Sound speed criterion for two-phase critical flow

Critical (choked) flow is a highly concerning phenomenon in safety analysis for nuclear energy. The discharge mass flow rate prediction is crucial for engineering design and emergency response in case of nuclear accidents. Unfortunately, the critical flow is difficult to predict especially when the two-phase flow exists. The accuracy is based on a deeper understanding of the complex phenomenon of critical flow. The influence of virtual mass force on the two-phase critical flow was seldom concentrated on owing to the lack of suitable critical flow models for studies in detail. This study is based on a developed 6-equation two-phase critical flow model. It is confirmed that the virtual mass force contributes to the stability and convergence of the critical flow simulation and it will impact not only the critical mass flux but also the thermal hydraulic parameters along the discharge duct. The magnitude depends on the geometry of the discharge duct and the upstream condition. It is larger when the duct is longer and the pressure is lower. Furthermore, the virtual mass force for each flow regime was studied in detail with a sensitivity study. The results show that the most sensible condition for the virtual mass force is annular flow along a long tube under relatively low pressure. The future work is to develop a correlation of virtual mass force for critical flow specifically since the correlations in the literature were developed under general two-phase flow process conditions.

Modelling wall shear stress in two-phase bubbly flow is crucial for a variety of engineering applications, including multiphase propulsion systems, heat exchangers, and advanced cooling systems. The interaction between the liquid and gas phases, particularly in bubbly flow regimes, significantly affects performance, efficiency, and safety. In such flows, the near-wall region is characterised by high void fractions and sharp gradients in turbulent shear stress, requiring a more detailed understanding of frictional behaviour to improve pressure drop predictions in turbulent gas–liquid flow systems. This study focuses on vertical two-phase bubbly flows at relatively low turbulence regimes, with flow velocities below 2 m/s in water. To address the challenges associated with these flow conditions, the turbulent viscosity in bubbly flow according to the model proposed by Sato is considered. The analysis in the near-wall zone has led to the development of a relatively simple formulation for turbulent shear stress in the bubbly boundary layer, expressed as a function of the turbulent shear stress in single-phase flow, The bubble size (db), The void fraction (α), dimensionless distances to the wall and the constants κSP and CSP for the logarithmic law in two-phase flow. This model is validated using experimental data from the literature on bubbly flows and shows improved accuracy by explicitly accounting for the dynamic interaction between bubbles and the wall. The results demonstrate excellent agreement between experimental data and numerical predictions of turbulent friction, highlighting the model's reliability. The enhanced accuracy of the proposed model has significant implications for optimising systems where precise control of two-phase flow behaviour is essential. These findings pave the way for more reliable design and optimisation of high-performance systems, enabling better prediction and management of wall shear stress in complex bubbly flow regimes.

Two-phase damping and interface surface area in tubes with vertical internal flow

In recent years, the effort put forth toward the advancement of steamflood technology for improved heavy oil - recovery has seen considerable growth. A significant portion of the costs associated with a steamflood operation may be attributed to the generation of the steam required for injection. It is extremely important, therefore, that a high degree of accuracy is maintained in the measurement and control of the resulting steam-water mixture at each individual well. In fields where the required injection pressures are relatively low, the most common method of controlling the flow rate utilizes critical flow static chokes. New data are presented for the flow of steam-water through critical flow static chokes at conditions representative of a typical steam flood operation. The experimental data are a result of testing in Texaco’s new Steam Flow Research Facility. The experimental data covers a wide range of inlet qualities (20 to 100%) and inlet pressures (400 to 800 psig) for static choke bean diameters of 24/64 and 28/64 inch. The Thornhill-Craver empirical correlation predicts all of the experimentally measured values of critical mass flow rate within ± 10%. For inlet qualities ≥ 40%, all data is predicted within ±5%; below 40%, the equation over-predicts the critical flow data. The Napier equation modified for wet steam by King and Crocker over-predicts the critical mass flow rate at the present range of operating conditions.

Local characteristics of upward gas-liquid flows

Although HFC-134a is a common refrigerant for residential and mobile refrigeration systems, investigators are dealing with replacing it with new alternatives because of its harmful environmental and global warming effects. Recently HFO-1234yf and HFO-1234ze have been introduced as suitable alternative refrigerants because they have zero ozone depletion potential (ODP) and low global warming potential (GWP) and possess thermophysical properties similar to those of HFC-134a. Because there is no experimental data on the performance of these new refrigerants in capillary tubes and short-tube orifices, a recently developed numerical model for analysis of critical two-phase flow through these tubes is used to predict the critical mass flow rate and pressure distribution of HFO-1234yf and HFO-1234ze under various operating conditions. The applied numerical model is based on a comprehensive two-fluid model including the effects of two-phase flow patterns and liquid-phase metastability. The numerical method has been validated by comparing numerical results of the critical flows of HFC-134a, R-410A, and HCFC-22 with available experimental data. The developed numerical simulation is applied in order to develop comparison and selection charts for short-tube orifices based on the common refrigerant HFC-134a and the alternative new refrigerants HFO-1234yf and HFO-1234ze.

Modeling of vertical downward gas-liquid flow for the design of a new contactor

Wave propagation in bubbly two-phase, two-component flow was analyzed to assess the validity of some interfacial transfer laws for two-fluid models of two-phase flow. A dispersion relation was derived from the linearized conservation equations and the Rayleigh equation. The phase velocity and wave attenuation calculated from the dispersion relation, compared well with existing high- and low-frequency data. The virtual mass term was found to have a significant effect on wave dispersion in the bubbly flow regime. Thermal effects were found to be important in determining the resonance phenomenon and wave scattering was a major source of damping at frequencies higher than the resonance frequency.

This paper investigates the countercurrent gas–liquid flow in an annular gap bubble column with a 0.24 m inner diameter by using experimental and numerical investigations. The two-phase flow is studied experimentally using flow visualizations, gas holdup measurements, and double fiber optical probes in the following range of operating conditions: superficial air velocities up to 0.23 m/s and superficial water velocities up to −0.11 m/s, corresponding to gas holdups up to 29%. The flow visualizations were used to observe the flow patterns and to obtain the bubble size distribution (BSD). The gas holdup measurements were used for investigating the flow regime transitions, and the double fiber optical probes were used to study the local flow phenomena. A computational fluid dynamics (CFD) Eulerian two-fluid modeling of the column operating in the bubbly flow regime is proposed using the commercial software ansys fluent. The three-dimensional (3D) transient simulations have been performed considering a set of nondrag forces and polydispersity. It is shown that the errors in the global holdup and in the local properties are below 7% and 16%, respectively, in the range considered.

Local void fraction and heat transfer characteristics around tubes in two-phase flows across horizontal in-line and staggered tube bundles

Image reconstruction from projections plays an important role in monitoring flow regimes by ultrasonic transmission mode tomography (UTMT) system. Fast and more accurate methods are necessary in case of on-line process e.g. bubbly flow regimes. In this work, analytical image reconstruction methods such as linear back projection (LBP), filter back projection (FBP) and convolution back projection (CBP) in bubbly flow regime is investigated and found that CBP is superior to other methods. Furthermore, different filters were applied to CBP to investigate the image quality improvement. Among different types of filters for CBP method, Ram-lack outperforms the others for UTMT. The peak signal to noise ratio (PSNR) of reconstructed images in this particular experiment was improved using Ram-lack in noiseless data.

Echo sounding and acoustic propagation in the hadal zone (depths below 6 km) rely on models of sound speed that suffer from uncertainty due to a paucity of measurements at those depths. In order to assess models of sound speed in deep water, and to provide additional measurements, the Deep Acoustic Lander, a passive acoustic profiler, was deployed into the Mariana Trench from the RV Pressure Drop in April 2021. The Deep Acoustic Lander houses an array of hydrophones along with an AML Scientific CTD and AML MinosX sound speed meter. Pressure, temperature and salinity data measured by the CTD were used to inform some of the most commonly used sound speed models. The modeled sound speed was then compared with direct measurements of the speed of sound in the hadal zone to depths beyond 10 000 m. The goodness of fit between each model and the direct measurements was then compared to assess the performance of each model in deep water.

Analysis of two-phase flow regimes and parameter distribution in 5 x 5 rod bundle using image processing techniques

The present study develops an interfacial area transport equation applicable to an air-water horizontal bubbly flow with a flow restriction. The experiments are performed in a round glass pipe of 50.3-mm inner diameter, along which a 90-deg elbow is installed at L/D = 206.6 from the two-phase mixture inlet. In total, 15 different flow conditions in the bubbly flow regime are studied. The detailed local two-phase flow parameters are acquired by a double-sensor conductivity probe at four different axial locations. The effect of the elbow is evident in the distribution of local parameters as well as in the development of interfacial structures. The elbow clearly promotes bubble interactions resulting in significant changes in both the void fraction and interfacial area concentration. In the present study, the elbow is found to promote the coalescence mechanism while reducing the disintegration mechanism. These geometric effects are also reflected in the axial development of one-dimensional two-phase flow parameters. In the present analysis, the interfacial area transport equation is developed in one-dimensional form via area-averaging based on the existing model for vertical flow. In the averaging process, characteristic nonuniform distributions of the two-phase flow parameters in horizontal two-phase flow are treated mathematically by covariance calculations. Furthermore, the change in pressure due to the minor loss of the elbow is taken into consideration by using a newly developed correlation analogous to Lockhart and Martinelli’s. In total, 60 area-averaged data points are employed to benchmark the present model. The present model predicts the data well with an average percent difference of approximately ±10%.

Accurate prediction of multiphase flow rate is of prime importance in controlling production of oil fields. Direct measurements using multiphase meters are time-consuming and very costly. On the other hand, none of the published models can be considered as a universal model and most of these models are designated only for the critical flow. The aim of this study is to develop and validate practical models for the Algerian Hassi Messaoud (HMD) oil field covering both critical and subcritical multiphase flows through chokes of naturally flowing and gas lift wells. The new choke models are developed on the basis of the Gilbert model by incorporating the downstream pressure of the choke under the subcritical conditions. A large data set is used to evaluate the new models and to compare their performance with previously published prediction models. These data are divided, for each flow regime, into five selected categories based on the gas–oil ratio and a nonlinear regression algorithm is implemented to validate the new models. The comparison revealed the accuracy of two new models that improved the predicted production rates of the current model of HMD field in 130 wells out of 174 and the sum of absolute differences between the measured and the predicted oil flow rates (SAD) was reduced by 16.68% on 6,786 measurements. For the wells that are assisted with gas lift, the predictability was improved considerably: There was improvement in 85 wells out of 93 and the SAD was reduced by 42.11% on 2,317 measurements.