Transient Two-phase Flow Research Articles

Numerical assessment of transient flow and energy dissipation in a Pelton turbine during startup

The Pelton turbine, known for its high application water head, wide efficient operating range, and rapid start-stop capability, is ideal for addressing intermittent and stochastic load issues. This study numerically analyzes the transient two-phase flow and energy dissipation during the startup of a Pelton turbine. Dynamic mesh technology controlled nozzle opening changes, and momentum balance equations managed runner rotation. Findings showed that the runner speed initially increased rapidly and then more slowly, and flow rate matched the nozzle opening variations. Runner torque first rose linearly, then decreased, with the fastest decline during nozzle closing. Hydraulic efficiency peaked early in nozzle reduction but then dropped sharply. Strong vortices formed due to upstream inflow and downstream backflow impact in the distributor pipe. The jet needle and guide vane improved flow in the converging section of nozzle, but flow began to diffuse with increased stroke. Initially, the jet spread fully on the bucket surface, but later only affected the bucket tips. Pressure fluctuations in the water supply mechanism were primarily due to jet needle motion, with higher amplitude during movement and lower when stationary. These fluctuations propagated upstream, weakening over distance. Reynolds stress work and turbulent kinetic energy generation, respectively, dominated energy transmission and energy dissipation, with their maximum contribution exceeding 96% and 70%. High-energy clusters corresponded to jet impact positions, highlighting jet-bucket interference as crucial for energy transport. This study established a performance evaluation method for Pelton turbine startups, supporting further investigation into characteristic parameters, flow evolution, and energy dissipation patterns.

Bubble image segmentation and dynamic feature extraction in gas–liquid two-phase transient flow

Bubble image segmentation and dynamic feature extraction in gas–liquid two-phase transient flow

Investigation of unsteady friction effects in transient two-phase pipe flow

Water hammer and transient cavitating flow may induce large pressure fluctuations in pipelines. Transient events in pipeline may cause a drop in pressure large enough to break liquid homogeneity and continuity (liquid column separation, distributed vaporous cavitation). Trapped air pockets in liquid may be a major problem in piping systems. The paper deals with mathematical tools for modelling unsteady skin friction, transient vaporous cavitation (liquid column separation) and transient gaseous cavitation (trapped air pockets). The method of characteristics transformation of the unsteady liquid pipe flow equations gives the water hammer solution procedure. A convolution-based unsteady skin friction model is explicitly incorporated into the staggered grid of the method of characteristics. Incorporating discrete cavities into the water hammer model leads to the discrete cavity model. An advanced discrete gas cavity model (DGCM) with consideration of unsteady pipe flow friction effects is presented in the paper. The DGCM is capable to simulate vaporous and gaseous cavitation at the same time. Pipeline apparatus for measurement of transient liquid flow (water hammer) and transient two-phase flow (vaporous and gaseous cavitation) is briefly described. The paper concludes with two distinct case studies showing profound effects of unsteady skin friction on pressure histories.

CFD Applications to Pressurized Thermal Shock-Related Phenomena

In pressurized water reactor accident scenarios, the injection of water from the emergency core cooling system (ECCS) (ECC injection) might induce a pressurized thermal shock (PTS), affecting the reactor pressure vessel (RPV) integrity. Therefore, PTS is a vital research issue in reactor safety, and its analysis is essential for evaluating the integrity of RPVs, which determines the reactor life. The PTS analysis comprises a coupled analysis between thermal–hydraulic and structural analyses. The thermal–hydraulic approach is particularly crucial, and reliable computational fluid dynamic (CFD) simulations should play a vital role in the future because predicting the temperature gradient of the RPV wall requires data on the transient temperature distribution of the downcomer (DC). Since one-dimensional codes cannot predict the complex three-dimensional flow features during ECC injection, PTS is one reactor safety issue where CFD simulation can benefit from complement evaluations with thermal–hydraulic system analysis codes. This study reviewed from the viewpoint of the turbulence models most affecting PTS analysis based on papers published since 2010 on single- and two-phase flow CFD simulation for the experiment on PTS performed in the Rossendorf coolant mixing model (ROCOM), transient two-phase flow (TOPFLOW), upper plenum test facility (UPTF), and large-scale test facility (LSTF). The results revealed that in single-phase flow CFD simulation, where knowledge and experience are sufficient, various turbulence models have been considered, and many analyses using large eddy simulation (LES) have been reported. For two-phase flow analysis of air–water conditions, interface capturing/tracking methods were used in addition to two-fluid models. The standard k–ε and shear stress transport (SST) k–ω models were still in the validated phase, and various turbulence models have yet to be fully validated. In the two-phase flow analysis of steam–water conditions, many studies have used two-fluid models and Reynolds-averaged Navier-Stoke (RANS), and NEPTUNE_CFD, in particular, has been reported to show excellent prediction performance based on years of accumulated validation.

Unleashing novel configurations of gravitational water vortex thermal energy exchanger

This study presents thermal and hydrodynamics investigations for novel configurations of gravitational water vortex heat exchanger (GWVHE). The proposed novel configurations of GWVHE include SWB (shell with baffles), CSFH (circular spiral flow helix) and RSFC (rectangular spiral flow channel). The thermal energy balance between two fluid domains has been calculated numerically for various operational conditions. An analytical model is developed using the Kern's approach, the effectiveness-NTU method, and the LMTD method for heat exchangers to calculate the heat transfer characteristics of two fluids to validate numerical results. Moreover, a transient two-phase flow numerical model has been solved to investigate the volume fraction of air and water during the development of the vortex at the center of the basin. The results show that a convincing thermal energy balance is present between both fluid streams for all the proposed configurations of GWVHE. However, the heat exchange rate for the RSFC configuration of GWVHE is higher than the SWB and CSFH of GWVHE. Because it has maximum heat exchange surface area of 1.08 m2 and thermal losses in RSFC are significantly lower than those computed in CSFH and SWB at different operating conditions. The thermal losses reported for RSFC are just 1 % compared to CSFH and SWB thermal losses of 2 % and 5 %, respectively. Moreover, the maximum volume fraction of air obtained at the center of basin during vortex formation is 18 %, indicating an effective vortex air core.

A novel transient hole cleaning algorithm for horizontal wells based on drift-flux model

With the continuous expansion of unconventional and offshore oil and gas fields, horizontal wells have become adopted as an economical and effective mining method. However, the inclined and horizontal sections make them prone to cuttings deposition in the wellbore, leading to the formation of a cuttings bed that adversely affects drilling operations. In this paper, we focus on the features of cuttings transport in the wellbore during drilling and propose a solid-liquid two-phase transient flow model by integrating the flow pattern and drift flux model. The model is discretized using a format based on the finite volume method and solved using a preprocessing method. It enables us to predict the flow parameters, cuttings bed distribution, and cuttings removal time in the wellbore of horizontal wells.To validate the model's effectiveness, we verify it using laboratory experimental data, which demonstrates its prediction accuracy. Furthermore, we use the established model to simulate the damage effect of the cuttings bed on the hole cleaning device during drilling. By comparing the complete return time of cuttings under different working conditions, we quantitatively analyze the hole cleaning device's effect and the backreaming operation's cleaning efficiency. The results indicate that the use of hole cleaning devices during drilling, backreaming, well washing, and other operations in the hole cleaning process can effectively suspend the cuttings deposited in the annulus, allowing them to return to the wellhead more quickly, which enhances the cleaning efficiency of the wellbore and reduces the overall construction time. Furthermore, by comparing and analyzing the effect of drilling flow rate, well cleaning flow rate, cutting particle size, temperature gradient and rate of penetration (ROP) on cuttings return efficiency, it was observed that the drilling flow rate and ROP have minimal impact on the time required for complete cuttings removal during drilling. However, cutting particle size has a significant impact on the effective distance of the hole cleaning tool. Meanwhile, the temperature gradient and the flow rate during the well cleaning has a decisive influence on the time needed for complete cuttings removal.

Experimental and numerical study on the ejector containing condensable species in the secondary flow for PEM fuel cell applications

Phase transitions in two-phase ejectors have gained attention in various applications, including refrigeration, desalination, and fuel cell systems. The phase transition of condensable components in the primary flow significantly affects the ejector performance. However, studies on the phase transition of condensable species in the secondary flow are scarce. Consequently, this study aims to investigate two-phase flow characteristics of the ejector containing condensable species in the secondary flow. A schlieren experimental system with a visual rectangular ejector was constructed, and a transient Eulerian-Lagrangian two-phase flow model incorporating non-equilibrium condensation was developed. The numerical simulations achieved an average deviation of 4.7% in the entrainment ratio compared to experimental measurements, with a maximum deviation of 11.6%. The schlieren experiment revealed that the condensable species in the secondary flow can condense when the primary pressure exceeds 0.30 MPa. The numerical results showed that the condensed droplets reach a minimum proximity of approximately 3 mm from the primary nozzle exit and exhibit a divergence angle ranging from 7° to 12° as they traverse with the gas flow. Additionally, increasing the primary flow pressure from 0.2 MPa to 0.5 MPa resulted in a noticeable lengthening of the first shock wave, from 1.45 mm to 3.00 mm.

Effects of Liquid Density on the Gas-Liquid Interaction of the Ionic Liquid Compressor for Hydrogen Storage

As a new and promising compression technology for hydrogen gas, the ionic liquid compressor inherits the advantages of the ionic liquid and the hydraulic system. The liquid density is one of the key parameters influencing the fluid flow field, the sloshing of the bulk liquid, and the movement of droplets generated during the compressor operation. An appropriate selection of the liquid density is important for the compressor design, which would improve the thermodynamic performance of the compressor. However, the density of the ionic liquid varied significantly depending on the specific combination of the cation and anions. This paper proposed the methodology to select the optimal liquid density used in the ionic liquid compressor for hydrogen storage. The gas-liquid interaction in the compression chamber is analysed through numerical simulations under varied liquid density values. Results found that the increase in the liquid density promoted the detachment of the ionic liquid from the cylinder cover during the suction procedure and the contact of the bulk liquid on the compressor cover when the gas is compressed in the cylinder during the compression procedure. Both the droplet size and the dimension of the derived gas vortex decreased when the liquid density increased. The lowest mass transfer of hydrogen through the outlet was obtained at the density of 1150 kg/m3. The density of the ionic liquid from 1300 to 1450 kg/m3 is suggested to the hydrogen compressor, taking into account the transient two-phase flow characteristics, the mass transfer, and the total turbulent kinetic energy.

Reappraisal of Upscaling Descriptors for Transient Two-Phase Flows in Fibrous Media

Reappraisal of Upscaling Descriptors for Transient Two-Phase Flows in Fibrous Media

A physics-informed convolutional neural network for the simulation and prediction of two-phase Darcy flows in heterogeneous porous media

The physics-informed neural network (PINN) is a general deep learning framework for simulating flows with limited or no labeled data. In the current study, we develop a physics-informed convolutional neural network (PICNN) for simulating transient two-phase Darcy flows in heterogeneous reservoir models with source/sink terms in the absence of labeled data, where the finite volume method (FVM) is adopted to approximate the PDE residual in the loss function such that flux continuity between neighboring cells of different properties is defined rigorously, and a well model is adopted to approximate the high pressure gradient near sources or sinks. The implicit-pressure explicit-saturation (IMPES) scheme is employed such that only a single CNN needs to be trained per time step. Dirichlet boundary conditions are not a mandatory requirement for PICNN-based implicit solver but act as labeled data that can help enhance accuracy. The proposed approach is validated in homogeneous and heterogeneous reservoirs and aspects including efficiency and accuracy are discussed. In addition, we demonstrate that the CNN structure can be trained as a data-driven surrogate for two-phase Darcy flows given sufficient labeled samples.

Resin infusion in porous preform in the presence of HPM considering complex geometry and gravity: Flow simulation and experimental validation

Present work demonstrates the complete numerical modeling and experimental validation of transient incompressible two-phase flow during vacuum infusion (VI) in the presence and absence of high permeability media (HPM) considering gravity effects. Coupled flow modeling based on continuity equations, Darcy’s law for porous media flow, including gravity effects with level set front tracking algorithm, has been developed on the multiblock-structured grid with higher-order finite-difference framework to predict the spatio-temporal preform saturation during infusion with/without HPM on the complex mold configurations. The model-predicted instantaneous change in pressure, thickness elevation, fill time, flow front positions, and influence of gravity have been validated with experiments for horizontal and vertical flat plates using pressure sensors and digital cameras. For the first time, the complete modeling and experimentation of transient VI in the presence or absence of HPM, including gravity, shows the ability to predict realistic preform saturation during VI in different mold geometry.

A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media, this problem has been seldom investigated using direct numerical simulation (DNS). Only a few studies have sought to numerically solve Navier–Stokes equations with level-set (LS) or volume-of-fluid (VoF) methods, each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume (CV) domain. The Shan–Chen multiphase multicomponent lattice Boltzmann method (SC-LBM) has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations. Therefore, this study applied it to explore two-phase displacement in a single representative elementary volume (REV) of two-dimensional (2D) porous media. As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media, this work seeks to identify dynamic nonequilibrium effects on capillary pressure–saturation relationship ( P c – S ) for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions. The simulation outcomes show that P c , S and specific interfacial area ( a nw ) had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions. With finer adjustments to the increase in pressure over more steps, dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasi-steady-state inflow/outflow conditions. Furthermore, triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical P c – S . The results showed overshoot and undershoot of P c to S in loops of the nonequilibrium hysteresis. In addition, the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers ( Re and Ca ). The analysis of REV-scale flow regimes showed higher Re (1 < Re < 10) for more significant dynamic nonequilibrium effects. This indicates that inertia is critical for transient two-phase flow in porous media under dynamic nonequilibrium conditions.

A Regularized Real-Time Integrator for Data-Driven Control of Heating Channels

In many contexts of scientific computing and engineering science, phenomena are monitored over time and data are collected as time-series. Plenty of algorithms have been proposed in the field of time-series data mining, many of them based on deep learning techniques. High-fidelity simulations of complex scenarios are truly computationally expensive and a real-time monitoring and control could be efficiently achieved by the use of artificial intelligence. In this work we build accurate data-driven models of a two-phase transient flow in a heated channel, as usually encountered in heat exchangers. The proposed methods combine several artificial neural networks architectures, involving standard and transposed deep convolutions. In particular, a very accurate real-time integrator of the system has been developed.

The study on the partition method of two-phase wall drag in the one-dimensional two-fluid model

The interfacial area transport equation(IATE) is being investigated to replace the flow regime map in the one-dimensional two-fluid model (1-D TFM). The partition of two-phase wall drag is a part of flow regime-dependent constitutive relations in the code using the 1-D TFM such as RELAP5. Hence, to develop the partition method for two-phase wall drag that is consistent with 1-D TFM using the IATE, the mechanism for the partition was investigated and clarified in this work. And the partition method for two-phase wall drag that can capture the dynamic change of two-phase flow structure was developed with the clarified mechanism. Furthermore, the method was preliminarily validated with the experimental data, which shows that the two-phase wall drag computed by the method can accurately capture the variation of flow structure and relative velocity in transient two-phase flow. Accordingly, the developed method is able to take advantage of the IATE.

Boltzmann transformation of radial two-phase black oil model for tight oil reservoirs

Tight oil accumulates in impermeable reservoir rocks, often shale or tight sandstones. The flow behaviour of tight oil in unconventional reservoirs is described by peculiar complexities such as the typical low permeability to viscosity ratio and the dissolution of some gases in the oil phase. Reservoir simulations that consider these complexities negligible stand the potential of poorly characterizing the reservoir flow dynamics. The adoption of similarity transformation effectively reduces the complexities associated with the flow equations through spatial variable (r) and temporal variable (t). The Boltzmann variable left(xi =dfrac{r}{sqrt{t}}right) is introduced to facilitate the reformulation of transient two-phase flow phenomenon in a radial geometry. The technique converts the two-phase Black oil model (thus highly nonlinear partial differential equations (PDEs)) to ordinary differential equations (ODEs). The resulting ODEs present a reduced form on the flow model which is solved by finite difference approximations (the Implicit-Pressure-Explicit-Saturation (IMPES)) scheme. No loss of vital flow characteristics was observed between the Black oil model and the similarity transform flow model. Furthermore, the similarity approach facilitated the determination of pressure and saturation equations as unique functions of the Boltzmann variable. This derivation is applied to an infinitely acting reservoir where the Boltzmann variable tends to infinity (xi rightarrow infty). Finally, this case study’s analytical solution formulated critical relations for fluid flow rate and cumulative production, which are useful for single-phase flow analysis.

A GPU-Based δ-Plus-SPH Model for Non-Newtonian Multiphase Flows

A multiphase extension of the δ-plus-SPH (smoothed particle hydrodynamics) model is developed for modeling non-Newtonian multiphase flow. A modified numerical diffusive term and special shifting treatment near the phase interface are introduced to the original δ-plus-SPH model to improve the accuracy and numerical stability of the weakly incompressible SPH model. The Herschel–Bulkley model is used to describe non-Newtonian fluids. A sub-particle term is added in the momentum equation based on a large eddy simulation. The graphic processing unit (GPU) acceleration technique is applied to increase the computational efficiency. Three test cases including, a static tank, Poiseuille flow, and submarine debris flow, are presented to assess the performance of the new multiphase SPH model. Comparisons with analytical solutions, experimental data, and previous numerical results indicate that the proposed SPH model can capture highly transient incompressible two-phase flows with consistent pressure across the interface.

Investigation on the oil transfer behaviors and the air-oil interfacial flow patterns in a ball bearing under different capillary conditions

Lubricant oil is crucial to the rolling bearings as the main medium of lubricating, cooling, cleaning, and so on. The oil starvation in and around the contacts is harmful to the performance and fatigue life of rolling bearings. Therefore, it is of necessity to understand the behaviors of oil transfer and the patterns of air-oil two-phase flow in bearings, especially with the influence of different capillary properties. This work established a transient air-oil two-phase flow model in a ball bearing based on computational fluid dynamics (CFD). Groups of cases are implemented to investigate the behaviors of oil transfer and air-oil flow under different capillary conditions with speed, surface tension, and viscosity. Flow patterns are classified by the morphological features of the air-oil flow. Staged phenomena are analyzed with flow patterns and reach good agreements with the observations from experiments. It is found that the oil distribution and air-oil flow behaviors in a ball bearing are strongly related to the speed and the ratio of oil viscosity and air-oil surface tension (μoil/σ). The flow maps imply that the levels of capillary number (Ca) may be the boundaries and the critical points of flow pattern transition between the different flow patterns in bearing.

Numerical Modeling of Transient Two-Phase Flow and the Coalescence and Breakup of Bubbles in a Continuous Casting Mold.

The multiphase flow and spatial distribution of bubbles inside a continuous casting (CC) mold is a popular research issue due to its direct impact on the quality of the CC slab. The behavior of bubbles in the mold, and how they coalesce and break apart, have an important influence on the flow pattern and entrapment of bubbles. However, due to the limitations of experiments and measurement methods, it is impossible to directly observe the multiphase flow and bubble distribution during the CC process. Thus, a three-dimensional mathematical model which combined the large eddy simulation (LES) turbulent model, VOF multiphase model, and discrete phase model (DPM) was developed to study the transient two-phase flow and spatial distribution of bubbles in a continuous casting mold. The interaction between the liquid and bubbles and the coalescence, bounce, and breakup of bubbles were considered. The measured meniscus speed and bubble diameter were in good agreement with the measured results. The meniscus speed increased first and then decreased from the nozzle to the narrow face, with a maximum value of 0.07 m/s, and appeared at 1/4 the width of the mold. The current mathematical model successfully predicted the transient asymmetric two-phase flow and completely reproduced the coalescence, bounce, and breakup of bubbles in the mold. The breakup mainly occurred near the bottom of the submerged entry nozzle (SEN) due to the strong turbulent motion of the molten steel after hitting the bottom of the SEN. The average bubble diameter was about 0.6 mm near the nozzle and gradually decreased to 0.05 mm from the nozzle to the narrow face. The larger bubbles floated up near the SEN due to the effect of their greater buoyancy, while the small bubbles were distributed discretely in the entire mold with the action of the molten steel jet. Overall, the bubbles were distributed in a fan shape. The largest concentration of bubbles was in the lower part of the SEN and the upper edge of the SEN outlet.

Evolution of gas kick and overflow in wellbore and formation pressure inversion method under the condition of failure in well shut-in during a blowout

With ongoing development of oil exploration and techniques, there is a significant need for improved well control strategies and formation pressure prediction methods. In this paper, a gas-liquid transient drift flow model was established according to the gas-liquid two-phase flow characteristics during the gas kick. A Roe scheme was used for numerical calculation based on the finite volume method. The changes of bottom-hole pressure, casing pressure, the development law of cross-sectional gas holdup, and gas velocity, along with the vertical well depth, were analyzed through simulation examples. The time-series characteristics of mud pit gain were obtained by adjusting the formation parameter. The complex nonlinear mapping relationship between the formation parameters and the mud pit gain was established. The long short-term memory network (LSTM) of deep learning was used to obtain a formation pressure inversion when the blowout is out of control and the well cannot be shut-in. Experimental data from a well were used to verify the gas-liquid two-phase transient drift flow model based on the finite volume method, demonstrating that this method is reliable, with greatly improved prediction accuracy. This approach provides theoretical support for the early monitoring of gas kick during drilling, and for well-killing design and construction after uncontrolled blowout.

Investigation of two-phase jet flow from a degassing pipe used for a lake with potential gas-driven eruption

Gas-driven limnic eruption can happen in a lake with an aqueous gas solution that becomes supersaturated due to some reason. In this case, the exsolution of massive gases dissolved in the water could occur in a very short time, resulting in a disaster as happened in the Lake Nyos (Cameroon, Africa) in 1986. Using degassing pipe to artificially release the dissolved gases is a good way to minimize the risk of an eruption. In this study, a transient multi-component gas-liquid two-phase flow model of the degassing pipe used in Lake Nyos has been established and verified with the observed eruption data. The drift flux model has been used for modelling of a transient multi-component gas-liquid flow formed due to the spontaneous exsolution of gases dissolved in the water inside the degassing pipe. The governing equations for the mechanistic drift model include continuity equation for each phase, a single momentum equation for a homogeneous mixture of the fluid, constitutive equations for mass transfer rates between the phases, and the drift velocity formulas. The model considered not only CO2 but also CH4 as dissolved gases. The “chain reaction” conjecture predicted to have the degassing-point migrating downward with time during the transient degassing process is verified by using this model. The relationship between the eruption height and the CO2 concentration at the bottom of the degassing pipe has been simulated in detail. This relationship supplies people with a quick and convenient way to estimate the CO2 concentration in the lake, based on which one can evaluate the risk of lake eruption and hence to formulate or adjust the degassing plan. In addition, the effects of diameter and equivalent roughness of the degassing pipe on the eruption height has been investigated. Meanwhile, the eruption height upper-limit in different lake-depth scenarios has also been determined. Finally, the role of CH4 component in the degassing process has been analyzed. Although the influence of CH4 on eruption height can be neglected in Lake Nyos' case, CH4 as a dissolved gas plays an important role at Lake Kivu. The multi-component gas-liquid flow model developed in this study is useful to study the role of CH4 in the degassing process.