Four-sensor Conductivity Probe Research Articles

Characterization of local parameters of inclined upward air–water bubbly two-phase flows in a round pipe

The present work seeks to develop a detailed experimental database and characterize the local effects of inclination on horizontal and upward bubbly air–water two-phase flows. Experimental conditions are selected to investigate bubbly flows at a variety of orientations while reducing the influence of flow regime transition. Detailed time-averaged data is collected using state-of-the-art four-sensor conductivity probes for measurements across the flow area for five flow conditions at five inclination orientations in a 25.4 mm inner diameter pipe. Using the newly established database, effects of inclination on bubbly flows are analyzed, as are changes in liquid and gas flow rate at different orientations. The observations include (1) bubble migration and agglomeration at the top pipe wall as orientation changes from vertical to horizontal; (2) reducing the angle from vertical reduces the local gas velocity, and correspondingly reduces the global slip from greater than unity at 90° to less than unity for 60° and lower; (3) changes in the bubble size distribution are primarily at the interface between the bubble cluster and the liquid region of the pipe, not coalescence within the bubble cluster. Physical mechanisms for these observations are proposed, and the present trends at different orientations support previous experiments in horizontal two-phase flows.

Bubble size distribution for bubbly-to-slug transition flow in narrow rectangular channel

To thoroughly understand the flow structure evolving characteristics in flow regime transition process from bubbly to slug flow in narrow rectangular channel, bubble size distribution (BSD) are experimentally measured by four-sensor conductivity probes. The results show that the T-location distribution fits the measured chord length distribution best in bubbly-to-slug transition flow and the fitting performance becomes worse in slug flow at high void fraction. To solve the problem, two-group bubble fitting for transition flow is proposed and obtains good performance. Function dependence of bubble coalescence and break-up rate is thoroughly analyzed for the transition flow considering its influence on BSD. According to the function dependence and fitting results, empirical correlations are proposed to predict BSD in bubbly and the transition flow. The evolving characteristics of BSD in transition flow are also discussed based on the trends of adjusted parameters in the predicted BSD.

Experimental study of bubble size distribution in bubbly and bubbly-to-slug transition flow

The current work experimentally investigates the evolving characteristics of bubble size distribution (BSD) in bubbly and bubbly-to-slug transition flow in a 25.4 mm inner diameter pipe. Four-sensor conductivity probes used in present research enables accurate acquisition of bubble chord length in the flows with void fraction varying from 0.1 to 0.6. The flow regime transition is implemented by increasing superficial gas velocity while keeping superficial liquid velocity constant. Six right-skewed probability distribution functions (PDFs) commonly used for predicting bubble chord length distribution (CLD) are selected and used to fit the chord length data. The goodness of fit for all PDFs is evaluated by R-square, root-mean-square error (RMSE) and corrected Akaike information criterion. The results show that the PDF which reasonably fits the CLD in bubbly flow fails to fit the CLD in bubbly-to-slug transition flow. The evolving characteristics of CLD in flow regime transition process are qualitatively and quantitatively discussed based on bubble coalescence and break-up mechanisms. It is found that the invalidation of uniform morphology assumption and different mechanisms of bubble coalescence and break-up may result in the failed fitting. To properly predict real bubble size distribution (BSD) in bubbly-to-slug transition flow from CLD, an analytical backward transformation method is proposed to relate the CLD to BSD based on the bubble geometrical characteristics in the transition flow. The predicted BSD can be applied to calculate the interfacial area concentration (IAC) in the transition flow. The calculated IAC shows good agreements with experimental data which demonstrates the validity of predicted BSD in the transition flow.

Two-group phase distribution characteristics for air-water flow in 5 × 5 vertical rod bundle channel with mixing vane spacer grids

The phase distribution in rod bundle channel was associated with the heat transfer coefficient, flow resistance and critical heat flux, which was of great significance for the design and safe operation of nuclear reactor and steam generator. In order to clarify the phase distribution characteristics and reveal the effect of mixing vane spacer grid (MVSG) in two-group air-water flow in rod bundle channel, the adiabatic upward air-water two-phase flow experiments were conducted in 5 × 5 rod bundles with MVSGs and the detailed local two-phase flow parameters were acquired with miniaturized four-sensor conductivity probe (MFSCP). Some interesting phenomena were reported: Group I and II void fraction profiles showed the core-peak features; Group I void fraction almost stayed at the region from 0.2 to 0.3 for two-group air-water flow at current flow conditions; the dissipation length of MVSG was larger than 32.1 L/D at current two-group flow conditions; and the influencing region of MVSG was divided into at least three regions along the axial direction with the flow development for current flow conditions.

Beyond time-averaged measurement of bubble parameters in steam-water flows with conductivity probes

Two-phase data from flashing experiments are presented beyond the traditional time-averaged approach in this work. Probability density functions of parameters such as bubble duration, velocity, chord length, and number frequency are obtained from four-sensor conductivity probes and presented here. The axial evolution of the distributions is discussed in detail along with high-speed videos for a qualitative description of the flow field. The distributions of bubble parameters are observed to be positive-skewed with a long tail, and the shape of the distributions is analyzed in terms of the skewness and kurtosis. The number frequency of spherical and cap bubbles in the liquid slug is studied, as well as the number ratios of each bubble type in the flow. Parametric studies are carried out to investigate the effects of mass flux and system pressure on the distributions of bubble parameters. Bubble diameter distribution functions such as the Nukiyama-Tanasawa, Weibull, and lognormal distributions are validated with the chord length data of spherical bubbles where the Nukiyama-Tanasawa distribution appears to fit the chord length data the best. Sensitivity study is performed to investigate the effects of the adjusting parameters on the accuracy of the fits. The data are potentially useful for the benchmark and validation of high-fidelity simulation tools and the development of modeling approaches for phase-change flows. This work also provides a template for reporting beyond-time averaged measurements in future datasets generated with conductivity probes.

Axial interfacial area transport and flow structure development in vertical upward bubbly and slug flow

To improve the interfacial area transport equation model in the bubbly to slug transition flow, experiments are performed using the four-sensor conductivity probe for upward bubbly and slug flow in a 25.4 mm ID pipe. A total of 24 flow conditions are measured at 3 different superficial liquid velocities ranging from 0.5 m/s to 2.0 m/s and 8 different void fractions ranging from 0.1 to 0.6. The axial development of flow profiles is analyzed for bubbly flow, bubble-to-slug transition flow, and slug flow. In addition, the velocity effects on fully developed flow structures are also explained and the probe results are verified using the flow visualization. One-dimensional interfacial area transport due to bubble coalescence and disintegration is presented and its dependence on void fraction and velocity are discussed. These data provide one of the few quantitative results of the velocity effect on flow structure development at the same void fraction.

Numerical simulation of single and two-phase flow across 90° vertical elbows

This study investigates elbow effects on single-phase and two-phase flows. ANSYS CFX is used to simulate the evolution of the single-phase velocity distribution and two-phase interfacial structure downstream of vertical elbows. Simulations are benchmarked with existing LDA data and detailed four-sensor conductivity probe data. It is found that elbows create secondary flow, containing two counter-rotating vortices in both single-phase and two-phase flows. The vortices shift to pipe center and develop into parabolic velocity profile downstream. The elbow effect dissipates exponentially and dissipates 90% of its initial maximum value at approximately 11D downstream, no matter the elbow direction. In two-phase flow, bubbles are entrained by the secondary flow to form double-peaked void fraction and interfacial area concentration distributions. The double-peaked distribution moves upward and becomes single-peaked distribution downstream. Due to the additional buoyant force, the elbow effect takes much longer length to dissipate in two-phase flow than in single-phase flow.

Experimental dataset with high-speed visualization for vertical upward steam-water flow with transition from annulus to circular channel

A new database for steam-water flow is developed by the Multiphase Thermo-fluid Dynamics Laboratory (MTDL) at the University of Illinois at Urbana-Champaign. The experiment is carried out in a test section spanning the transition from an annulus to pipe, with one of the goals to study the effects of flow-geometry change on two-phase transport. Four-sensor conductivity probes are used to measure local two-phase parameters such as void fraction, interfacial area concentration, Sauter mean diameter, and gas velocity at 11 radial locations across the flow channel and five axial locations along the flow channel. The radial and axial profiles for selected conditions are presented and their features are discussed extensively. Parametric study is also carried out to understand the impact of flow parameters on steam-water flows under flashing condition. Besides, glass viewports are installed at three axial locations in the test section to observe the flow structure especially at the point of transition between the annulus and the pipe. The dataset, along with the high-speed videos, are valuable for the validation of the modeling and simulation of steam-water flows.

Four-sensor droplet capable conductivity probe for measurement of churn-turbulent to annular transition flow

In churn-turbulent to annular transition two-phase flow, both gas and liquid phase exist in the form of either continuous field (gas core/liquid film) or dispersed field (bubble/droplet). The complexity of the flow structure makes it very difficult to obtain experimental data in the churn-turbulent to annular transition flow. A novel four-sensor conductivity probe has been designed to measure interfacial structures at the churn-turbulent to annular flow regime transition. The new probe incorporates a sensor close to the detection point to serve as a common electrode for the other four sensors. Relatively large droplets can be identified and distinguished from the continuous liquid phase such as a liquid ligament or a film attached to the wall. To satisfy the higher requirements of the probe signal quality for the churn-turbulent and annular transition flow, the probe circuit has been optimized for a faster signal response and less interference. The new probe was tested in a 200 mm × 10 mm channel with an inlet superficial gas velocity up to 19.91 m/s. The measurement results are cross-checked by area-averaging the local superficial liquid and gas velocities and comparing with the measurements from a vortex flow meter and rotameter. The error is less than 10% for the superficial gas velocity and less than 20% for the superficial liquid velocity. The measured droplet size distribution is compared with a previous model, and good agreement is obtained. The effect of superficial gas velocity on droplet and ligament volume fraction as well as interfacial area concentration are investigated using the local measurement results of the three churn-turbulent to annular flow conditions.

Experimental study of vibration effects on local interfacial parameters in boiling flow

In this paper, the subcooled boiling flow experiments in a vertical annulus were conducted to study the effect of vibration on local interfacial characteristics. The local interfacial parameters including void fraction, bubble velocity, interfacial area concentration and Sauter mean diameter were measured by four-sensor conductivity probe. The time-averaged local parameters under vibration conditions were firstly measured and analyzed. It is found that the effects of vibration on time-averaged void fraction and interfacial area concentration are very limited. Therefore, we have developed the phase partitioning method to obtain the instantaneous variation of void fraction for further investigation. The instantaneous void fraction along the radial direction varies periodically with the vibration phase. The additional forces induced by vibration are analyzed and compared with each other. Among them, the tangential force is the dominant, which can account for the change tendency of void fraction under vibration. Besides, the variations of void fraction depend on different working conditions. The change tendencies of void fraction near the inner wall and outer wall are opposite in relatively low averaged void fraction regime while those in relatively high averaged void fraction regime are consistent.

Flow structure of bubbly to slug transition flow in a small pipe

To develop a mechanistic constitutive model to characterize the flow structure development in more than one flow regime, the detailed measurement of the flow structure is indispensable. In this study, the void fraction, interfacial area concentration, and bubble velocity profiles of upward air-water two-phase flow has been measured using the four-sensor conductivity probe in a 25.4 mm ID pipe. The test matrix has two features that distinguish it from previous studies, which is the void fraction-based flow condition selection and the wide range. The test matrix consists of 24 flow conditions with 3 different superficial liquid velocities (0.5, 1.0, 2.0 m/s) and 8 different void fractions (0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.45, 0.60). The results indicate that the flow characteristics and flow structures not only depend on the void fraction but also significantly depend on the superficial mixture velocity. The velocity effects on various flow characteristics are discussed such as void distribution, cap bubble generation, interfacial area. Besides, a velocity correlation has been developed to predict the bubble velocity radial distribution, with the mean absolute percentage error of 10.05% for the current data.

Interfacial Structures in Bubbly-to-Slug Transition Flows in a Duct

As a critical closure equation to the two-fluid model and an important tool to characterize the two-phase-flow interfacial transport, the interfacial area transport equation (IATE) was formulated by taking various physical mechanisms causing interfacial area change into account. To fulfill the dynamic prediction advantage of IATE and further replace the flow regime–based constitutive relations, the IATE model should be validated by transition data to ensure model reliability and robustness. Air-water experiments are performed in bubbly-to-slug transition flows in a 200 × 10-mm narrow rectangular duct. Four-sensor conductivity probes are used to measure the local void fraction, interfacial area concentration (IAC), and bubble velocity at three axial locations. The void fraction distribution changes significantly with the flow developing. Flow conditions with a similar area-averaged void fraction but different superficial mixture velocities are compared, and it is found that the superficial mixture velocity significantly affects the IAC. In addition, the two-group IATE model for narrow rectangular channel is evaluated using the collected data. The average relative error for the total IAC prediction is 11.4%, but the group II IAC is overestimated for most flow conditions.

A robust image analysis technique for the study of horizontal air-water plug flow

The current work develops a robust image analysis technique for quantitative measurements in horizontal plug flow. To do this, experiments are performed to capture high-speed videos for horizontal air-water plug flow for two test conditions in a 38.1 mm ID pipe. A visualization block-mirror system is designed and fabricated to allow the simultaneous visualization of two-phase flow from both top and side views using a single camera. To obtain images of high quality for analysis, the angle and position of the camera relative to the visualization block are verified. With the obtained images, an algorithm is developed to detect and track the interface of plug bubbles. Due to the existence of contacting or overlapping small bubbles, additional algorithms are developed to segment the interfaces of plug bubble from those of small bubbles, including distance checking, interface breakpoints detection, and convex curvature segmentation. As a result, the nose position, local time-averaged axial velocity, and area-averaged time-averaged void fraction for plug bubbles can be obtained with this newly developed image analysis technique. To benchmark the newly developed image analysis code, local four-sensor conductivity probe measurements are performed. The axial velocity for plug bubbles generally agrees within ±10% between image analysis technique and the four-sensor conductivity probe measurement technique, while the plug bubble reconstruction approach can generate an area-averaged void fraction within ±10% of the probe measured value.

Measurement of subchannel void fraction in 5 × 5 rod bundles using an impedance void meter

In order to improve the ability to predict nuclear reactor behaviour, reliable measurement of the void fraction in a subchannel is essential. A subchannel impedance void meter (SCIVM) is developed and applied in air–water two-phase flow in 5 × 5 rod bundles, which consists of a six-strip emitter electrode and six-strip receiver electrode to cover the whole subchannel. Because of the lack of accurate void fraction calculation in the subchannel, the developed impedance void meter is calibrated by a four-sensor conductivity probe with a quartic polynomial function. The void fractions in different subchannels are measured with a sampling frequency of 10 kHz to capture the dynamic features of the rapidly changing phase distribution in two-phase flow. The phase distributions in rod bundles are discussed based on the void fractions measured in different subchannels, and among all flow regimes, the cap turbulent flow has the largest void fraction differences between the inner, side and corner subchannel on the same cross-section due to the effect of the casing tube. Moreover, the dynamic features of the subchannel void fraction are analysed for different flow regimes, including bubbly, cap bubbly, cap turbulent, churn turbulent, and annular flow. It is demonstrated that the newly designed subchannel impedance void sensor is an effective tool to measure the void fraction in the subchannel and figure out its dynamic features.Highlights• A novel SCIVM is designed to measure the void fraction in the subchannel.• The measured subchannel void fraction is calibrated with a four-sensor conductivity probe and verified with empirical drift-flux correlations.• The differences in void fraction are discussed for different subchannels on the same cross-section.• The dynamic features of the subchannel void fraction are analysed for different flow regimes.

One-dimensional interfacial area transport for bubbly two-phase flow in vertical 5 × 5 rod bundle

For the modeling of the interfacial structure characteristics, an experiment of vertical adiabatic air-water flow has been conducted under an atmosphere pressure condition. The experimental facility is composed of 5 × 5 rods arranged on a square pitch in a square casing with 9.5 mm outside rod diameter and 12.6 mm pitch, simulating a prototypic rod bundle in nuclear reactors. The miniaturized four-sensor conductivity probe has been developed to allow for the experimental measurement in the small flow channel. Extensive data are acquired for one-dimensional flow parameters including axial development of void fraction, interfacial area concentration and gas velocity. The effect of a prototypic spacer grids with mixing vanes on the flow structure has been discussed at various flow conditions based on the experimental data. Two competing effects, “swirling effect” and “bubble breaker effect”, are identified. The effect vanishes out within a short distance from the space grid. A drift-flux correlation is developed for predicting void fraction of adiabatic bubbly two-phase flow in a vertical rod bundle. Existing interfacial area correlations are tested and Hibiki-Ishii correlation (2002b) is recommended as most accurate correlation to predict the interfacial area concentration. It is expected that the newly obtained data in the 5 × 5 rod bundle is useful for developing the interfacial area transport equation and benchmarking a computational code.

Interfacial area transport models for horizontal air-water bubbly flow in different pipe sizes

The current work seeks to develop the interfacial area transport models for horizontal bubbly flow applicable to various pipe sizes. A steady-state one-dimensional, one-group interfacial area transport equation (IATE) for horizontal adiabatic air-water bubbly flow is presented. The models discussed include: (a) frictional pressure drop prediction based on Lockhart–Martinelli approach; (b) drift-flux based closure relations for void-weighted bubble velocity and void fraction; (c) bubble interaction mechanisms; and (d) local void fraction reconstruction to calculate covariance parameters associated with asymmetric bubble distribution in horizontal bubbly flow. To develop these models, experiments are performed to establish local databases in bubbly flow using the four-sensor conductivity probe in horizontal test facilities with three different inner diameters (38.1 mm, 50.8 mm, and 101.6 mm). In total, 23 test conditions with superficial liquid and gas velocities in the ranges of 3.00–6.00 m/s and 0.08–1.00 m/s, respectively, are employed in the current work. The range of void fraction for the established database is 0.017–0.193. It is demonstrated that, the void weighted bubbly velocity (<<vg>>), void fraction (<α>), and frictional pressure loss can be predicted very well with an averaged percent difference of ±4.8%, ±4.7%, and ±2.1%, respectively. The covariance parameters can be predicted generally within ±30% using the current approach for void fraction reconstruction. As a result, the IATE can predict the measured interfacial area concentration with an averaged percent difference of ±5.9%, except for the test conditions with large bubbles generated as flow develops. Meanwhile, it is found that decreasing liquid velocity decreases the contributions to the total change of interfacial area concentration by random collision induced bubble coalescence, and turbulent impact induced bubble breakup.

Air-water two-phase bubbly flow across 90° vertical elbows. Part I: Experiment

This study performs experimental investigation on two-phase bubbly flow through 90° vertical elbows going from vertical-upward to horizontal and horizontal to vertical-downward orientations. The elbows have an inner diameter of 50.8 mm and a radius of curvature of 152.4 mm. A detailed database for local and global two-phase flow parameters in different flow orientations and across vertical elbows is established with a state-of-the-art four-sensor conductivity probe, a pressure transducer, and a high-speed video camera. The evolution of void fraction, interfacial area concentration, bubble velocity, and two-phase pressure drop along the axial development length in different orientations and across elbows are presented. It is observed that elbows create secondary flow and cause redistribution of the bubbles, which significantly affect the development of two-phase flow parameters. The effects occur across the elbows and remain for a significant length downstream. The effects on the void fraction distribution downstream of the elbow are discussed in detail for both elbow orientations. Characteristic differences in the elbow effects due to the elbow orientation are observed. For the vertical-upward elbow, a similar trend in the evolution of the void fraction distribution is observed for all flow conditions investigated while two different trends are observed downstream of the vertical-downward elbow. It is found that the effects of the vertical-downward elbow dissipate faster than that of the vertical-upward elbow. The elbow effects on interfacial area concentration, bubble velocity, and two-phase pressure drop are also discussed. The evolution of the interfacial area concentration is similar to that of the void fraction evolution in the straight pipe sections. However, it increases significantly across both elbows due to the promotion of the bubble breakup induced by the secondary flow. The void-weighted area-averaged bubble velocity is subject to significant changes across and immediately downstream of the elbows due to the redistribution of the bubbles. Additionally, the two-phase pressure gradients across the vertical-upward and vertical-downward elbows are approximately 1.5 and 2 times of that in the straight pipe sections.

Phase distribution characteristics of bubbly flow in 5 × 5 vertical rod bundles with mixing vane spacer grids

In order to predict the thermal–hydraulic parameters in nuclear reactor accurately, it is essential to reveal the phase distribution characteristics, the mechanisms of phase interactions and the effects of the mixing vane spacer grid (MVSG) in rod bundles, based on which the drift-flux model and interfacial area transport equation could be developed further. The profiles of local two phase flow parameters could give an insight into these phenomena. Therefore, the adiabatic air–water upward two-phase flow experiments are performed to measure local parameters in 5 × 5 rod bundles with mixing vane spacer grids (MVSGs) under different bubbly flow conditions. The miniaturized four-sensor conductivity probe (MFSCP) has been developed to measure local two-phase flow parameters, such as void fraction, interfacial area concentration (IAC), bubble velocity and bubble chord length. The detail local parameters are measured and analyzed in the bubbly flow. Typical wall peaks for void fraction are identified and the bubble velocity profiles have a reverse phase position with void fraction profiles. The mixing vane spacer grid (MVSG) plays an important role in phase distribution in rod bundles: the skewed peaks of void fraction is associated with the direction of mixing vanes; a larger value of area-averaged void fraction is induced at the downstream of MVSG; compared with other factors, the MVSG plays a leading role in interfacial area transportation. Moreover, the dissipation length of MVSG is less than 19.4 L/D for current bubbly flow conditions.

Frictional pressure drop analysis for horizontal and vertical air-water two-phase flows in different pipe sizes

This study performs an experimental investigation of frictional pressure drop in air–water two-phase flows in straight pipes. A reliable experimental database for the two-phase pressure drop and void fraction is established with a differential pressure transducer and a four-sensor conductivity probe, respectively. The two-phase flow investigated focuses on gas-dispersed flow regimes in different pipe diameters of 38.1 mm, 50.8 mm, and 101.6 mm. Systematic study on the effects of flow orientation, flow regime and pipe size is performed. The most commonly used predictive models for the two-phase frictional pressure drop are evaluated with the newly established database and the existing databases found in the literature. It is demonstrated that both the conventional Lockhart-Martinelli approach and the ϕf – <α> correlation can generally predict the two-phase frictional pressure drop very well with different suggested values of coefficients C and n for different flow orientations, based on the established data. Meanwhile, the results show that the values of C and n are independent of the pipe size and the flow regime. The homogeneous flow model is evaluated with four β (ratio of volumetric flow rates) based mixture viscosity correlations. The predictions with the Beattie and Whalley mixture viscosity correlation are found to be the best regardless of the flow orientation. The Lockhart-Martinelli approach with the coefficient C calculated by correlation employed in the nuclear system analysis code RELAP5-3D and the Müller-Steinhagen and Heck correlation are also evaluated. It is found that these two modeling approaches as well as the homogeneous flow model tend to underestimate most of the experimental data. Improvements for pressure drop prediction in nuclear reactor safety analysis codes are observed.

Experimental study of horizontal air-water plug-to-slug transition flow in different pipe sizes

The current work investigates the plug-to-slug transition in horizontal air–water two-phase flow in small (38.1 mm) and large (101.6 mm) diameter pipes. An extensive database is established to study the local interfacial structure in plug-to-slug transition flow. Detailed measurements across the flow area are performed for nine and six test conditions in small and large pipes, respectively, at three different axial locations downstream of the inlet using the local four-sensor conductivity probe. The effects of jg, jf, development length and pipe size are investigated. It is found that the number of small bubbles in the liquid plug/slug increases significantly in plug-to-slug transition with increasing jg, which are generated by the strong shear between the gas slug and liquid film. Due to the relative motion, these small bubbles either coalesce with the nose of the following plug/slug bubble, or slide between the plug/slug bubble and the wall, and then travel around the pipe circumference to reside beneath the large bubbles. This explains the large number of small bubbles observed at the top of the liquid film for the conditions at high gas flow rates. In the process of traveling downwards, some of the small bubbles coalesce with the slug bubbles. It is also found that increasing jg or jf decreases the size of the small bubbles. While shearing-off is believed to dominate as jg increases, turbulent-impact is enhanced as jf increases due to the increasing turbulence level in the liquid phase. Increasing jg, development length, or decreasing jf slightly increases the depths of the plug/slug bubbles; however, significant growth of plug/slug bubbles is observed in the axial direction. For the same condition, the contribution from large bubbles to total void fraction increases as pipe size increases, while the distribution of total void fraction is similar. The size of both small and large bubbles is found to be larger in the large diameter pipe. Due to the current bubble injection mechanism, small bubbles are generated at the inlet; they coalesce into large bubbles as the flow develops. The large bubble is found to accelerate as it grows along the axial direction, which can lead to a decreasing void fraction although pressure keeps decreasing.