Studies of two-phase flow through a sudden expansion using electrical capacitance tomography

Highlights

• Void fraction was measured immediately after a sudden expansion using capacitance tomography.

• A correlation was proposed to model the void fraction behavior occurring right after an expansion.

• The proposed correlation improved the predictive ability over existing correlations.

Abstract

In this work, electrical capacitance tomography (ECT) was used to measure the changes in void fraction immediately after a sudden expansion for horizontally flowing refrigerant R-134a. The two-phase flow behavior occurring in the sudden expansion was also analyzed using a high-speed camera for two different area ratios of 0.145 and 0.44. Void fractions determined from correlations found in the literature were compared with experimental measurements made immediately after a sudden expansion. It was found that none of the correlations examined could represent the behavior of the void fraction immediately after the expansion. A modified correlation was proposed to model the void fraction behavior occurring right after the expansion. This new correlation was able to predict the void fraction within a ± 20% error band when compared with experimental data at mass velocities of 50 to 250 kg m⁻²s⁻¹ and area ratios of 0.145 and 0.44.

Introduction

The ever-increasing thermal loads imposed on military aircraft have led to the use of new aircraft thermal management systems to remove heat. Future aircraft may rely on a vapor compression system (VCS) for cooling (Emo et al., 2014). A VCS uses the relatively large latent heat of vaporization of a refrigerant to absorb heat (Emo et al., 2014). The design of a VCS needs to consider two-phase flow through expansions and contractions. A VCS designed for practical aircraft applications requires an understanding of the flow behavior through these geometries. While significant work has been done in the past to understand the behavior of two-phase flow in constant area passages, very little work has considered the behavior of two-phase flow through sudden expansions. Furthermore, even less work has been performed to study changes in the void fraction occurring across sudden expansions. This paper focuses primarily on two-phase flows through expansions. The following paragraphs describe past research relevant to this physical situation.

Khodaparast et al. (2014) used micro particle shadow velocimetry to study the flow of water through microcircular sudden expansions with diameter ratios of 1.51 and 1.96 and Reynolds numbers below 120. They studied the dependency of the vortex length on the Reynolds number, the expansion ratio, and the shape of the axisymmetric annular vortex. Their work confirmed that the correlations considered in their experiments could not predict measured pressure drop coefficients for the range of Reynolds numbers used. They found that the pressure drop coefficient depended on the inlet Reynolds number for Reynolds numbers below 50, which are typical in microchannel applications.

Ahmed et al. (2008) performed experiments to characterize the behavior of an air-oil mixture in two-phase flow downstream from a sudden expansion. The area ratios of the two expansions studied were 0.145 and 0.44, and the horizontal test section had a total length of 3.5m. Hot film anemometry was used to measure the time-averaged local void fraction, mean liquid velocity, and turbulence intensity downstream from the expansion. They found that the void fraction increased as the flow approached the expansion and further increased immediately after the expansion. They attributed the void fraction increase before the expansion to the flow velocity decreasing under the influence of the downstream pressure gradient. More specifically, the upstream pressure gradient was significantly smaller than the downstream pressure gradient due to the large cross-sectional area change between the two sections. The increase in void fraction immediately after the expansion was attributed to an air recirculation zone after the expansion. Void fraction correlations were not addressed in their study.

Chen et al. (2007) studied two-phase flow pattern changes and frictional pressure losses that occur in sudden expansions. The sudden expansion in this study consisted of a small diameter tube connected to a small rectangular channel. The area ratios of the expansions selected for the study were in the range 0.145 to 0.44. The experiments were designed to characterize air-water mixtures that flow horizontally. The measured pressure differences resulting from an abrupt expansion were compared with values calculated using nine correlations found in the literature. None of the correlations adequately predicted the pressure measurements, and they attributed the departure from the correlations to an inconsistency in the method used to obtain the void fraction. Chen et al. (2007) noted that most of the correlations used in their investigation required the void fraction. However, they found that only a few previous studies provided the location (i.e., upstream or downstream from an expansion) for the measured input data used in void fraction correlations. In addition, only a few studies provided the specific correlation used to estimate the void fraction. Chen et al. (2007) found that the best agreement between measured and predicted frictional pressure losses were obtained using the Wadle (1989) correlation with a mean deviation of ~ 200%. Although they adjusted an empirical constant in the Wadle (1989) correlation for improved predictions, they were still only able to obtain a mean deviation of ~95% between the measured and predicted values.

In another study, Wang et al. (2010) considered the use of existing pressure correlations for two-phase flow through sudden expansions. They used a total of 282 experimental measurements of the pressure drop from five different publications in their investigation. They found that most correlations could not adequately predict the entire set of measurements. Most correlations could only reasonably predict values from which the empirical fits were derived. Wang et al. (2010) found that the homogenous model had the poorest performance. However, by incorporating the Bond number, quality, Weber number, Froude number, Reynolds number, and area ratio into the homogeneous model, a considerable improvement was achieved. Similar to Chen et al. (2007), Wang et al. (2010) also noted from the review of pressure drop correlations for an expansion that the void fraction was required for all correlations except the homogeneous model. Moreover, most pressure loss correlations base their parameters (e.g., void fraction, quality, mass velocity, and density) on the inlet flow condition and a constant void fraction. Regardless, none of the correlations considered by Wang et al. (2010) were able to represent the measured pressure drop across an expansion.

In the above previous studies the void fraction influenced the results obtained for pressure drop correlations. However, the study of void fraction immediately after a sudden expansion was not considered in all these previous works. The need to further explore the behavior of the void fraction immediately after a sudden expansion is necessary for using correlations to predict pressure drop across a sudden expansion.

This paper explores changes in the void fraction immediately after a sudden expansion. Two-phase flow at different qualities within a sudden expansion was observed using a high-speed camera, and the images were compared with the results obtained from an electrical capacitance tomography (ECT) system. Calculations of the void fraction using several void fraction correlations found in the literature were compared to measurements using ECT immediately after the expansion. Lastly, a new void fraction correlation is proposed, and is believed to have the potential to represent the void fraction behavior occurring immediately after the expansion.