Studies on Two-Phase Flows at Normal and Microgravity Conditions

TWO-PHASE GAS-LIQUID (AND VAPOR-LIQUID) flows occur in a wide variety of situations in chemical processing, power generation, and energy production facilities. Some practical applications include condensers and reboilers, gas-liquid reactors (used in the production of pharmaceuticals and specialty chemicals), trickle-bed contactors (used in hydrodesulfurization, hydrogenation and hydrocracking), wetted wall absorbers, falling film reactors, power systems, and core cooling of nuclear power plant under emergency conditions. In addition to normal gravity applications, two phase flows also occur in many planned space operations (i.e., in active thermal control systems, power cycles, propulsion devices and storage and transfer of cryogenic fluids).

MICROGRAVITY--UH PI's Larry Witte (l.) and Vemuri Balakotaiah (r.) at NASA-JSC study two-phase flow gas-liquid (and vapor liquid) flows in chemical processing, power generation, and energy production. Two-phase flow patterns are simplified in microgravity where only three major flow patterns are observable--bubble, slug, and annular. Two-phase flows in normal gravity are characterized by seven dimensionless parameters. In space, the number of dimensionless groups required to characterize two-phase flows is reduced by two because of the absence of the magnitude of gravity and the angle of orientation with respect to gravity.

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 to exhibit 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, orientation of it with respect to the direction of flow has a strong impact on the flow patterns observed and also on the flow pattern transition boundaries.

The importance of predicting different flow patterns in two-phase flows is well established. Two-phase flow patterns are somewhat simplified in microgravity, as only three major flow patterns (bubble, slug and annular) have been observed under such conditions. Annular flow is obtained for a wide range of gas and liquid flow rates in microgravity and it is the preferred flow pattern for the operation of two-phase systems in space. Therefore, it is important to be able to accurately predict the flow pattern which exists under given operating conditions of a two-phase system. We present a flow pattern transition criteria based on dimensionless parameters and validate it.

Annular flow is the most common and widely occurring of the two-phase flow patterns. It is known that the 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 the transfer rates. One goal of our research program is to determine the characteristics of wavy films in microgravity.

Flow Pattern Transitions in Microgravity
The absence of gravity reduces the number of observed flow patterns to three. It also reduces the number of dimensionless groups required to characterize two-phase flows by two, because of absence of the magnitude of gravity and the angle of orientation with respect to gravity. (Normal gravity two-phase flows in smooth pipes are characterized by seven dimensionless parameters.) For microgravity two-phase flows in a smooth pipe, a dimensional analysis shows that there are five relevant dimensionless groups:

gas and liquid Reynolds numbers, Re_GS = r_GU_GSD / m_G and Re_LS = r_LU_LSD / m_L

ratios of gas to liquid densities and viscosities, r_G / r_L and m_G / m_L

Here, U_LS is the superficial velocity of the liquid based on a single phase flow and U_GS is the superficial gas velocity. The viscosity, density, and surface tension are denoted by m, r, and s, respectively. When the last two ratios are small, the flow pattern transition boundary may be assumed to be a weak function of those two ratios. The number of dimensionless groups were further reduced to two by combining Re_LS and We_LS and by ignoring the influence of We_LS alone.

For microgravity two-phase flows, we developed a pair of dimensionless flow pattern transition maps. We have suggested that flow pattern transition in microgravity can be predicted using the maps shown in Figs. 1 and 2. These were developed using experimental data on microgravity two-phase flows in various systems. These maps suggest the importance of Suratman number (Su = Re²_LS /We_LS = r_LDs/m²_L) in determining the transitions between the flow patterns.

Bubble-Slug Transition
It is found that the 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 particular value of the ratio (Re_GS/Re_LS). This transitional value, (Re_GS/Re_LS)t, depends on the Suratman number as follows:

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 Figs. 1 and 2 suggest the following numerical values for the constants in the above equations.

K₁ = 464.16,                         (4a)
K₂ = 4641.6,                         (4b)
K₃ = 2 x 10^-9.                        (4c)

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.

Validation of Slug-Annular Transition at Low Suratman Numbers
A number of tests were carried out during the last year to validate the proposed slug-annular flow pattern transition boundary for microgravity two phase flows with low Suratman numbers. These tests were carried out on board NASA-LeRC DC-9 and NASA-JSC KC-135 aircraft using a two-phase flow loop. These aircraft allowed us to achieve a reduced gravity level of about one hundredth of the normal gravity for a time interval up to 20 seconds. This computer controlled flow loop provided gas and liquid flow rates required to obtain the desired two-phase flow. The flow conditions such as pressures, temperatures and flow rates and relevant data of the two-phase flow such as the instantaneous (local) film thickness and pressure gradients were measured and stored. A high speed video camera system was used for flow visualization. A flow development length of about 74 pipe diameters was used in these tests.

A number of different liquids were used to change the Suratman number of the two-phase system. Glycerin-water solutions of different concentrations were used to vary the viscosity of the liquid phase. A surfactant was used to change the liquid surface tension. Figure 3 shows the results of these experiments. The agreement between the predicted slug-annular flow pattern transition boundary (i.e., Eq. (1)) and the experimental data is very good. The predicted bubble-slug flow pattern transition boundary (i.e., Eq. (2)) and the experimental data do not agree with each other. Either the bubble flow does not exist at low Suratman number two-phase systems or the way we conducted the experiments suppressed the bubble flow. This discrepancy is being investigated further.

System Specific, 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. 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 for such a system is a two-phase thermal control system using a refrigerant.

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

x_t,B-S = (K₁(m_G / m_L)Su^-2/3) / (1 + K₁(m_G / m_L)Su^-2/3). (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 depends 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) and a simple material balance on the two-phase flow.

x_t,B-S = (K₂(m_G / m_L)Su^-2/3) / (1 + K₂(m_G / m_L)Su^-2/3) (if Su < 10⁶) (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,

where

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

is low.

Wavy Films in Microgravity
We also studied the characteristics of the wavy films in microgravity annular flows. A lot of data has been collected 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.] This data is shown in Fig. 4. Here the dimensionless film thickness is defined as

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

where (t_i) is the average interfacial stress and D is the tube diameter. We derived the following relationship between h⁺ and Re_L in a more direct way by assuming a velocity profile in the film.

A plot of this equation is also shown in Fig. 4. The agreement with data is good. Comparison with an existing empirical correlation shows that normal gravity data is also well correlated by this equation. Thus, the mean film thickness correlation is nearly identical in normal and reduced gravity.

The rms value of the film thickness fluctuations (from the mean film thickness) is normalized using the same length scale defined using the friction velocity u*, and it is denoted as h⁺_rms. We found the following correlation predicts the measured h⁺_rms values for various flow conditions:

Here, A is a coefficient which depends only on the gas flow. The available data suggests that

Figure 5 is a comparison of the predicted h⁺_rms values with the experimental values.

Another quantity of interest that can provide some estimate of the differences between the normal and microgravity films is the gas friction factor based on the interfacial stress. This is defined by

The microgravity data is shown in Fig. 6 along with an existing correlation based on normal gravity data. Here, h⁺_G is calculated using the gas phase properties (instead of the liquid phase properties) in Eq. 9. Though microgravity data is more scattered, it is clear that the interfacial friction factor fi is higher in microgravity than in normal gravity. We have proposed correlations for microgravity two-phase flows.

Thus, when properly non-dimensionalized using the pressure gradient, the mean film thickness of an annular flow can be predicted using the liquid Reynolds number. The correlation between them was derived using the universal velocity profile. Since the same correlation predicts the mean film thickness in upward and downward annular flows, it is not surprising to see that a single correlation can predict the normal and microgravity mean film thickness values. Agreement between the experimental data and the predicted h⁺ using the liquid Reynolds number based on superficial velocity suggests that entrainment of liquid droplets in microgravity annular flows is small. This speculation requires further experimental validation.

The differences between the normal and microgravity annular liquid films are apparent when we compare the interfacial friction factor and wave celerities. It is found that both of these quantities are higher in microgravity conditions than those observed in normal gravity downward annular flows. Unlike in normal gravity, microgravity wave celerities are strongly affected by the gas Reynolds number.

Acknowledgements
This work is supported by a grant from the NASA-Lewis Research Center (NAG3-1840) and the UH-JSC aerospace post-doctoral fellowship program.

MICROGRAVITY—UH PI’s Larry Witte (l.) and Vemuri Balakotaiah (r.) at NASA-JSC study two-phase gas-liquid (and vapor-liquid) flows in chemical processing, power generation, and energy production. Two-phase flow patterns are simplified in microgravity where only three major flow patterns are observable—bubble, slug, and annular. Two-phase flows in normal gravity are characterized by seven dimensionless parameters. In space, the number of dimensionless groups required to characterize two-phase flows is reduced by two because of the absence of the magnitude of gravity and the angle of orientation with respect to gravity.

Vemuri Balakotaiah
Publications
Jayawardena, S. S. and V. Balakotaiah. "Studies on Flow Pattern Transitions and Wavy Films in Gas-Liquid Two-Phase Flows in Microgravity," Proc. of the ASME Fluids Engineering Division, FED 244 (1997): 87-95.
Balakotaiah, V., S. S. Jayawardena, and L. T. Nguyen. "Studies on Normal and Microgravity Annular Two-Phase Flows," Proc. of the 4th Microgravity Fluid Physics Conf., NASA-LeRC, Cleveland, OH, (1998). (In press.)
Presentations
Nguyen, L. T., S. S. Jayawardena, and V. Balakotaiah. "Studies on Flow Pattern Transitions and Wavy Films in Gas-Liquid Two-Phase Flows in Microgravity," AIChE Annual Mtg., 1997.
Funding
"Regular and Chaotic Spatio-Temporal Patterns in Catalytic Systems." Robert A. Welch Foundation, 1998-2001, $42,000 per year.
"Studies of Heat and Mass Transfer, Flow Patterns and Flow Characteristics in the Entry Region of Two-Phase Flows in Reduced Gravity." NASA-LeRC GSRP Fellowship grant to Luan Nguyen, 1996-1999, $66,000.
"Two-Phase Gas-Liquid Flows in Microgravity: Experimental and Theoretical Investigations of the Annular Flow." NASA-LeRC, 1996-2000, $320,000.

Larry Witte
Publications
Witte, L., Y. Chin, and D. K. Hollingsworth. "A Study of Convection in an Asymmetrically Heated Duct Using Liquid Crystal Thermography" Proc. of the AIAA/ASME Thermophysics and Heat Transfer Conf., Albuquerque, NM, June 1998, HTD 357-2. 63-70.
Witte, L. and G. Warrier. "On the Application of the Hyperbolic Heat Equation in Transient Heat Flux Estimation during Flow Film Boiling," Proc. of the AIAA/ASME Thermophysics and Heat Transfer Conf., Albuquerque, NM, June 1998, HTD 375-3. 131-40.
Witte, L., Y. Chin, and D. K. Hollingsworth. "Investigation of Flow Boiling Incipience in a Narrow Rectangular Channel Using Liquid Crystal Thermography," Proc. of the AIAA/ASME Thermophysics and Heat Transfer Conf., Albuquerque, NM, June 1998, HTD 375-3. 71-78.
Witte, L., S. S. Jayawardena, and V. Balakotaiah. "Flow Pattern Transition Maps for Microgravity Two-Phase Flows," AIChE J. 43.6, (June 1997): 1637-40.
Witte, L. "External Flow Film Boiling," chapter in The Handbook of Phase Change, Taylor and Francis, 1998. (To be published.)
Witte, L. "External Flow Film Boiling," chapter in 1997 Annual Review of Heat Transfer, New York: Begell House. 315-58.
Funding
"Two-Phase Systems for Mars-g." NASA-JSC, NAG9-1012, May 1, 1998-April 30, 1999, $49,394.
"Sliding Bubbles: Using Liquid Crystal to Determine the Heat Transfer Enhancement Mechanism." Texas Advanced Research Project, ARP 003652-762, Jan. 1, 1998-Aug. 31, 1999, $86,890.
"Convection and Boiling in Narrow Channels." Co-Principal Investigator: D. K. Hollingsworth; National Science Foundation, CTS-9701556, $150,000, Sept. 1997-Aug. 2000.

Investigative Team

UH PI: Vemuri Balakotaiah, Ph.D., Professor, Department of Chemical Engineering
bala@uh.edu

UH Co-PI: Larry C. Witte, Ph.D., Professor, Mechanical Engineering
witte@uh.edu

JSC PI: Eugene Ungar, Ph.D., Crew and Thermal Systems
eungar@grp901.jsc.nasa.gov

UH Post-Doctoral Fellow: Subash. S. Jayawardena, Ph.D., Chemical Engineering
subash@uh.edu

Kathryn Miller-Hurlbert, doctoral student, Mechanical Engineering

Re_L = 2h^+²	0 < h⁺ < 10	(12a)
Re_L = 3.28h⁺ + 11.12h⁺lnh⁺ - 88.8	10 < h⁺	(12b)