Studies on Two-Phase Flows at
Normal and Microgravity Conditions

Vemuri Balakotaiah, Ph.D., Professor, UH
Larry C. Witte, Ph.D., Professor, UH
Eugene Ungar, Ph.D., JSC
Subash S. Jayawardena, Ph.D., Post-Doctoral Fellow, UH

TWO-PHASE GAS-LIQUID and vapor-liquid flows occur in a wide variety of situations in chemical processing, power generation, and energy production facilities. In addition to these normal gravity applications, such flows also occur in many space operations such as active thermal control systems, power cycles, propulsion devices, and storage and transfer of cryogenic fluids.

Two-phase flows can be grouped into a number of different flow patterns. These flow patterns are based on the spatial and temporal distribution of the vapor (or gas) and liquid phases. Gravity is a major reason for such two-phase flows exhibiting a wide range of flow patterns with different characteristics. The gravitational body force acting on the phases with different densities causes stratification. In addition to the magnitude of that body force, its orientation with respect to the direction of flow has a strong impact on the flow patterns observed and also on flow pattern transition boundaries. For example, normal gravity vertical upward co-current flow exhibits the following four flow patterns: annular, churn, slug, and bubbly. On the other hand, normal gravity horizontal flow exhibits the following flow patterns: smooth stratified, wavy stratified, elongated bubble, dispersed bubble, plug, slug, and annular.

Above. Dr. Larry C. Witte studies two-phase liquid and vapor liquid flows with applications in power generation and energy facilities.

Experimental data indicate that two-phase flow patterns are somewhat simplified in microgravity. For example, only three major flow patterns (bubble, slug, and annular) have been observed. In addition, annular flow is obtained for a wide range of gas and liquid flow rates in microgravity. It is the preferred flow pattern for the operation of two-phase systems in space. Slug flow is avoided, because vibrations caused by slugs result in unwanted accelerations. In many cases, bubbly flow should also be avoided because of the difficulty of preventing the transition from bubbly flow to slug flow. Therefore, it is important to be able to accurately predict the flow pattern which exists under given operating conditions of a two-phase system.

Wavy liquid film in annular flow has a profound influence on the transfer of momentum and heat between the gas and the liquid. Thus, an understanding of the characteristics of the wavy film is essential for developing accurate correlations that may be used to predict transfer rates.

The main goal of our work is to understand two-phase gas-liquid flows in pipes under normal as well as microgravity conditions through a combined program of experimental and modeling studies. The specific objectives are: (1) collection of experimental data on flow patterns, pressure drop, and heat transfer on developing and fully developed two-phase flows in microgravity (2) modeling studies on the scale-up of two-phase flows to develop the design equations, models and correlations needed for designing equipment in which two-phase flows occur.

We have collected experimental data on gas-liquid two-phase flows by using the aircraft KC-135 (of NASA-JSC) and DC-9 (of the NASA-Lewis Research Center) which in parabolic trajectories give about 20 seconds of microgravity. Initial data were collected using the air-water flow loop. Experiments planned for the future will use refrigerant (R134a) flow loop. These experiments will include detailed measurements of the liquid film in two-phase annular flows, and these measurements will be used to validate the mathematical models being developed. Normal gravity measurements under comparable conditions will be conducted at the two-phase flow laboratory at the University of Houston. Techniques needed to make detailed measurements will be developed at the University of Houston and then incorporated into the test rigs at NASA-JSC or at NASA Lewis Research Center.

We are currently working with researchers at NASA's Johnson Space Center and the Lewis Research Center in Cleveland, Ohio, on the design of a long duration shuttle experiment to collect scientific and technological data on two-phase gas-liquid flows in microgravity. This experiment will provide data that will lead to a greater understanding of how gas-liquid and vapor-liquid flows behave in microgravity. Data collected in this experiment may be used by engineers to design better thermal control devices (heating and cooling systems) for the international space station, which will be more efficient and require less energy and space than the single phase devices used at present.

Flow Pattern Transitions
For microgravity two-phase flows, we have developed a pair of dimensionless flow pattern transition maps (Jayawardena et al., 1997). Flow pattern transition in microgravity can be predicted using the maps shown in Figs. 1 and 2. These were developed using experimental data collected by ourselves and other researchers using different tube sizes and different working fluids.

These maps suggest the importance of Suratman number

in determining the transitions between the flow patterns. The Suratman number can be considered as equivalent to a Reynolds number for the two-phase system defined based on the capillary velocity, diameter and liquid phase properties. The capillary velocity is defined by the ratio (). The definitions of these dimensionless numbers are as follows:

These numbers take into account the effects of surface tension, inertial, and viscous forces acting on microgravity two phase flows.

Bubble-Slug Transition
Bubble-slug flow pattern transition occurs at a particular value of the ratio (Re_GS/Re_LS). This transitional value, (Re_GS/Re_LS)_t, depends on the Suratman number as given below:

Slug-Annular Transition
The slug annular transition cannot be represented by a single line. When the Suratman number is less than 10⁶, slug-annular flow pattern transition occurs at a particular value of the ratio (Re_GS/Re_LS). This transitional value, (Re_GS/Re_LS)_t, depends on the Suratman number as given below:

When the Suratman number is greater than 10⁶, slug-annular flow pattern transition is a function of the gas Reynolds number, Re_GS. This transitional value, (Re_GS)_t, depends on the Suratman number as given below:

Experimental data plotted in above figures suggest the following numerical values for the constants in the above equations.

Since the Suratman number is determined by the tube diameter and physical properties of the fluid, the proposed map can be used to identify the flow pattern for a given two-phase system with selected liquid and vapor flow rates.

The separation of the slug-annular flow pattern transition boundary into two different forms at a Suratman number of 10⁶ suggests that two different mechanisms are controlling the slug-annular flow pattern transition. Current investigations are aimed at determining those mechanisms.

Dimensional Flow Pattern Maps
It is customary to use flow pattern maps plotted using two-phase quality vs. mass flow rate for a given fluid in a selected tube size. Obviously, such flow pattern maps are system specific. The flow pattern maps in Figs. 1 and 2 may be used to create system specific flow pattern maps useful for a single-component, two-phase system. In space (microgravity) applications, an example of such a system is a two-phase thermal control system using a refrigerant.

The two-phase quality x, is defined as

(5)

For any Suratman number, the bubble-slug flow pattern boundary is obtained by Eq. (6) given below, which is derived from Eqs. (1), (5) and a simple material balance on the two-phase flow.

(6)

This transitional quality, x_t,B-S, is independent of the total mass flow rate.

As shown above, criteria for the slug-annular transition depend on the Suratman number of the system. When the Suratman number is smaller than about 10⁶, the slug-annular flow pattern boundary is obtained by Eq. (7), which is derived from Eqs. (2) and (5) with a simple material balance on the two-phase flow.

(7)

This transitional quality, x_t,S-A, is also independent of the total mass flow rate.

When the Suratman number is larger than 10⁶, the slug-annular flow pattern boundary is obtained by Eq. (8). This can be derived from Eqs. (30) and (5) and a simple material balance.

(8)

where m is the total mass flow rate of the two-phase flow. Equation (8) suggests that it is possible to obtain slug flow at higher values of quality, provided m is low. The terms appearing in Eq. (8) are grouped such that the influence of liquid phase properties, vapor phase properties and tube size on the flow pattern boundary can be seen clearly.

Figure 3 shows the flow pattern boundaries on a two-phase quality vs. mass flow rate map, for a selected two-phase system in microgravity. The working fluid of that system is R-134a at 70^oF, and the tube diameter is 25.4 mm. For this system the Suratman number is about 5.8 x 10⁶.

The bubble flow pattern can only be observed in an extremely small range. The calculated value for x_t,B-S at that transition is about 0.04%.

Wavy Films in Microgravity
Bousman (1994) has collected data on wavy film profiles in microgravity using air water, air-water-glycerin and air-water-Zonyl systems. (Zonyl is a surfactant and when mixed with water, reduces the surface tension of water from 0.072 Nm^-1 to about 0.021 Nm^-1 without affecting the viscosity.) These data are shown in Fig. 4. Here, the dimensionless film thickness is defined as

(9)

Since the wall shear stress (t_w) measurement was not accurate, Bousman approximated t_w using the measured gas-phase pressure gradient:

tw = = -(dPG/dx)(D/4),

(10)

where is the average interfacial stress and D is the tube diameter. The liquid Reynolds number Re_L is defined as

ReL = 4/vL = ReLS,

(11)

where is the flow rate per unit perimeter. Bousman's empirical fit of the data gave the correlation

We derive the relationship between h⁺ and Re_L in a more direct way by assuming a velocity profile in the film and using the relation

(13)

Here, u⁺ is the dimensionless velocity in the film (u⁺ = u/u^*). When the film is laminar, we have

while for turbulent films, we use the universal profile

(15)

Substitution of Eqs. (14) and (15) into (13) gives the following relations:

(16)

A plot of this equation is shown in Fig. 4 as the solid line. The agreement with data is good.

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ISSO -- Institute for Space Systems Operations
1996-1997 Annual Report