WAVE PROPAGATION IN TWO-PHASE FLOW BASED ON A NEW HYPERBOLIC TWO-FLUID MODEL

A high-resolution up wind scheme based on the flux vector splitting method is developed for the two-fluid six-equation model to solve the wave propagation problems of two-phase flow. The interfacial pressure jump terms make the governing equations hyperbolic without any conventional source terms in the momentum equations. Real eigenvalues are obtained for all the bubbly, slug, and annular flow regimes. Calculated speeds of sound have shown excellent agreement with the existing experimental data. Solutions to wave propagation problems withinitial pressure and void distribution are presented. The Edwards pipe problem accompanied by sudden depressurization and flashing also is solved as a benchmark test.     

Modelling approaches to acoustic cavitation in transmission pipelines

A general treatment of acoustic cavitation was presented, including both fluid dynamics instabilities that can occur at cavitation inception as well as non-equilibrium thermal and mechanical effects during bubble dynamics. Different approaches to cavitation modelling were considered and compared.A novel barotropic cavitation model has been developed, based on the partial differential equations governing the mass-conservation and momentum balance. The fluid has been taken as a homogenous mixture of a pure liquid, its vapor and a quantity of gas, both dissolved and undissolved. The analytical expression for the vapor source term driving cavitation has been carried out by means of the energy conservation equation and a general formula for the sound speed in homogeneous bubbly flows has been derived.A recently developed conservative, implicit, high-resolution, second-order accurate numerical scheme was applied to solve the equations governing the pipe flow. The resultant computational algorithm was assessed through comparison with experimental data referring to a system made up of a pipe connecting two constant-pressure reservoirs of water. The model predictions were examined and discussed in order to underline the most interesting fluid-dynamic phenomena, such as the dynamics of shock waves arising at cavitation collapse.The influence of the frequency-dependent friction on the simulation of the pressure wave dynamics in the presence of cavitation was also analyzed and discussed.     

Nonlinear interaction and reflection of waves in vapor–liquid bubbly mixtures

A mathematical model was developed for investigation of waves in bubbly liquids with planar, cylindrical and spherical symmetry. The problems of reflection of waves from free surface and rigid wall and interaction of waves were considered. It is shown that the reflection of pressure wave from free surface in bubbly mixture is considerably different than in the case of pure liquid.For the reflection of shock waves from rigid wall, the nonlinear enhancement of wave was established. It is shown that in the system under high static pressure, nonlinearity during the reflection from rigid wall manifest itself stronger. It was established that decreasing of void fraction and increasing of initial bubble radius lead to the increasing of the value of maximum pressure at the wall surface.     

Analysis of magnetohydrodynamics peristaltic transport of hydrogen bubble in water

This paper established the theoretical and analytical analysis of a unidirectional laminar bubbly two-phase flow in a symmetric channel with flexible wall. The two-phase model uses water as base fluid with hydrogen bubble suspended in it. Rayleigh-Plesset equation in term of volume fraction is used to model void produce due to presence of hydrogen. The flow is driven by symmetric peristaltic movement of the wall. A uniform magnetic field in the transverse direction to peristaltic motion is applied. Homotopy perturbation Method (HPM) is utilized to formulate the series solution, after simplifying the differential governing equations under the influence of long wave length and low Reynolds number. The volume of the void and radius of the bubble is analyzed graphically. The consequence demonstrates that the void fraction bubbles rapidly approaches to unity, which is due to quasi-statically unstable. Due to Lorentz force fluid velocity suppresses by increasing the transverse magnetic field while reverse performance is noted for Weber number and power law index.     

Numerical simulation of bubbly two-phase flow in a narrow channel

An advanced numerical simulation method on fluid dynamics - lattice-Boltzmann (LB) method is employed to simulate the movement of Taylor bubbles in a narrow channel, and to investigate the flow regimes of two-phase flow in narrow channels under adiabatic conditions. The calculated average thickness of the fluid film between the Taylor bubble and the channel wall agree well with the classical analytical correlation developed by Bretherton. The numerical simulation of the behavior of the flow regime transition in a narrow channel shows that the body force has significant effect on the movement of bubbles with different sizes. Smaller body force always leads to the later coalescence of the bubbles, and decreases the flow regime transition time. The calculations show that the surface tension of the fluid has little effect on the flow regime transition behavior within the assumed range of the surface tension. The bubbly flow with different bubble sizes will gradually change into the slug flow regime. However, the bubbly flow regime with the same bubble size may be maintained if no perturbations on the bubble movement occur. The slug flow regime will not change if no phase change occurs at the two-phase interface.     

Predicting bubble size and bubble rate data in water and in froth flotation-like slurry from computational fluid dynamics (CFD) by applying deep neural networks (DNN)

Accurate characterization of two phase bubbly flows is crucial in many industrial processes such as fluidized reactors, ore froth flotation, etc. The bubble size determines the rate at which components present in the gas phase are transferred to the surroundings and vice versa while bubble rate defines the appropriate bubbly flow regime occurring in the heterogeneous system. This research work employs deep neural networks (DNNs) to predict bubble size and bubble rate using data obtained from validated computational fluid dynamics (CFD) computations. Pure water and slurry (in conditions similar to those employed in mineral froth flotation) case studies are evaluated. It is found that the DNN can predict the CFD results accurately when using four hidden layers, describing discontinuities in the bubbly flow regime. The relative errors computed between the CFD data and the prediction obtained by the DNN is as low as 8.8% and 1.8% for bubble size and bubble rate, respectively. These results confirm that the DNN can be applied to sophisticated fluid dynamics systems and allow developing better control process strategies since once the DNN is trained critical variables can be computed very efficiently. The slurry case study, although restricted to the application of mineral froth flotation, can also be generalized to other industrial operations keeping the exact same procedure.     

Flow pattern of boiling in micro-channel by numerical simulation

Boiling flows of R-134a and R-22 fluids in a 0.50 mm circular channel have been simulated to analyze bubbly flow, bubbly/slug flow, slug flow and slug/semi-annular flow depending on bubble evolution. The vapor–liquid interface was captured using VOF method. We studied the behavior of bubble growth and coalescence related to flow pattern transitions (bubbly/slug flow to slug flow, slug flow to slug/semi-annular flow) and analyzed the effect of fluid properties on transition lines. Some parameters, including heat flux, mass velocity, ONB point, vapor velocity, bubble lifting diameter, growth rate and generation frequency, have been analyzed in detail. The results show that bubble growth and coalescence are important factors for flow pattern transitions. The flow patterns at the micro-channel outlet predicted by simulation were in agreement with phenomena observed in experiments for bubbly/slug flow, slug flow and slug/semi-annular flow. In addition, the peak bubble frequency at the outlet was predicted and the general shape of the bubble frequency distribution at the outlet from simulation was found to be consistent with the achieved experimental results.     

双点激光点火直接起爆的数值模拟

针对双点激光点火直接起爆过程中爆轰波的形成、发展和传播问题,采用高精度数值模拟方法求解带化学反应的二维欧拉方程组,研究了不同环境压力情况对流场结构与波系变化的影响.结果表明,环境压力会影响激波强度与爆轰波的传播速度,是决定双点激光点火形成的火核在碰撞过程中能否实现爆轰并维持爆轰波传播的重要因素,利用双激光点相互作用形成...     

Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger

The complex physicochemical phenomena occurring in the contact line region of an evaporating meniscus are described using a unique combination of high-resolution experimental data and three complementary models. The following were used: (1) high-resolution experimental liquid profile data (thickness, slope, curvature and curvature gradient) to obtain the pressure gradient in the evaporating pentane meniscus in a vertical constrained vapor bubble (VCVB); (2) macroscopic outside surface temperature profile data; (3) a finite element model to obtain the two-dimensional heat conduction profile in the solid substrate wall (macro-model) and the solid–liquid interfacial temperature profile in the evaporating meniscus region; (4) a continuum fluid-dynamics model (micro-model) to obtain the liquid–vapor interfacial temperature, mass flow rate, Marangoni stresses, and evaporative heat flux profiles along the length of the evaporating meniscus; and (5) the Kelvin–Clapeyron model to obtain the vapor temperature profile (liquid–vapor interfacial temperature jump) in the evaporating meniscus region.The retarded dispersion constant and high-resolution thickness, slope, curvature and curvature gradient profiles were obtained from the experimental reflectivity profiles. There was a substantial increase in the measured curvature in the transition region, where the evaporation rate and flux are a maximum. To obtain numerical closure between the three complementary models, the continuum fluid dynamics model (micro-model) required slip at the solid–liquid interface to support the observed high mass flow rates in the evaporating pentane meniscus. Mass flow rates due to Marangoni stresses, capillary pressure and disjoining pressure are compared. Depending on the liquid thickness, Marangoni stresses can either enhance or hinder fluid flow towards the contact line for the evaporating pure pentane meniscus. Due to the high heat removal rate by the evaporating pentane meniscus in the transition region, dips in the vapor, liquid–vapor and solid–liquid interface temperature were obtained. The results demonstrate and describe the sensitivity and complexity of the phase change process in micro-regions.     

Distribution parameter and drift velocity of drift-flux model in bubbly flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for bubbly flow regime. The constitutive equation that specifies the distribution parameter in the bubbly flow has been derived by taking into account the effect of the bubble size on the phase distribution, since the bubble size would govern the distribution of the void fraction. A comparison of the newly developed model with various fully developed bubbly flow data over a wide range of flow parameters shows a satisfactory agreement. The constitutive equation for the drift velocity developed by Ishii has been reevaluated by the drift velocity calculated by local flow parameters such as void fraction, gas velocity and liquid velocity measured under steady fully developed bubbly flow conditions. It has been confirmed that the newly developed model of the distribution parameter and the drift velocity correlation developed by Ishii can also be applicable to developing bubbly flows.     

Modeling aspects of vapor bubble condensation in subcooled liquid using the VOF approach

Direct contact condensation of a vapor bubble during subcooled boiling flow scenario has diverse applications in many fields such as thermal, chemical, and nuclear energies. The present work aims at the exploration of the underlying physics of single vapor bubble condensation in subcooled water following the volume of fluid method approach using ANSYS FLUENT 14.5. This work emphasizes on the modeling of the mass transfer rate using interfacial jump conditions for investigating the effect of various parametric conditions on the collapse phenomenon. A comparative study is also performed between the interface jump approach and the models based on the proposed empirical correlations to assess the condensation heat transfer (in terms of the collapse rate and Nusselt number) and bubble shape. The mass transfer model based on the interfacial jump condition is found to be the more realistic among all models for capturing the collapse rate as well as its shape.     

Numerical Study of Bubbly Flow Using the Second-Order Moment Turbulence Model and the Population Balance Method

A comprehensive computational fluid dynamics (CFD) turbulence model, coupled with a population balance method (PBM), is presented to simulate the two-phase gas–liquid bubbly flow. The simulation results are in good agreement with the experimental data. Furthermore, considering the bubble size distribution including the drag force and lift force, the results showed that the calculated results are in good agreement with the experimental measurements. The studies reveal the liquid recirculation and bubble uprising flow patterns, and anisotropic liquid and bubble normal Reynolds stresses. Moreover, both the liquid velocity gradient and the bubble–liquid interaction are important for the generation of liquid turbulence.     

Detecting and modeling oxygen bubble evolution and detachment in proton exchange membrane water electrolyzers

In this work, we discuss the effect of multiphase flow dynamics on the performance of a PEM electrolyzer. We obtained images of a flow system consisting of O₂ and water at two stages of gas production: gas evolution via bubbles and gas exiting through the channels of a flow field. We processed the obtained images of bubble evolution with a MATLAB-based bubble detection and counting algorithm, and we found that the bubble detachment sizes remained invariant within a water flow range between 0.07 and 4.65 l h⁻¹. We measured an average bubble detachment radius of 22.47 μm. We applied a bubble force balance developed by van Helden et al. [1] to model the observed effect of water flow on bubble evolution, and we found that the bubble detachment radius is a weak function of water flow when the water flow is below 60 l h⁻¹. We found that the variables that affect the bubble detachment radius the strongest were the electrode's hydrophobicity and pore size.     

Numerical study on the formation of Taylor bubbles in capillary tubes

Numerical simulations have been carried out for the transient formation of Taylor bubbles in a nozzle/tube co-flow arrangement by solving the unsteady, incompressible Navier–Stokes equations. A level set method was used to track the two-phase interface. The calculated bubble size, shape, liquid film thickness, bubble length, drift velocity, pressure drop and flow fields of Taylor flow agree well with the literature data. For a given nozzle/tube configuration, the formation of Taylor bubbles is found to be mainly dependent on the relative magnitude of gas and liquid superficial velocity. However, even under the same liquid and gas superficial velocities, the change of nozzle geometry alone can drastically change the size of Taylor bubbles and the pressure drop behavior inside a given capillary. This indicates that the widely used flow pattern map presented in terms of liquid and gas superficial velocities is not unique.     

Effects of wall slip and temperature jump on heat and mass transfer characteristics of an evaporating thin film

A new mathematical model is developed to predict heat and mass transport characteristics of the evaporating thin film. The model considers effects of velocity slip and temperature jump at the solid-liquid interface, disjoining pressure, and surface tension. Three-dimensional nonequilibrium molecular dynamics simulations for coupling between the momentum and heat transfer at the nanoscale solid-liquid interface are performed to obtain the slip length and interfacial thermal resistance length. It is found that both slip length and interfacial thermal resistance length decrease significantly with the decreasing interface wettability of the liquid to the wall. Velocity slip and temperature jump at the solid-liquid interface intend to reduce the superheat degree of the evaporating thin film, and thus result in a sharp decrease of the heat and mass transport characteristics of the evaporating thin film. It is also noted that velocity slip and temperature jump at the solid-liquid interface show a more pronounced effect as the superheat degree increases.     

An experimental study on local interfacial area concentration using a double-sensor probe

Interfacial area concentration is an important parameter in modeling the interfacial transfer terms in the two-fluid model. In this paper, the interfacial area concentration, void fraction, and bubble Sauter mean diameter for air-water bubbly flow through a vertical transparent pipe with 40 mm internal diameter was investigated experimentally using both digital high-speed camera system and a double-sensor conductivity probe. Based on the experimental data of digital high-speed camera system, the statistical models derived by different researchers for local interfacial area concentration measurement using double-sensor conductivity probe were evaluated. The results show that there are obvious differences among the values of local interfacial area concentration calculated by different statistical models even from the same probe signals. The section-averaged values of the local interfacial area concentration calculated using the statistical model by Kataoka et al. agree best with experimental data of digital high-speed camera system. Therefore, the statistical model developed by Kataoka et al. is recommended for the local measurement of interfacial area concentration using a double-sensor conductivity probe in bubbly two-phase flow. Using the verified double-sensor probe method, we carry out experiment to study the local distribution characteristic of the interfacial area concentration and void fraction in air-water bubbly flow through a vertical pipe.     

A continuum model for the propagation of discrete phase-change fronts in porous media in the presence of coupled heat flow,fluid flow and species transport processes

In this paper we derive the equations governing the transport of energy and mass in a porous medium saturated by a multiphase multi-constituent fluid mixture under conditions that yield steep continuous moving fronts and abrupt discontinuous moving phase-change interfaces. In these equations the volume fractions of each phase, the potentials, such as, the temperature, pressure and concentration, and the corresponding fluxes, are permitted to jump in value across the phase-change interfaces. As an example of application of the derived continuum model, we specialize the theory to the problem of propagation of melting/freezing interfaces in a salt-water saturated porous medium for a coupled process governed by heat flow, fluid flow and species transport.     

Experimental study and three-dimensional simulation of premixed hydrogen/air flame propagation in a closed duct

An experimental and numerical study of premixed hydrogen/air flame propagation in a closed duct is presented. High-speed schlieren photography is used in the experiment to record the changes in flame shape and location. The pressure transient during the combustion is measured using a pressure transducer. A dynamic thickened flame model is applied to model the premixed combustion in the numerical simulation. The four stages of the flame dynamics observed in the experiment are well reproduced in the numerical simulation. The oscillations of the flame speed and pressure growth, induced by the pressure wave, indicate that the pressure wave plays an important role in the combustion dynamics. The predicted pressure dynamics in the numerical simulation is also in good agreement with that in the experiment. The close correspondence between the numerical simulation and experiment demonstrate that the TF approach is quite reliable for the study of premixed hydrogen/air flame propagation in the closed duct. It is shown that the flame wrinkling is important for the flame dynamics at the later stages.     

Hydrodynamics and heat transfer in bubbly flow in the turbulent boundary layer

In the work presented is a new approach to modelling the bubbly flow in the boundary layer. The approach is based on summation of dissipation energy coming from the shearing turbulent flow in the absence of bubbles and the dissipation contribution from the presence of bubbles. As a result we obtain the dissipation of equivalent single phase turbulent flow. The model has been solved using the method of asymptotic correction to provide an explicit differential equation describing the velocity profile. That can be solved with the assumption of constant void fraction distribution to yield the analytical velocity profile. Alternatively, author has developed his own model of lateral void migration, which is distinct from other models by virtue of presence of another rotational velocity. Velocity distributions calculated using the new model have been compared against the experimental data of turbulent bubble flows with small void fraction. A good consistency between calculations performed using a new model and available experimental data has been obtained. Additionally, a solution of the temperature field is also given. In the case of a constant void fraction distribution analytical distribution of the Nusselt number is given or the set of differential equations needs to be solved.     

Influence of convective heat transfer modeling on the estimation of thermal effects in cryogenic cavitating flows

The accuracy of numerical simulations for the prediction of cavitation in cryogenic fluids is of critical importance for the efficient design and performance of turbopumps in rocket propulsion systems. One of the main remaining challenges is efficiency in modeling of the physics, handling the multi-scale properties involved and developing robust numerical methodologies. Such flows involve thermodynamic phase transitions and cavitation bubbles that are on a smaller scale than the global flow structure. Cryogenic fluids are thermo-sensitive, and therefore, thermal effects and strong variations in fluid properties can alter the cavitation properties. The aim of this work is to address the challenge posed by thermal effects. The Rayleigh–Plesset equation is modified by the addition of a term for convective heat transfer at the interface between the liquid and the bubble coupled with a bubbly flow model to assess the prediction of thermal effects. We perform a parametric study by considering several values of and models for the convective heat transfer coefficient, h_b, and we compare the resulting temperature and pressure profiles with the experimental data. Finally, the results of a 2D simulation with a commercial CFD code are presented and compared with the previous results. We note the importance of the choice of h_b for the correct prediction of the temperature drop in the cavitating region, and we assess the most efficient models, underlining that the choice of h_b estimation model in a cryogenic cavitating flow is more important in the bubble growth phase than in the bubble collapse phase.