence intensity was much larger than the measured result in air–water flow systems; this might be attributed to the smaller liquid velocity in the present experimental condition, where the bubble-induced turbulence may be dominant.

Fig. 11.4 Typical measurement results: void fraction (a), interfacial area concentration (b), axial liquid velocity (c), and turbulence intensity (d)

Comparison of Interfacial Area Concentration

Interfacial area concentration measured by the four sensor probes was compared with existing correlations (Fig. 11.5). The vertical axis shows the estimation error between the measured and calculated interfacial area concentration. All the correlation overestimates the interfacial area concentration by 50–90 %, which might be caused by the differences in bubble size and shape. Most of the correlations were formulated with air–water two-phase flow data for a bubbly flow regime. However, the bubble shape in a liquid metal two-phase flow might be strongly distorted by the momentum exchange at the gas–liquid interface. Thus, a more

Fig. 11.5 Comparison of interfacial area concentration with existing correlations

Bubble-Induced Turbulence

The turbulence intensity measured in this study could be divided into wall turbulence and bubble-induced turbulence. However, turbulent production from bubbles is dominant at the pipe center. Thus, the turbulence intensity at r/R ¼ 0 was plotted against the void fraction measured by the four-sensor probe (Fig. 11.6). In addition, the present results were compared with the previous experimental data of the bubble-induced turbulence in an air–water two-phase flow system. The solid line in this figure denotes the calculated value by the following semi-theoretical equation [5].

In this equation, the velocity field around the bubble is assumed as potential flow and the rotational component of the wake is ignored. In addition, the value calculated by the empirical equation for air–water two-phase flow [6] is also drawn as the dashed line in Fig. 11.6; the equation is represented as follows:

Although the fluid properties are different with the air–water two-phase flow, the measured turbulence intensity agrees with Eq. (11.3) and the previous data [7–9], except the result at z/D ¼ 3.2. However, Eq. (11.3) was derived for an air–water flow system and its applicability to liquid metal flow was not clear. Therefore, the mechanism of turbulence production in liquid metal two-phase flow should be investigated in more detail. On the other hand, the turbulence intensity at z/ D ¼ 3.2 was slightly larger than other plots and Eq. (11.3). The measurement

Fig. 11.6 Bubble-induced turbulence

position at z/D ¼ 3.2 was relatively close to the gas injector, so it is expected that the flow was not fully developed.


A liquid metal two-phase flow was investigated by using a four-sensor probe and an electromagnetic probe. From the measurement results of two-phase flow structure and turbulence characteristics, the following knowledge was obtained.

• Radial profile of void fraction changes from wall peak to core peak along the flow direction.

• Axial development of the liquid velocity field shows different tendency for the void fraction profiles.

• Existing correlations for interfacial area concentration overestimate interfacial area concentrations at present experimental conditions, which might be attributed to the difference in bubble size. A new correlation should be modeled with further consideration of bubble size and the wall conditions.

• Bubble-induced turbulence at the pipe center in lead–bismuth two-phase flow agrees well with the previous experimental data for air–water flows. However, the mechanism should be clarified by measuring the liquid–metal two-phase flow in a wide range of flow conditions.

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