Multiphase Flow Regime Identification in Cryogenic Nitrogen using Electrical Capacitance Measurement Technology

Cryogenic fluids are becoming increasingly important in a variety of industrial processes. In space applications, cryogenic propellants are replacing more hazardous traditional propellants and are being investigated for use in interplanetary missions with current research on storage and transport for in-space propellant depots, microgravity mass gauging, and in-situ resource generation on the lunar surface [1]. In ground applications, cryogenic liquid hydrogen is a promising and fast-growing alternative to fossil fuels and is being investigated for use in trains, planes, and ships [2] [3]. In all these applications, generating, storing, and transporting cryogenic fluids presents engineering challenges. Cryogenic fluid handling is often associated with two-phase flow, as heat leakage from the environment and pressure drops in the transfer lines induce boiling. This phenomenon causes problems with many sensors, pumps, and systems designed for single-phase fluids. It increases system complexity, especially in aerospace applications where avoiding propellant boil-off losses is more critical.

To effectively model and optimize next-generation cryogenic systems, an in-depth understanding of two-phase flow is required across various acceleration environments. Knowledge of the multiphase flow regime is required to accurately calculate the pressure drop and heat transfer design parameters [4]. Flow correlations for these parameters exist for ground applications [5] [6], but microgravity and lunar gravity environments are a new frontier that has yet to be fully characterized [4] [7] [8]. NASA is actively pursuing research into characterizing low-gravity multiphase flow [1] and the development of a universal flow correlation [9]. However, current data is collected indirectly by measuring pressure fluctuations, the heat transfer to the fluid, or through visual or X-ray imaging and qualitative classification [10] [11] [12] [13] [14]. The flow regime can be correlated with the data from many sensors and used to construct empirical flow regime maps. However, the use of these maps requires more sensors and information than is typically available outside the laboratory and is limited by dependence on specific flow orientation and gravity conditions. There is a need in industry for an on-line direct flow measurement device that can universally quantify the flow regime across a wide range of liquid/gas volume fraction and mass flow rate conditions [15]. A device with these capabilities is not currently commercially available [16], although capacitance techniques are being investigated [17]. This makes the development and expansion of flow correlations difficult and costly which in turn hampers the development of next-generation cryogenic space systems. A direct flow regime measurement device would also be beneficial to systems that require feedback control in multiphase systems. Some systems may require real-time measurement of multiphase flow regime and flow rate to optimize heat transfer, detect system chilldown, troubleshoot system performance, and alert the operator if the system approaches the critical heat flux [12].

Capacitance Mass Flow Meters (CMFMs) have been used to measure two-phase solids conveyance [18] [19] [20], three-phase oil-gas-water flows [21] [22], and two-phase saturated fluid flow. A two-phase saturated liquid CMFM was recently developed in the author’s prior work and applied to cryogenics [23]. CMFMs can measure liquid volume fraction and velocity with high resolution in the time domain, parameters that are directly related to the multiphase flow regime [10]. Data was collected using a CMFM with liquid nitrogen in various mass flow rates, volume fractions, and flow regimes. Previously, the authors proved the accuracy of the instrument to a calibrated single-phase reference standard [24]. In this work, the data from the instrument is used to develop a model for real-time classification of the multiphase flow regime. The regime classification is then compared to established correlations to validate the performance of the algorithm.

CMFMs use electrical capacitance measurement techniques where electrode plates are arrayed around a non-conducting tube, and the region of interest (RoI) is interrogated with a low-frequency quasi-static field. The basic technique is illustrated in Figure 1. First, the liquid volume fraction of a two-phase flow, ϕ, is measured based on the electrical permittivity of a cross section of the RoI. Then, two different axially separated measurements are cross-correlated in the time domain to calculate the fluid velocity, v. Finally, a temperature measurement is taken to calculate the density of the liquid and gas phases, ρ_l and ρ_g respectively, and the mass flow rate, ṁ can be calculated according to equation 1 where A is the cross-sectional area of the tube. A ½″ diameter CMFM from Tech4Imaging, LLC is used. (1) m˙=Av[ρlϕ+ρg (1−ϕ)] <![CDATA[ [[\[\dot m = Av[{\rho _l}\phi + {\rho _g}\,(1 - \phi )]\]

Figure 1.

Concept of Operations for Flow Regime Identification. A Capacitance Mass Flow Meter (CMFM) is installed in a two-phase system. The volume fraction is measured in a cross-section. The velocity is measured through the cross-correlation of two axially separated capacitance measurements. This information is then processed to determine the mass flow rate and flow regime.

The CMFM is installed in a system that is capable of independently varying the flow rate, volume fraction, and saturation condition of a multiphase cryogenic flow. The system is illustrated in Figure 2. Saturated liquid nitrogen is stored in a dewar. Nitrogen gas is then used to pressurize the dewar and subcool the liquid nitrogen. The subcooled liquid flows through a vacuum jacketed line where the temperature is measured using a Lakeshore Cryotronics DT-670A-SD silicon diode, and pressure is measured using a Unik 5000 transducer. The fluid reaches a control valve, and different liquid/vapor volume fractions are generated by adjusting the pressure drop across the valve. After the valve, the temperature and pressure are measured again, and the multiphase fluid passes through the CMFM. After passing through the CMFM, an additional valve controls back pressure. Then, the fluid is vaporized, and the single-phase gas mass flow rate is measured and used to calibrate the CMFM. The system was operated to collect data over a wide range of volume fraction and velocity conditions, as shown in Figure 3.

Figure 2.

Diagram of Cryogenic Nitrogen Flow Loop. Diagram shows the nitrogen gas supply used to subcool the liquid nitrogen, Pressure, and Temperature probe points (PT), the Capacitance Mass Flow Meter (CMFM), control valves, vaporizer, and reference gas Flow Meter (FM).

Figure 3.

Velocity and Volume Fraction Flow Conditions Achieved with Two-phase Nitrogen Flow Loop. Colors indicate contours of constant Mass Flow Rate (MFR) as measured by the reference gas flow meter.

Depending on the fluid properties, flow rates, volume fractions, and tubing orientation, multiphase flows exist in specific flow regimes, illustrated in Figure 4. Flow regime identification is typically conducted using a sight glass and visual qualitative classification [14]. However, a sight glass section was unavailable for this setup. Previous investigators have already visually correlated capacitance measurements to flow regimes [25] [26], and that information is used to inform the development of our algorithm. In this paper, the collected capacitance data is sorted into flow regimes, and categorization terms are developed that can quantitatively determine, in real time, the multiphase flow regime. The flow regime identification algorithm is verified by comparing the results to published flow regime maps and the data recorded from the reference sensors in the flow loop.

Figure 4.

Multiphase Flow Regimes in Horizontal and Vertical Flows: A – Single Phase Liquid Flow, B – Single Phase Gas Flow, C – Annular Flow, D – Mist Flow, E – Slug Flow, F – Bubble Flow, G – Stratified Flow, H – Stratified Wavy Flow, I – Bubble Flow, J – Churn Flow.

The recorded capacitance data was visually analyzed and sorted into flow regimes based on the data presented in [25] and [26]. The flow regime categories, a plot of the capacitance data, and a description of the characteristic behavior of that regime are presented in Figure 5. The sorted data is plotted in Figure 6 and colored by flow regime. Some vertical flow data is included for reference. Figure 6 shows that the volume fraction and velocity data are nearly sufficient to sort the data into flow regimes, but some bubbly and intermittent data overlap with other regimes.

Figure 5.

Raw Capacitance Data sorted into Flow Regimes and Descriptions of Volume Fraction (VF) Signal Characteristics used for Sorting.

Figure 6.

Flow Data Points from CMFM Sorted into Flow Regimes

Two categorization terms are developed to distinguish between flow regimes in real-time: Flow Symmetry (2) and Range (3). These terms are evaluated periodically based on a window of 600,000 volume fraction (ϕ) datapoints collected at 17,857 Hz. The concept of flow symmetry is displayed graphically in Figure 7 and is related to the size and frequency of slugs in the multiphase flow. The use of these categorization terms permits a fast computation of flow regime using statistical analysis of a window of data. (2) Symmetry=mean(ϕ)−max(ϕ)+min(ϕ)2mean(ϕ) \[Symmetry = \frac{{mean(\phi ) - \frac{{{\rm \max} (\phi ) +{\rm \min} (\phi )}}{2}}}{{mean(\phi )}}\] (3) Range=max(ϕ)−min(ϕ) \[Range = max (\phi ) - min (\phi )\]

Figure 7.

Symmetric and Asymmetric Capacitance Signals Displayed Graphically.

When the data is mapped on an axis of Range vs Symmetry in Figure 8, the distinguishing boundaries between flow regimes become clear. However, the bubbly and intermittent flow regimes are interspersed, and a velocity categorization term is added in an additional step to distinguish them.

Figure 8.

Capacitance Flow Data Points Sorted into Flow Regime Maps using Rangy, Symmetry, and Velocity Characterization Terms.

The dividing lines from the categorization maps in Figure 8 are used to develop an algorithm to identify the flow regime in real-time. The algorithm is presented in Figure 9.

Figure 9.

Flow Regime Identification Algorithm. Illustrates how flow regime classification is performed on the Volume Fraction (VF) signal based on the velocity, symmetry (sym.), and range features.

The effectiveness of the flow regime identification algorithm can be verified by using data from the reference sensors to plot the test points on an established flow regime map. One of the most established flow regime maps uses the densimetric Froude number (Fr) for the Liquid and Gas components to identify the flow regime [27] [28]. The Froude number is dimensionless, which relates the fluid inertial forces to the gravitational forces, allowing the map to be insensitive to physical properties and pipe geometry. There is, however, a different flow regime map for different pipeline orientations due to the varying influence of gravity. The Froude maps are created using 1-G data, and their accuracy may vary with microgravity. However, because the capacitance method depends on flow characteristics and not gravity, verifying multiple existing 1-G Froude maps validates the performance across various gravity environments. The Liquid and Gas Froude numbers are calculated according to (4) and (5), where g is gravity, and D is the hydraulic diameter. The liquid and gas density (ρ_L,ρ_G) are determined by a temperature measurement at the CMFM. The liquid and gas velocity (v_L,v_G) are determined by cross-correlation. The liquid velocity is cross-correlated with a window size of 16384 frames or 0.92 seconds, while the gas velocity is cross-correlated with a window size of 2048 frames or 0.11 seconds. The different window sizes allow the high-frequency features from the gas flow to be separated from the low-frequency features from the liquid flow. The collected test points are plotted on a Froude number-based flow regime map in Figure 10. The data is sorted into appropriate categories on the flow regime map, with some transition regions evident between flow regimes.

Figure 10.

Test Points Plotted on Froude Map for Horizontal Flow

The transition regions correlate well with existing data, falling around the lines delineating the different flow regimes. The flow regime maps themselves are based on subjective correlations of visual data, and this, along with the gradual transition between regimes, makes it difficult to calculate an accuracy metric without a rigid definition of what constitutes a flow regime boundary [29] [30] [27]. Nevertheless, the flow regime identification algorithm aligns well with the flow regime map, showing clear sorting into the appropriate regions with gradual transitions between regions. In horizontal flow, the algorithm correctly classifies 91.7% of Intermittent, 72.7% of Slug, 100% of Bubbly-Annular, 62.5% of Annular, and 66% of Bubbly test points based on the published Froude maps. Additional data was collected in a vertical upward flow orientation and plotted in Figure 11, demonstrating that the sorting algorithm performs well even with changing orientations. In vertical flow the algorithm correctly classifies Bubbly, Bubbly-Annular, and Annular test points with 100% accuracy to the Froude map. (4) FrG=vGρG(ρL−ρG)gD \[F{r_G} = {v_G}\sqrt {\frac{{{\rho _G}}}{{({\rho _L} - {\rho _G})gD}}} \] (5) FrL=vLρL(ρL−ρG)gD \[F{r_L} = {v_L}\sqrt {\frac{{{\rho _L}}}{{({\rho _L} - {\rho _G})gD}}} \]

Figure 11.

Test Points Plotted on Froude Map for Vertical Upward Flow

The mass flow rate, volume fraction, and velocity data collected by multiphase CMFMs, along with the additional categorization terms of flow symmetry and range, can be used effectively to identify the multiphase flow regime of a cryogenic flow in real-time. Because this method relies on quantitative data to determine flow regimes, it promises higher accuracy and repeatability than the qualitative visual flow regime classification commonly used today. Additionally, because the method relies on flow characteristics for direct classification, it is independent of the gravity environment and, after further study, may result in a universal sensor that can be applied across various fluids and environments. This makes the device well-suited for the many current investigations on fluid behavior in low and changing gravity. The real-time feedback of system-independent flow regime data can be instrumental in developing more accurate fluid models, studying hazardous multiphase materials, feedback control of multiphase heat exchangers, and creating compact and efficient multiphase flow experiments. These features are particularly advantageous when studying the effects of gravity and acceleration on multiphase flows, enabling the development of next-generation cryogenic space systems.

A universal capacitance-based flow regime identification algorithm has the potential to work over a wide array of fluids, flow orientations, line sizes, and gravity environments because it senses signal variations directly related to the flow regime. However, additional study on various fluids, line sizes, and flow rates is required to expand the algorithm and parameterize it for changing conditions. A robust flow regime identification algorithm also promises to increase the usefulness of CMFMs, as knowledge of the flow regime can be used to compensate for mass flow rate calculation methods when slip velocity is present.